Weak decays of doubly heavy baryons: $ {\cal B}_{cc}\to {\cal B} D^{(*)} $

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Run-Hui Li, Juan-Juan Hou, Bei He and Ya-Ru Wang. Weak decays of doubly heavy baryons: $ {\cal B}_{cc}\to {\cal B} D^{(*)} $ [J]. Chinese Physics C.
Run-Hui Li, Juan-Juan Hou, Bei He and Ya-Ru Wang. Weak decays of doubly heavy baryons: $ {\cal B}_{cc}\to {\cal B} D^{(*)} $ [J]. Chinese Physics C. shu
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Weak decays of doubly heavy baryons: $ {\cal B}_{cc}\to {\cal B} D^{(*)} $

    Corresponding author: Run-Hui Li, lirh@imu.edu.cn
  • School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China

Abstract: The discovery of $ \Xi_{cc}^{++} $ inspires the new interest in studying the doubly heavy baryons. In this paper the weak decays of a doubly charm baryons $ {\cal B}_{cc} $ to a light baryon $ {\cal B} $ and a charm meson $ D^{(*)} $ (either a pseudoscalar or a vector one) are calculated. Following our previous work, we calculate the short distance contributions under the factorization hypothesis and the long distance contributions are modeled as the final state interactions which are calculated with the one particle exchange model. We find that the $ {\cal B}_{cc}\to {\cal B} D^{*} $ decays' branching ratios are obviously larger, since they receive contributions of more polarization states. Among the decays we investigated, the following ones have the largest branching fractions. $ {\cal BR}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}) \in [0.46 \%, 3.33 \%] $ estimated with $ \tau_{\Xi_{cc}^{++}} = 256 $ fs, $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) \in [0.38 \%, 2.63 \%] $ and $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.45 \%, 3.16 \%] $ with $ \tau_{\Xi_{cc}^+} = 45 $ fs, ${\cal BR}(\Omega_{cc}^{+}\rightarrow \Xi^{0} D^{*+}) \in [0.27 \%, 1.03 \%]$ , $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+}) \in [0.07 \%, 0.44 \%] $ and $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.06 \%, 0.45 \%] $ with $ \tau_{\Omega_{cc}^+} = 75 $ fs. Comparing the decay widths of pure color commensurate channels with those of pure bow-tie ones, we find that the bow-tie mechanism plays an important role in charm decays.

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    I.   INTRODUCTION
    • The study of doubly heavy baryons which contain two heavy constituent quarks (c or b quark) has lasted for a long time. They are predicted by the quark model and allowed by the quantum chrodynamics theory. Physicists believe their existence, even though they had not been found in experiments. The SELEX collaboration announced the discovery of $ \Xi_{cc}^+ $ in 2002 and 2005 [1, 2]. However, the reported production is large and the lifetime they measured is very long. Their results do not agree with the theoretical predictions and are not confirmed by the other experiments. In 2017 the LHCb collaboration declared the discovery of $ \Xi_{cc}^{++} $ via $ \Xi_{cc}^{++}\to \Lambda_c^+ K^-\pi^+\pi^+ $ with $ m_{\Xi_{cc}^{++}} = 3.621 $ GeV [3]. In 2018 the LHCb collaboration measured its lifetime as $ 256 $ fs [4] and confirmed their discovery via $ \Xi_{cc}^{++}\to \Xi_c^+\pi^+ $ [5]. $ \Xi_{cc}^{++} $ is the first doubly heavy baryon discovered in experiments whose properties agree with the theoretical expectations. Its discovery is meaningful to the study of hadron spectrum and baryon decays. Physicists have already done a lot of research on the spectrum of doubly heavy baryons. However, figuring out a proper framework to study their weak decays is a really challenging task. A lot of studies about this topic has been performed [6-24], and the form factors as well as the semileptonic decays of a doubly heavy baryon to a singly heavy baryon are studied under various of frameworks. However, there are still few systematic methods to deal with even the two body nonleptonic decays, which is essential to guiding new particle discoveries, understanding the dynamics of strong interaction, and testing the standard model precisely.

      In 2017 we applied the final state interactions (FSIs) to baryon decays at the charm scale to estimate the branching fractions of two body nonleptonic weak decays of doubly charm baryons [25]. We suggested two golden discovery channels of $ \Xi_{cc}^{++} $ , which, mentioned above, are adopted by the LHCb collaboration and help to discover the $ \Xi_{cc}^{++} $ particle. The discovery inspires the research of doubly heavy baryons and more questions are presented. Which are the golden discovery channels of the other doubly charm baryons and what else can we find in the decays of doubly charm baryons? To answer these questions, more research of the weak decays of doubly heavy baryons are required. In our previous work, we calculate the decays of a doubly charm baryon to a singly charm baryon and a light vector meson. We also talk about the possibility of these decays as potential discovery channels [26]. After discovering $ \Xi_{cc}^{++} $ , measuring its lifetime, and confirming the discovery with another decay, the LHCb collaboration also pay attention to the weak decays of $ \Xi_{cc}^{++} $ with a charm meson in the final state [27]. Motivated by the theoretical questions and experimental efforts, we study the two body nonleptonic decays of a doubly charm baryon $ {\cal B}_{cc}\to {\cal B} D^{(*)} $ in this paper, where $ {\cal B}_{cc} $ represents a doubly charm baryon, $ {\cal B} $ denotes a light baryon, and $ D^{(*)} $ is either a pseudoscalar or a vector charm meson.

      There are many interesting physics to be explored in baryon decays. For example, the CP violations have already been observed in K, B and D meson decays, but not been observed in baryon decays. Theoretical progress of this topic is slow because how to calculate the dynamics is a challenging work. No systematic factorization method is established so far even for the two body nonleptonic decays. Usually the contributions in two body nonleptonic baryon decays are classified topologically into several types as T, C, E and B [28]. In b baryon decays the E and B contributions are numerically small [29]. In the charm sector the picture is different and the E and B contributions may become important [30]. The study of these decays will help to understand the dynamics of baryon decays at the charm scale.

      This paper is organized as follows. In section II the phenomenological framework is introduced, the contributions in these decays are talked about, and the analytical expressions are presented. In section III some inputs, tables of our results and the discussions are collected. In section IV a summary is given. For shortage of the paper, we list all the expressions of the amplitudes in appendix B and the strong couplings are gathered in appendix C.

    II.   THEORETICAL FRAMEWORK AND ANALYTICAL CALCULATIONS

      A.   Theoretical framework

    • In our previous work we extend the model of final state interactions to baryon decays [25, 26] and suggest the discovery channels for $ \Xi_{cc}^{++} $ successfully. In our work we also find a misunderstanding on FSIs in some earlier literatures, and interested readers are referred to our upcoming paper. In the beginning of this section we would like introduce this framework briefly by following the ideas proposed in the Ref. [33]. Supposed that the weak Hamiltonian is in the form $ {\cal H}_W = \lambda_i Q_i $ , where $ \lambda_i $ are the combinations of quark mixing matrix elements and $ Q_i $ are time reversal invariant weak operators. The amplitude of $ {\cal B}_{cc}\to i $ can be decomposed as

      $ \langle i;{\rm{out}} \,| Q |\, {\cal B}_{cc}; {\rm{in}}\rangle ^* = \sum_j S_{ji}^* \langle j;{\rm{out}}\,| Q | \,{\cal B}_{cc}; {\rm{in}}\rangle, $

      (1)

      where $S_{ji}\equiv \langle i;{\rm{out}}\,|j;{\rm{in}}\rangle$ is the strong interaction S matrix element. Using the unitarity of the S-matrix and $ S = 1+{\rm i}T $ , one can obtain a identity related to the optical theorem as

      $ 2 {\cal A}bs\,\langle i;{\rm{out}} \,| Q |\, {\cal B}_{cc}; {\rm{in}}\rangle = \sum_j T^*_{ji} \langle j;{\rm{out}}\,| Q | \,{\cal B}_{cc}; {\rm{in}}\rangle. $

      (2)

      Specifically, the absorptive part in the amplitude of $ {\cal B}_{cc}\to {\cal B} {D^{(*)}} $ decay can be obtained as

      $ \begin{aligned}[b] {\cal A}bs\, {\cal M}({\cal B}_{cc}\to {\cal B} {D^{(*)}}) =\;& \frac{1}{2} \sum_j \left(\prod_{k = 1}^j \int \frac{{\rm d}^3 q_k}{(2\pi)^3 2 E_k}\right)(2\pi)^4 \delta^4\left(p_{\cal B}+p_{D^{(*)}}-\sum_{k = 1}^j q_k\right)\\ &\times {\cal M}(p_{{\cal B}_{cc}}\to \{q_k\}) T^*(p_{\cal B}p_{D^{(*)}}\to \{q_k\}). \end{aligned} $

      (3)

      Eqs. (1) and (3) indicate that the decay process can be divided into two steps. One is the generation of an intermediate state under weak interactions, which is dominated by short distance dynamics, the other is the formation of a final state subsequently through the strong interactions among intermediate particles. In principle one have to consider all the possible intermediate states. However, basing on the argument that the $ 2 $ -body $ \rightleftharpoons $ n-body rescattering is negligible [31, 32] we only need consider the intermediate states with two particles.

      The weak decays $ {\cal B}_{cc}\to {\cal B} {D^{(*)}} $ are induced by charged current $ c \to s/d $ . For charm decays induced by the flavor changing neutral current with quark loop effect, there exits cancellation between d and s quark loop contributions, therefore the FCNC contributions can be ignored safely. The low energy effective hamiltonian with charged current is given by

      $ {\cal H}_{\rm eff} = \frac{G_{\rm F}}{\sqrt{2}} \sum\limits_{q = d,s} V^{*}_{cq} V_{uD} \big[ C_{1}({\mu}) O^{q}_{1}({\mu}) + C_{2}({\mu}) O^{q}_{2}({\mu})\Big] + {\rm{h.c.}} , $

      (4)

      with

      $ \begin{aligned}[b]& O^{q}_{1} = ({\bar{u}}_{\alpha}D_{\beta} )_{V-A} ({\bar{q}}_{\beta} c_{\alpha})_{V-A}, \\ & O^{q}_{2} = ({\bar{u}}_{\alpha}D_{\alpha})_{V-A} ({\bar{q}}_{\beta} c_{\beta} )_{V-A}, \end{aligned} $

      (5)

      where $ D = s,\,d $ , $ V_{cq} $ and $ V_{uD} $ are the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements whose values are used from the CKMfitter Group [34], $ C_{1/2}(\mu) $ stand for the Wilson coefficients, the Fermi constant $ G_{\rm F} = 1.166\times 10^{-5}\;{\rm{ GeV}}^{-2} $ , and $ O^q_{1/2} $ are the local four-quark operators in which $ \alpha $ and $ \beta $ are color indices.

      The contributions induced by the above Hamiltonian in two body nonleptonic decays of $ {\cal B}_{cc} $ can be classified into eight topological diagrams, which are depicted in Fig. 1. The external W emission contribution is denoted by the symbol T. The internal W emission contributions can be classified into two types. In the C diagram the two constituent quarks of the meson are all from the weak vertex. And in the $ C^\prime $ diagram one constituent quark of the meson is from the initial state baryon. The diagrams in the second line of Fig. 1 are all W exchange diagrams. In $ E_1 $ the light quark which is from the c quark by emitting a W boson is picked up by the final state baryon, while in $ E_2 $ it is picked up by the final state meson. In the bow-tie diagram (denoted by B) both the two light quarks generated in the weak interaction are picked up by the final state baryon. The strong interactions in Fig. 1, both short and long distance, are included although they are not drawn.

      Figure 1.  Topological diagrams of $ {\cal B}_{cc}\to{\cal B}_{(c)} M(D^{(*)}) $ at tree level. $ {\cal B}_{(c)} $ denotes a light baryon or singly charm baryon. M is a light meson. The thick lines represent c quarks and the wave lines represent W bosons.

      The short distance strong interactions are associated with the weak vertex, and this part of contribution occurs at a high energy scale that the perturbative calculation is still valid. Borrowing the experience of studying b baryon decays [28, 29], one can see that the W exchange contribution can be neglected safely at short distance. It is different when one considers the long distance contributions, which is thought to be dominating because of low energy releasion and the W exchange mechanism may become important [33]. A decay process of $ {\cal B}_{cc} \to {\cal B}D^{(*)} $ can be divided into two steps: a $ {\cal B}_{cc} $ baryon firstly decays to $ {\cal B}_c {\cal M} $ and then to $ {\cal B}D^{(*)} $ via long distance interactions. The former step happens at short distance, therefore the W exchange contribution can be omitted. The long distance part, nonperturbative essentially, is hard to be calculated. In this work we model it as the final state interactions (FSIs) and perform the calculation at hadron level. In this model the long distance dynamics are realized by exchanging hadron-state particles(depicted in Fig. 2). Now we arrive at the step to calculate an amplitude in details.

      Figure 2.  Decay process indicated at hadron level. The black square is a weak vertex at which the intermediate state $ {\cal B}_c {\cal M} $ is generated. The gray ellipse represents the strong interactions between intermediate particles, which is realized by exchanging hadrons

    • B.   Calculation of weak vertices

    • As stated in the above subsection, the first step of getting an amplitude is to calculate the weak production of an intermediate state. In order to avoid double counting, this part of contribution is short distance dynamics in principle. At hadron level this part is represented by a weak vertex. At short distance the W exchange mechanism can be neglected safely. Therefore the weak vertex can be calculated reliably with the factorization hypothesis. Given the Hamiltonian in Eqs. (4) and (5), a T diagram in the factorization hypothesis is factorized as

      $ {\cal A}({\cal B}_{cc}\to {\cal B}_c {\cal M}) = \frac{G_{\rm F}}{\sqrt{2}} \sum\limits_{q = d,s} V^{*}_{cq} V_{uD} \left(C_2+C_1/N_C\right) \langle{\cal M}|({\bar{u}}_{\alpha}D_{\alpha})_{V-A}|0\rangle \langle{\cal B}_c| ({\bar{q}}_{\beta} c_{\beta} )_{V-A}|{\cal B}_{cc}\rangle $

      (6)

      with $ N_c = 3 $ . The weak transition of $ {\cal B}_{cc} $ to a spin- $ 1/2 $ singly charm baryon $ {\cal B}_c $ is parameterized as

      $ \begin{aligned}[b] \langle {\cal B}_c(p^\prime,s_z^\prime)| (V-A)_\mu |{\cal B}_{cc}(p,s_z)\rangle =\; & \bar u(p^\prime,s^\prime_z)\left[ \gamma_\mu f_1(q^2) + {\rm i}\sigma_{\mu\nu}\frac{q^\nu}{M} f_2(q^2) +\frac{q^\mu}{M} f_3(q^2) \right] u(p,s_z) \\ &- \bar u(p^\prime,s^\prime_z)\left[ \gamma_\mu g_1(q^2) + {\rm i}\sigma_{\mu\nu}\frac{q^\nu}{M} g_2(q^2) +\frac{q^\mu}{M} g_3(q^2) \right] \gamma_5 u(p,s_z), \end{aligned} $

      (7)

      with $ q = p-p^\prime $ , M is the mass of $ {\cal B}_{cc} $ and $ f_i $ , $ g_i $ are the form factors.

      The expressions of $ f_i $ and $ g_i $ , which can be obtained with the help of kinds of quark models or sum rules, are used as inputs here. In this paper we adopt the results calculated under the light-front quark model in Ref. [10].

      The decay constants of pseudoscalar and vector mesons are defined respectively as

      $ \begin{array}{l} \langle 0|A_\mu|P(q)\rangle = {\rm i}f_Pq_\mu \, , \end{array} $

      (8)

      and

      $ \begin{array}{l} \langle 0|V_\mu|V(q)\rangle = f_Vm_V\epsilon_\mu \, , \end{array} $

      (9)

      where the "P" and "V" in subscripts correspond to a pseudoscalar and vector meson, respectively. Combining Eqs. (7)-(9), the weak vertex of $ {\cal B}_{cc}\to{\cal B}_c P $ is expressed as

      $ W_T({\cal B}_{cc}\to{\cal B}_c P) = {\rm i}\frac{G_{\rm F}}{\sqrt{2}} V^*_{cq} V_{uD} a_1 f_P \bar u(p^\prime,s^\prime_z)\left[(M-M^\prime) f_1(m_P^2)+ (M+M^\prime) g_1(m_P^2) \gamma_5 \right] u(p,s_z)\, . $

      (10)

      C diagram can be calculated via its relation to T diagram under Fierz transformation,

      $ W_C({\cal B}_{cc}\to{\cal B}_c P) = {\rm i}\frac{G_{\rm F}}{\sqrt{2}} V^*_{cq} V_{uD} a_2 f_P \bar u(p^\prime,s^\prime_z)\left[(M-M^\prime) f_1(m_P^2)+ (M+M^\prime) g_1(m_P^2) \gamma_5 \right] u(p,s_z)\, . $

      (11)

      In the above equations $ a_1 = C_2+C_1/N_C $ and $ a_2 = C_1+ C_2/N_C $ are the combinations of Wilson coefficients. In this work, the decays are under the charm scale, so we use $ a_1(m_c) $ and $ a_2(m_c) $ in Ref. [34]. $ M^\prime $ is the mass of $ {\cal B}_c $ . We omit the terms with $ f_3 $ and $ g_3 $ in Eq. (11), because they are suppressed by $ m_P^2/M^2 $ .

      For $ {\cal B}_{cc}\to{\cal B}_c V $ there are

      $ \begin{aligned}[b] W_T({\cal B}_{cc}\to{\cal B}_c V) = &\frac{G_{\rm F}}{\sqrt{2}} V^*_{cq} V_{uD} a_1 f_V \epsilon^*_\mu \bar u(p^\prime,s^\prime_z)\left[\left(f_1(m_V^2)-\frac{M+M^\prime}{M}f_2(m_V^2)\right)\gamma^\mu +\frac{2}{M}f_2(m_V^2)p^{\prime\mu} \right. \\ &-\left.\left(g_1(m_V^2)+\frac{M-M^\prime}{M}g_2(m_V^2)\right)\gamma^\mu\gamma_5 -\frac{2}{M}g_2(m_V^2)p^{\prime\mu}\gamma_5\right] u(p,s_z)\, ,\\ W_C({\cal B}_{cc}\to{\cal B}_c V) =& \frac{G_{\rm F}}{\sqrt{2}} V^*_{cq} V_{uD} a_2 f_V \epsilon^*_\mu \bar u(p^\prime,s^\prime_z)\left[\left(f_1(m_V^2)-\frac{M+M^\prime}{M}f_2(m_V^2)\right)\gamma^\mu +\frac{2}{M}f_2(m_V^2)p^{\prime\mu}\right. \\ &-\left.\left(g_1(m_V^2)+\frac{M-M^\prime}{M}g_2(m_V^2)\right)\gamma^\mu\gamma_5 -\frac{2}{M}g_2(m_V^2)p^{\prime\mu}\gamma_5\right] u(p,s_z)\, . \end{aligned} $

      (12)
    • C.   Rescattering at long distance

    • The rescattering between the intermediate particles is nonperturbative dynamics in nature and really difficult to calculate. In this work we employ the framework of FSIs and perform the calculation with one-particle-exchange model at the hadron level [33, 35, 36]. In the following, we take $ \Omega_{cc}^{+}\to\Xi^{0} D_s^+ $ as an example to show the detailed progress of our calculation. This decay can proceed as $ \Omega_{cc}^{+}\to\Omega_c^0(K^+/K^{*+})\to\Xi^{0} D_s^+ $ , $ \Omega_{cc}^{+}\to(\Xi_c^+/\Xi_c^{\prime +})(\phi/\eta_1/\eta_8)\to \Xi^{0} D_s^+ $ and $ \Omega_{cc}^{+}\to(\Xi_c^0/\Xi_c^{\prime 0})(\pi^+/\rho^+)\to\Xi^{0} D_s^+ $ . The first one is induced by $ c\to s u \bar s $ at quark level and the last two ones are induced by $ c \to d u \bar d $ , which indicates that it is a singly CKM suppressed decay. The intermediate states $ \Omega_c^0(K^+/ K^{*+}) $ and $ (\Xi_c^0/\Xi_c^{\prime 0})(\pi^+/\rho^+) $ are generated via the T diagram and $ (\Xi_c^+/\Xi_c^{\prime +})(\phi/\eta_1/\eta_8) $ origin from C mechanism.

      As mentioned above and depicted in Fig. 2, the long distant contributions are calculated at hadron level. The calculation is performed with the chiral Lagrangian. One can draw all the leading diagrams in the meaning of perturbation theory with only one particle exchanged as in Fig. 3. The Lagrangian used in this paper are from Refs. [37-40]. The readers can refer to Ref. [25] for specific expressions.

      Figure 3.  Leading FSI contributions to $ \Omega_{cc}^{+}\to\Xi^{0} D_s^+ $ manifested at hadron level. The black squares denote weak vertices and dots represent strong vertices. Each thick line in diagram (g), (h) and (i) denotes a resonant structure. Diagrams (a), (d) and (g) are induced by the rescattering between $ \Omega_c^0 $ and $ K^+/K^{*+} $ , diagrams (b), (c), (e) and (h) by the rescattering between $ \Xi_c^+/\Xi_c^{\prime +} $ and $ \phi/\eta_1/\eta_8 $ , and diagram (f) by $ \Xi_c^0/\Xi_c^{\prime 0} $ and $ \pi^+/\rho^+. $

      The three diagrams of s channel, Figs. 3(g), (h) and (i), contributes sizably only when the mass of each resonant state is quite near to the mass of the mother particle $ \Omega_{cc}^{+} $ . Among the discovered singly charmed baryons even the heaviest one is about $ 500 $ MeV lighter than $ \Xi_{cc}^{++} $ . Therefore, these contributions are supposed to be suppressed by the off-shell effect. As a result we neglect these contributions in our calculation and only consider the t channel contributions which are typical triangle diagrams depicted in Figs. 3(a)-(f). Eq. (3) is employed to calculate the absorptive part of these diagrams. In principle the amplitude of the diagram can be obtained via the dispersion relation

      $ A(m_1^2) = \frac{1}{\pi}\int_s^\infty \frac{{\cal A}bs\,A(s^\prime)}{s^\prime - m_1^2-i\epsilon} {\rm{d}}s^\prime. $

      (13)

      Different from QCD sum rules, our calculation is performed in the physical kinematics region, where a singularity in the above integration exists. In this paper we follow the scheme adopted by Hai-Yang Cheng, Chun-Khiang Chua and Amarjit Soni in Ref. [35]. Only the absorptive part of the amplitude is kept for order estimation. An additional phenomenological factor is associated with the exchanged particle to account for its off-shell effect and make the theoretical framework consistent. The expression of this factor is given in the next subsection.

    • D.   Analytic expressions for the diagrams

    • Combing the discussions in section II B and II C, we derive the analytic expressions of the amplitudes in this subsection. In order to simplify the subscripts we assign numbers to the particles in a triangle diagram as shown in Fig. 4, in which the momentum flows are also defined. We use $ M_{a/b/c/d/e/f}(P2;P3;P4) $ to denote the amplitude of such a triangle diagram. The subscripts " $ a/b/c/d/e/f $ " correspond to Figs. 3(a)-(f), and $ P2 $ , $ P3 $ and $ P4 $ denote the particles at positions $ 2 $ , $ 3 $ and $ 4 $ , respectively.

      Figure 4.  Numbers assigned to the lines in a triangle diagram. The arrows define the momentum directions in our calculation

      Specificly, the absorptive part of Fig. 3(a) is given by set $ P2 = K^+ $ , $ P3 = \Omega_c^0 $ and $ P4 = D^{*0} $

      $ \begin{aligned}[b] {\cal A}bs\,M_{a}(K^{+};\Omega_{c}^{0};D^{*0}) =& \int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{1}f_{K^+} \frac{F^{2}(t,m_{D^{*0}})}{t-m_{D^{*0}}^{2}+{\rm i}m_{D^{*0}}\Gamma_{D^{*0}}}g_{D^{*0}D_s^{+}K^+}p_{2\alpha}\\ &\times\overline{u}(p_{6},s^{\prime}_{z}) \left[f_{1\Omega_{c}^{0}\Xi^{0}D^{*0}}\gamma_{\mu}(-g^{\mu\alpha}+\frac{p_{4}^{\mu}p_{4}^{\alpha}}{m_{D^{*0}}^{2}}) +\frac{f_{2\Omega_{c}^{0}\Xi^{0}D^{*0}}}{m_{\Omega_{c}^{0}} +m_{\Xi^{0}}}\sigma_{\mu\nu}{\rm i}p_{4}^{\mu} (-g^{\nu\alpha}+\frac{p_{4}^{\nu}p_{4}^{\alpha}}{m_{D^{*0}}^{2}})\right]\\ &\times(/\kern-0.57 em {{p_{3}}}+m_{\Omega_{c}^{0}}) \left[(m_{\Omega_{cc}^{+}}-m_{\Omega_{c}^{0}})f_{1}(m^{2}_{K^+}) +(m_{\Omega_{cc}^{+}}+m_{\Omega_{c}^{0}})g_{1}(m^{2}_{k^+})\gamma_{5}\right] u(p_{1},s_{z}). \end{aligned} $

      (14)

      In calculation summations over the polarization states of intermediate and exchanged particles need to be performed. For example, in Fig. 3(a) one needs to sum over the polarization states of $ \Omega_{c}^{0} $ and $ D^{*0} $ . $ \theta $ and $ \phi $ in Eq. (14) are the polar and azimuthal angles of $ \vec{p_3} $ in the spherical coordinate system. $ g_{D^{*0}D_s^{+}K^+} $ , $ f_{1\Omega_{c}^{0}\Xi^{0}D^{*0}} $ and $ f_{2\Omega_{c}^{0}\Xi^{0}D^{*0}} $ are strong coupling constants. $ P2 $ and $ P3 $ are set to be on-shell. To account for the off-shell effect and make the theoretical framework self-consistent, a Breit-Wigner structure and a form factor $ F(t,m) $ are associated with the exchanged particle. The form factor $ F(t,m) $ is parameterized as [35]

      $ F(t,m) = \left(\frac{\Lambda^2-m^2}{\Lambda^2-t}\right)^n, $

      (15)

      normalized to $ 1 $ at $ t = m^2 $ . m is the mass of the exchanged particle. The cutoff $ \Lambda $ is given as

      $ \Lambda = m + \eta \Lambda_{\rm QCD} $

      (16)

      with $ \Lambda_{\rm QCD} = 330\,{\rm MeV} $ . The phenomenological parameter $ \eta $ depends on all the particles at the strong vertex. Because a large number of strong vertices appear in the calculation, one requires huge amount of experimental data to determine these parameters one by one. In our calculation we set $ \eta = 1.5 $ and vary it from $ 1 $ to $ 2 $ for error estimations. n in Eq. (15) is another phenomenological parameter that needs to be extracted from experimental data. For lack of experimental data, we borrow the experience of Ref. [35] and set it to $ 1 $ .

      Similarly the absorptive part of Fig. 3(d) is given as

      $ \begin{aligned}[b] {\cal A}bs\,M_{d}(K^{*+};\Omega_{c}^{0};D^{0}) = & -{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{1}f_{K^{*+}} \frac{F^{2}(t,m_{D^{0}})}{t-m_{D^{0}}^{2}+{\rm i}m_{D^{0}}\Gamma_{D^{0}}} g_{\Omega_c^{0}\Xi^{0}D^{0}} g_{D_s^{+}D^{0}K^{*+}}(p_{5\alpha}+p_{4\alpha})\\ &\times\overline{u}(p_{6},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Omega_{c}^{0}}) \left(-g^{\mu\alpha}+\frac{p_{2}^{\mu}p_{2}^{\alpha}}{m_{K^{*+}}^{2}}\right)\times\left[ \left(f_{1}(m^2_{K^{*+}}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Omega_{c}^{0}}}{m_{\Omega_{cc}^{+}}}{f_{2}(m^2_{K^{*+}})}\right)\gamma_{\mu}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{K^{*+}})}p_{3\mu}\\ &\left.-\left (g_{1}\left(m^2_{K^{*+}}\right)+\frac{m_{\Omega_{cc}^{+}}-m_{\Omega_{c}^{0}}}{m_{\Omega_{cc}^{+}}}g_{2}\left(m^2_{K^{*+}}\right)\right) \gamma_{\mu}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}g_{2}\left(m^2_{K^{*+}}\right)p_{3\mu}\gamma_{5} \right] u(p_{1},s_{z}), \end{aligned} $

      (17)

      where the spin summation over the polarization states of $ \Omega_c^0 $ and $ K^{*+} $ is performed. It should be stressed that some symbols of strong coupling constants looks similar to those of weak transition form factors. Readers can distinguish them by the feature that strong coupling constants have particle names as subscripts. The expressions of the rest diagrams in Fig. 3 are given in appendix A. With all the diagrams calculated the amplitude of $ \Omega_{cc}^{+}\to\Xi^{0} D_s^+ $ is given as

      $ \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\to\Xi^{0} D_s^+) =& {\rm i} {\cal A}bs[ M_{a}(K^{+};\Omega_{c}^{0};D^{*0})+M_{b}(\phi;\Xi_c^+;D_s^{+})+M_{b}(\phi;\Xi_c^{\prime +};D_s^{+})+M_{c}(\phi;\Xi_c^+;\Xi^0)\\ &+M_{c}(\phi;\Xi_c^{\prime +};\Xi^0)+M_{c}(\eta_1;\Xi_c^+;\Xi^0)+M_{c}(\eta_1;\Xi_c^{\prime +};\Xi^0)+M_{c}(\eta_8;\Xi_c^+;\Xi^0)\\ &+M_{c}(\eta_8;\Xi_c^{\prime +};\Xi^0)+M_{d}(K^{*+};\Omega_{c}^{0};D^{0})+M_{e}(\eta_1;\Xi_c^{+}; D_s^{*+})+M_{e}(\eta_1;\Xi_c^{\prime +};D_s^{*+})\\ &+M_{e}(\eta_8;\Xi_c^{+};D_s^{*+})+M_{e}(\eta_8;\Xi_c^{\prime +};D_s^{*+})+M_{f}(\pi^+;\Xi_c^0;\Xi^-)+M_{f}(\pi^+;\Xi_c^{\prime 0};\Xi^-)\\ &+M_{f}(\rho^+;\Xi_c^0;\Xi^-)+M_{f}(\rho^+;\Xi_c^{\prime 0};\Xi^-)]. \end{aligned} $

      (18)

      The amplitudes of the other decays can be obtained in the same way. For shortage of the paper, we collect these expressions in appendix B.

    III.   NUMERICAL RESULTS AND DISCUSSIONS
    • The decay width of $ {\cal B}_{cc}\to{\cal B}D^{(*)} $ can be calculated at the rest frame of $ {\cal B}_{cc} $ by

      $ \Gamma({\cal B}_{cc}\to {\cal B}D^{(*)}) = \frac{\sqrt{(m_{{\cal B}_{cc}}^2-(m_{\cal B}+m_{D^{(*)}})^2)((m_{{\cal B}_{cc}}^2-(m_{\cal B}-m_{D^{(*)}})^2}}{32\pi m_{{\cal B}_{cc}}^3}\sum_{\rm pol.}|{\cal A}({\cal B}_{cc}\to {\cal B}D^{(*)})|^2, $

      (19)

      where the summations are performed over the polarizations of initial and final states. In addition a factor $ 1/2 $ has already been multiplied to average over the polarizations of the mother particle $ {\cal B}_{cc} $ .

      The calculation of the short distance contribution needs the decay constants of some pseudoscalar and vector mesons, which are gathered in Table 1. Besides, large amount of strong couplings are in need. Most of them are from Refs. [35, 41-47]. Some strong couplings that can not be found in the literatures are calculated under the $ SU(3)_F $ symmetry. For shortage of the paper, the data of strong couplings are listed in appendix C.

      $ f_{\pi} $ $ f_{K} $ $ f_{\eta_8} $ $ f_{\eta_1} $ $ f_{\rho} $ $ f_{K^*} $ $ f_{\omega} $ $ f_{\phi} $
      130 156 163 152 216 217 195 233

      Table 1.  Decay constants of light pseudoscalar and vector mesons collected from Refs. [49,50] (in unit of MeV). $ f_{\eta_8} $ and $ f_{\eta_1} $ are calculated with the formulas in Ref. [48].

      Now we can obtain the numerical values of the related decays. We use the lifetime $ \tau_{\Xi_{cc}^{++}} = 256\,{\rm fs} $ which is measured by the LHCb collaboration [4] to calculate the branching fractions of $ \Xi_{cc}^{++} $ decays, and our results are collected in Table 2. One can see that the branching ratios of $ \Xi_{cc}^{++}\to {\cal B} D^* $ decays tend to be larger than those of $ \Xi_{cc}^{++}\to {\cal B} D $ mode when the quark constituents are the same. It can be easily understood by the fact that $ \Xi_{cc}^{++}\to {\cal B} D^* $ decays have more polarization states. Among these decays the CKM favored ones have the largest branching ratios doubtlessly. The branching ratio of $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+} $ is estimated to reach the percentage level.

      Channels $ {\cal BR}(10^{-3}) $ CKM Channels $ {\cal BR}(10^{-3}) $ CKM
      $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{+} $ $ 2.98_{-2.02}^{+3.16} $ CF $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+} $ $ 16.06_{-10.50}^{+17.28} $ CF
      $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{+}_{s} $ $ 0.17_{-0.12}^{+0.18} $ SCS $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}_{s} $ $ 2.68_{-1.71}^{+2.64} $ SCS
      $ \Xi_{cc}^{++}\rightarrow p D^{+} $ $ 0.16_{-0.11}^{+0.18} $ SCS $ \Xi_{cc}^{++}\rightarrow p D^{*+} $ $ 2.96_{-2.06}^{+3.38} $ SCS
      $ \Xi_{cc}^{++}\rightarrow p D^{+}_{s} $ $ 0.01_{-0.00}^{+0.02} $ DCS $ \Xi_{cc}^{++}\rightarrow p D^{*+}_{s} $ $ 0.11_{-0.07}^{+0.13} $ DCS

      Table 2.  Our results for branching ratios of $ \Xi_{cc}^{++}\to{\cal B} D^{(*)} $ . The "CF", "SCS" and "DCS" represent CKM favored, singly CKM suppressed and doubly CKM suppressed processes, respectively. The errors are estimated by varying $ \eta $ from $ 1 $ to $ 2 $ , and the central values are given at $ \eta = 1.5 $ . Topologically these decays are all classified to the $ C^\prime $ diagram.

      We give in Tables 3 and 4 the decay widths of $ \Xi_{cc}^+ $ and $ \Omega_{cc}^+ $ decays in stead of branching ratios, because there is no experimental data of their lifetimes. Among decays of the same mode, $ {\cal B}_{cc}\to {\cal B} D $ or $ {\cal B}_{cc}\to {\cal B} D^* $ , the CKM favored, singly CKM suppressed and doubly CKM suppressed decays fall into a hierarchy naturally.

      Channels $ \Gamma/{\rm GeV} $ CKM Contributions Channels $ \Gamma/{\rm GeV} $ CKM Contributions
      $ \Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{+} $ $ (5.93_{-4.05}^{+6.31})*10^{-15} $ CF $ C^\prime $ B $ \Xi_{cc}^{+}\rightarrow\Lambda D^{*+} $ $ (1.82_{-1.26}^{+2.03})*10^{-13} $ CF $ C^\prime $ B
      $ \Xi_{cc}^{+}\rightarrow\Lambda D^{+} $ $ (5.84_{-3.98}^{+6.16})*10^{-15} $ CF $ C^\prime $ B $ \Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+} $ $ (2.17 _{-1.51}^{+2.45})*10^{-13} $ CF $ C^\prime $ B
      $ \Xi_{cc}^{+}\rightarrow\Sigma^{+} D^{0} $ $ (1.23 _{-0.77 }^{+1.24 })*10^{-15} $ CF B $ \Xi_{cc}^{+}\rightarrow\Sigma^{+} D^{*0} $ $ (6.77 _{-4.46}^{+7.37})*10^{-14} $ CF B
      $ \Xi_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{+} $ $ (4.52 _{-3.49}^{+5.22})*10^{-16} $ CF B $ \Xi_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{*+} $ $ (2.52 _{-1.48 }^{+2.23})*10^{-14} $ CF B
      $ \Xi_{cc}^{+}\rightarrow p D^{0} $ $ (1.85 _{-1.27}^{+2.02})*10^{-15} $ SCS B $ \Xi_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{*+} $ $ (1.15_{-0.85}^{+1.41})*10^{-14} $ SCS $ C^\prime $ B
      $ \Xi_{cc}^{+}\rightarrow\Lambda D_{s}^{+} $ $ (3.00_{-2.00}^{+2.93})*10^{-16} $ SCS $ C^\prime $ B $ \Xi_{cc}^{+}\rightarrow\Lambda D_{s}^{*+} $ $ (1.58_{-1.09}^{+1.73})*10^{-14} $ SCS $ C^\prime $ B
      $ \Xi_{cc}^{+}\rightarrow n D^{+} $ $ (1.59 _{-1.13}^{+1.87})*10^{-16} $ SCS $ C^\prime $ B $ \Xi_{cc}^{+}\rightarrow n D^{*+} $ $ (1.04 _{-0.87 }^{+1.41})*10^{-15} $ SCS $ C^\prime $ B
      $ \Xi_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{+} $ $ (2.85_{-1.78}^{+2.72})*10^{-16} $ SCS $ C^\prime $ B $ \Xi_{cc}^{+}\rightarrow p D^{*0} $ $ (9.46 _{-6.49}^{+10.20 })*10^{-15} $ SCS B
      $ \Xi_{cc}^{+}\rightarrow n D_{s}^{+} $ $ (3.26 _{-2.41}^{+3.88})*10^{-17} $ DCS $ C^\prime $ $ \Xi_{cc}^{+}\rightarrow n D_{s}^{*+} $ $ (1.47 _{-1.00}^{+1.57})*10^{-16} $ DCS $ C^\prime $

      Table 3.  Our results for branching ratios of $ \Xi_{cc}^{+}\to{\cal B} D^{(*)} $ . The "CF", "SCS" and "DCS" represent CKM favored, singly CKM suppressed and doubly CKM suppressed processes, respectively. The errors are estimated by varying $ \eta $ from $ 1 $ to $ 2 $ , and the central values are given at $ \eta = 1.5 $ . B and $ C^\prime $ represent the contributions in Fig. 1.

      Channels $ \Gamma/{\rm GeV} $ CKM Contributions Channels $ \Gamma/{\rm GeV} $ CKM Contributions
      $ \Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+} $ $ (1.88_{-1.25}^{+1.97})*10^{-14} $ CF $ C^\prime $ $ \Omega_{cc}^{+}\rightarrow\Xi^{0} D^{*+} $ $ (4.99_{-2.62}^{+4.05})*10^{-14} $ CF $ C^\prime $
      $ \Omega_{cc}^{+}\rightarrow\Sigma^{+} D^{0} $ $ (1.76_{-1.07}^{+1.71})*10^{-15} $ SCS B $ \Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+} $ $ (1.80_{-1.27}^{+2.14})*10^{-14} $ SCS $ C^\prime $ B
      $ \Omega_{cc}^{+}\rightarrow\Lambda D^{+} $ $ (1.75_{-1.21}^{+1.98})*10^{-15} $ SCS $ C^\prime $ B $ \Omega_{cc}^{+}\rightarrow\Lambda D^{*+} $ $ (7.65_{-5.32}^{+8.69})*10^{-15} $ SCS $ C^\prime $ B
      $ \Omega_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{+} $ $ (9.93_{-6.84}^{+10.87})*10^{-16} $ SCS $ C^\prime $ B $ \Omega_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{*+} $ $ (4.26_{-2.81}^{+4.06})*10^{-16} $ SCS $ C^\prime $ B
      $ \Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{+} $ $ (2.37_{-1.20}^{+2.14})*10^{-16} $ SCS $ C^\prime $ B $ \Omega_{cc}^{+}\rightarrow\Sigma^{+} D^{*0} $ $ (6.91_{-4.15}^{+6.24})*10^{-15} $ SCS B
      $ \Omega_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{+} $ $ (1.17_{-6.57}^{+10.93})*10^{-16} $ DCS $ C^\prime $ B $ \Omega_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{*+} $ $ (1.68_{-1.18}^{+1.92})*10^{-16} $ DCS $ C^\prime $ B
      $ \Omega_{cc}^{+}\rightarrow p D^{0} $ $ (1.74_{-1.23}^{+2.05})*10^{-17} $ DCS B $ \Omega_{cc}^{+}\rightarrow p D^{*0} $ $ (3.83_{-2.74}^{+4.85})*10^{-16} $ DCS B
      $ \Omega_{cc}^{+}\rightarrow n D^{+} $ $ (4.32_{-3.30}^{+5.56})*10^{-17} $ DCS B $ \Omega_{cc}^{+}\rightarrow\Lambda D_{s}^{*+} $ $ (1.06_{-0.75}^{+1.27})*10^{-16} $ DCS B
      $ \Omega_{cc}^{+}\rightarrow\Lambda D_{s}^{+} $ $ (7.00_{-4.85}^{+7.87})*10^{-18} $ DCS B $ \Omega_{cc}^{+}\rightarrow n D^{*+} $ $ (2.74_{-2.09}^{+3.29})*10^{-17} $ DCS B

      Table 4.  The same as Table 3 but for decay widths of $\Omega_{cc}^{+}\to{\cal B} D^{(*)}.$

      $ \Xi_{cc}^{+}\rightarrow\Lambda D^{*+} $ and $ \Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+} $ own the largest decay widths among $ {\Xi}_{cc}^+\to {\cal B} D^{(*)} $ decays. Estimated with a recent calculated lifetime $ \tau_{\Xi_{cc}^+} = 45\; \rm{fs} $ in Ref. [51], their branching ratios are given by

      $ \begin{aligned}[b] &{\cal BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+})\in [0.38 \%, 2.63 \%],\\ &{\cal BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+})\in [0.45 \%, 3.16 \%]. \end{aligned} $

      (20)

      The lifetime of $ \Omega_{cc}^+ $ is predicted to lies in the range $ 75\sim 180 $ fs in Ref. [51]. Here we use the boundary $ 75 $ fs to estimate the three largest branching fractions in $ \Omega_{cc}^+ \to {\cal B} D^{(*)} $ decays, which are given as

      $ \begin{aligned}[b] & {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{*+}) \in [0.27 \%, 1.03 \%],\\ & {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+}) \in [0.07 \%, 0.44 \%],\\ & {\cal BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.06 \%, 0.45 \%]. \end{aligned} $

      (21)

      In the tables we also specify the topological contributions in the decays. One can see that the bow-tie mechanism contribute sizably in charm decays. Let us take $ \Omega_{cc}^+\to \Xi^0 D^+ $ and $ \Omega _{cc}^ + \to {\Sigma ^ + }{D^0}$ as an example to make it clear. The former decay is a pure color commensurate process and the later one is purely dominated by the bow-tie mechanism. One can see in Table 4 that

      $ \frac{\Gamma(\Omega_{cc}^+\to \Xi^0 D^+)}{\Gamma(\Omega_{cc}^+ \to \Sigma^+ D^0)}\sim 10. $

      (22)

      The ratio of their CKM matrix elements is

      $ \frac{V_{cs}V^*_{ud}}{V_{cs}V^*_{us}}\sim 4.4. $

      (23)

      Taking it into consideration that the CKM factors are squared in calculation of decay widths, one can find that the CKM factors will cause a difference of about $ 20 $ times. It means the bow-tie mechanism and the color commensurate mechanism contribute at the same order.

    IV.   SUMMARY
    • The discovery of $ \Xi_{cc}^{++} $ in 2017 inspires the interest of studying doubly charm baryons. Among all the topics, how to calculate their weak decays is a meaningful and challenging one. It can give valuable suggestions for experimental searches as well as helps to understand the dynamics of baryon decays. In our previous work we apply the model of final state interactions to baryon decays and realize the estimation of two body nonleptonic decays of charm baryons.

      In this paper we calculate the decays of a doubly charmed baryon to a light baryon and a charm meson. In the same decay mode, $ {\cal B}_{cc} \to {\cal B} D $ or $ {\cal B}_{cc} \to {\cal B} D^* $ , the CKM favored, singly CKM suppressed and doubly CKM suppressed decays fall into a hierarchy naturally. The $ {\cal B}_{cc} \to {\cal B} D^* $ decays tends to have larger branching ratios or decay widths because they have more polarization states. $ \Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+} $ has the largest branching ratio in $ \Xi_{cc}^{++} \to {\cal B} D^{(*)} $ decays, which lies in $ (0.46\sim 3.33) \% $ . The two largest branching ratios in $ \Xi_{cc}^{+} \to {\cal B} D^{(*)} $ mode are $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) \in [0.38 \%, 2.63 \%] $ and $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.45 \%, 3.16 \%] $ , which are estimated with $ \tau_{\Xi_{cc}^+} = 45 $ fs. For $ \Omega_{cc}^{+} \to {\cal B} D^{(*)} $ mode $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{*+}) \in [0.27 \%, 1.03 \%] $ , $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+}) \in [0.07 \%, 0.44 \%] $ , and $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.06 \%, 0.45 \%] $ are three largest ones, and they are calculated with $ \tau_{\Omega_{cc}^+} = 75 $ fs.

      Comparing the decay widths of pure color commensurate processes with those of pure bow-tie processes, we find that the bow-tie mechanism also plays an important role in charm decays.

    APPENDIX A. EXPRESSIONS OF DIAGRAMS (C)-(I) IN FIG. 3
    • $ \begin{aligned}[b] {\cal A}bs\,M_{b}(\phi;\Xi_c^+;D_s^{+}) =\;& {\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\phi} \frac{F^{2}(t,m_{D_s^{+}})}{t-m_{D_s^{+}}^{2}+{\rm i}m_{D_s^{+}}\Gamma_{D_s^{+}}} g_{\Xi_c^{+}\Xi^0D_s^{+}} g_{D_s^+D_s^+\phi}(p_{4\alpha}+p_{5\alpha})\\ &\times\overline{u}(p_{6},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Xi_{c}^{+}}) \left(-g^{\mu\alpha}+\frac{p_{2}^{\mu}p_{2}^{\alpha}}{m_{\phi}^{2}}\right)\times\left[ \left(f_{1}(m^2_{\phi}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}}}{m_{\Omega_{cc}^{+}}}{f_{2}\left(m^2_{\phi}\right)}\right)\gamma_{\mu}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{\phi})}p_{3\mu}\\ &\left.-\left (g_{1}(m^2_{\phi})+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}}}{m_{\Omega_{cc}^{+}}}{g_{2}(m^2_{\phi})}\right) \gamma_{\mu}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}(m^2_{\phi})}p_{3\mu}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} \tag{A1}$

      $\tag{A2} \begin{aligned}[b] {\cal A}bs\,M_{b}(\phi;\Xi_c^{\prime +};D_s^{+}) = & \;{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\phi} \frac{F^{2}(t,m_{D_s^+})}{t-m_{D_s^+}^{2}+{\rm i}m_{D_s^{+}}\Gamma_{D_s^{+}}} g_{\Xi_c^{\prime+}\Xi^0D_s^{+}} g_{D_s^+D_s^+\phi}(p_{4\alpha}+p_{5\alpha})\\ &\times\!\overline{u}(p_{6},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{3}}}\!+\!m_{\Xi_{c}^{\prime +}}) \left(-g^{\mu\alpha}+\frac{p_{2}^{\mu}p_{2}^{\alpha}}{m_{\phi}^{2}}\right)\!\times\!\left[ \left(f_{1}\left(m^2_{\phi}\right) \!-\!\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime+}}}{m_{\Omega_{cc}^{+}}}{f_{2}\left(m^2_{\phi}\right)}\right)\gamma_{\mu}\right. \!+\!\frac{2}{m_{\Omega_{cc}^+}}{f_{2}\left(m^2_{\phi}\right)}p_{3\mu}\\ &\left.-\left (g_{1}\left(m^2_{\phi}\right)+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime+}}}{m_{\Omega_{cc}^{+}}}{g_{2}\left(m^2_{\phi}\right)}\right) \gamma_{\mu}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}\left(m^2_{\phi}\right)}p_{3\mu}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} $

      $ \tag{A3}\begin{aligned}[b] {\cal A}bs\,M_{e}(\eta_1;\Xi_c^{+}; D_s^{*+}) = & -\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_1} \frac{F^{2}(t,m_{D_s^{*+}})}{t-m_{D_s^{*+}}^{2}+{\rm i}m_{D_s^{*+}}\Gamma_{D_s^{*+}}}g_{D_s^{*+}D_s^{+}\eta_1}p_{2\alpha}\\ &\times\overline{u}(p_{6},s^{\prime}_{z}) \left[f_{1\Xi_{c}^{+}\Xi^{0}D_s^{*+}}\gamma_{\mu}\left(-g^{\mu\alpha}+\frac{p_{4}^{\mu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right) +\frac{f_{2\Xi_{c}^{+}\Xi^{0}D_s^{*+}}}{m_{\Xi_{c}^{+}} +m_{\Xi^{0}}}\sigma_{\mu\nu}{\rm i}p_{4}^{\mu} \left(-g^{\nu\alpha}+\frac{p_{4}^{\nu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{3}}}+m_{\Xi_{c}^{+}}) \left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}})f_{1}(m^{2}_{\eta_1}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}})g_{1}(m^{2}_{\eta_1})\gamma_{5}\right] u(p_{1},s_{z}), \end{aligned} $

      $ \tag{A4}\begin{aligned}[b] {\cal A}bs\,M_{e}(\eta_1;\Xi_c^{\prime +};D_s^{*+}) = & -\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_1} \frac{F^{2}(t,m_{D_s^{*+}})}{t-m_{D_s^{*+}}^{2}+{\rm i}m_{D_s^{*+}}\Gamma_{D_s^{*+}}}g_{D_s^{*+}D_s^{+}\eta_1}p_{2\alpha}\\ &\times\overline{u}(p_{6},s^{\prime}_{z}) \left[f_{1\Xi_{c}^{\prime +}\Xi^{0}D_s^{*+}}\gamma_{\mu}\left(-g^{\mu\alpha}+\frac{p_{4}^{\mu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right) +\frac{f_{2\Xi_{c}^{\prime +}\Xi^{0}D_s^{*+}}}{m_{\Xi_{c}^{\prime +}} +m_{\Xi^{0}}}\sigma_{\mu\nu}{\rm i}p_{4}^{\mu} \left(-g^{\nu\alpha}+\frac{p_{4}^{\nu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{3}}}+m_{\Xi_{c}^{\prime +}}) \left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime +}})f_{1}(m^{2}_{\eta_1}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime +}})g_{1}(m^{2}_{\eta_1})\gamma_{5}\right] u(p_{1},s_{z}), \end{aligned} $

      $\tag{A5} \begin{aligned}[b] {\cal A}bs\,M_{e}(\eta_8;\Xi_c^{+};D_s^{*+}) = & -\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_8} \frac{F^{2}(t,m_{D_s^{*+}})}{t-m_{D_s^{*+}}^{2}+{\rm i}m_{D_s^{*+}}\Gamma_{D_s^{*+}}}g_{D_s^{*+}D_s^{+}\eta_8}p_{2\alpha}\\ &\times\overline{u}(p_{6},s^{\prime}_{z}) \left[f_{1\Xi_{c}^{+}\Xi^{0}D_s^{*+}}\gamma_{\mu}\left(-g^{\mu\alpha}+\frac{p_{4}^{\mu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right) +\frac{f_{2\Xi_{c}^{+}\Xi^{0}D_s^{*+}}}{m_{\Xi_{c}^{+}} +m_{\Xi^{0}}}\sigma_{\mu\nu}{\rm i}p_{4}^{\mu} \left(-g^{\nu\alpha}+\frac{p_{4}^{\nu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{3}}}+m_{\Xi_{c}^{+}}) \left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}})f_{1}(m^{2}_{\eta_8}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}})g_{1}(m^{2}_{\eta_8})\gamma_{5}\right] u(p_{1},s_{z}), \end{aligned} $

      $\tag{A6} \begin{aligned}[b] {\cal A}bs\,M_{e}(\eta_8;\Xi_c^{\prime +};D_s^{*+}) = & -\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_8} \frac{F^{2}(t,m_{D_s^{*+}})}{t-m_{D_s^{*+}}^{2}+{\rm i}m_{D_s^{*+}}\Gamma_{D_s^{*+}}}g_{D_s^{*+}D_s^{+}\eta_8}p_{2\alpha}\\ &\times\overline{u}(p_{6},s^{\prime}_{z}) \left[f_{1\Xi_{c}^{\prime +}\Xi^{0}D_s^{*+}}\gamma_{\mu}\left(-g^{\mu\alpha}+\frac{p_{4}^{\mu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right) +\frac{f_{2\Xi_{c}^{\prime +}\Xi^{0}D_s^{*+}}}{m_{\Xi_{c}^{\prime +}} +m_{\Xi^{0}}}\sigma_{\mu\nu}{\rm i}p_{4}^{\mu} \left(-g^{\nu\alpha}+\frac{p_{4}^{\nu}p_{4}^{\alpha}}{m_{D_s^{*+}}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{3}}}+m_{\Xi_{c}^{\prime +}}) \left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime +}})f_{1}(m^{2}_{\eta_8}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime +}})g_{1}(m^{2}_{\eta_8})\gamma_{5}\right] u(p_{1},s_{z}), \end{aligned} $

      $\tag{A7} \begin{aligned}[b] {\cal A}bs\,M_{c}(\phi;\Xi_c^+;\Xi^0) =& \;-{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\phi} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}}g_{\Xi_c^{+}\Xi^0D_s^{+}}\\ &\times\overline{u}(p_{5},s^{\prime}_{z}) \left[ f_{1\Xi^0\Xi^0\phi}\gamma_{\mu} \left(-g^{\alpha\mu}+\frac{p_{2}^{\alpha}p_{2}^{\mu}}{m_{\phi}^{2}}\right) +\frac{f_{2\Xi^{0}\Xi^{0}\phi}}{m_{\Xi^{0}}+m_{\Xi^{0}}}\sigma_{\mu\nu}(-ip_{2}^{\mu}) \left(-g^{\alpha\nu}+\frac{p_{2}^{\alpha}p_{2}^{\nu}}{m_{\phi}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{+}}) \left[ \left(f_{1}(m^2_{\phi}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}}}{m_{\Omega_{cc}^{+}}}{f_{2}(m^2_{\phi})}\right)\gamma_{\alpha}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{\phi})}p_{3\alpha}\\ & \left.-\left (g_{1}(m^2_{\phi})+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}}}{m_{\Omega_{cc}^{+}}}{g_{2}(m^2_{\phi})}\right) \gamma_{\alpha}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}(m^2_{\phi})}p_{3\alpha}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} $

      $ \tag{A8}\begin{aligned}[b] {\cal A}bs\,M_{c}(\phi;\Xi_c^{\prime +};\Xi^0) = &\; -{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\phi} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}}g_{\Xi_c^{\prime +}\Xi^0D_s^{+}}\\ &\times\overline{u}(p_{5},s^{\prime}_{z}) \left[ f_{1\Xi^0\Xi^0\phi}\gamma_{\mu} \left(-g^{\alpha\mu}+\frac{p_{2}^{\alpha}p_{2}^{\mu}}{m_{\phi}^{2}}\right) +\frac{f_{2\Xi^{0}\Xi^{0}\phi}}{m_{\Xi^{0}}+m_{\Xi^{0}}}\sigma_{\mu\nu}(-ip_{2}^{\mu}) \left(-g^{\alpha\nu}+\frac{p_{2}^{\alpha}p_{2}^{\nu}}{m_{\phi}^{2}}\right)\right]\\ &\times(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{\prime +}}) \left[ \left(f_{1}(m^2_{\phi}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime +}}}{m_{\Omega_{cc}^{+}}}{f_{2}(m^2_{\phi})}\right)\gamma_{\alpha}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{\phi})}p_{3\alpha}\\ & \left.-\left (g_{1}(m^2_{\phi})+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime +}}}{m_{\Omega_{cc}^{+}}}{g_{2}(m^2_{\phi})}\right) \gamma_{\alpha}\gamma_{5}\right.\left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}(m^2_{\phi})}p_{3\alpha}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} $

      $ \tag{A9}\begin{aligned}[b] {\cal A}bs\,M_{c}(\eta_1;\Xi_c^+;\Xi^0) = & {\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_1} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}} g_{\Xi^{0}\Xi^{0}\eta_1} g_{\Xi_c^{+}\Xi^{0}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{+}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}})f_{1}(m^{2}_{\eta_1}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}})g_{1}(m^{2}_{\eta_1})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $\tag{A10} \begin{aligned}[b] {\cal A}bs\,M_{c}(\eta_1;\Xi_c^{\prime +};\Xi^0) = &\; {\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_1} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}} g_{\Xi^{0}\Xi^{0}\eta_1} g_{\Xi_c^{\prime +}\Xi^{0}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{\prime +}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime +}})f_{1}(m^{2}_{\eta_1}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime +}})g_{1}(m^{2}_{\eta_1})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $\tag{A11} \begin{aligned}[b] {\cal A}bs\,M_{c}(\eta_8;\Xi_c^+;\Xi^0) =& \;{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_8} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}} g_{\Xi^{0}\Xi^{0}\eta_8} g_{\Xi_c^{+}\Xi^{0}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{+}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{+}})f_{1}(m^{2}_{\eta_8}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{+}})g_{1}(m^{2}_{\eta_8})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $ \tag{A12}\begin{aligned}[b] {\cal A}bs\,M_{c}(\eta_8;\Xi_c^{\prime +};\Xi^0) = & \;{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cs}^{*}V_{us}a_{2}f_{\eta_8} \frac{F^{2}(t,m_{\Xi^{0}})}{t-m_{\Xi^{0}}^{2}+{\rm i}m_{\Xi^{0}}\Gamma_{\Xi^{0}}} g_{\Xi^{0}\Xi^{0}\eta_8} g_{\Xi_c^{\prime +}\Xi^{0}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{0}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{\prime +}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime +}})f_{1}(m^{2}_{\eta_8}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime +}})g_{1}(m^{2}_{\eta_8})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $\tag{A13} \begin{aligned}[b] {\cal A}bs\,M_{f}(\pi^+;\Xi_c^0;\Xi^-) =& \;{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cd}^{*}V_{ud}a_{2}f_{\pi^+} \frac{F^{2}(t,m_{\Xi^{-}})}{t-m_{\Xi^{-}}^{2}+{\rm i}m_{\Xi^{-}}\Gamma_{\Xi^{-}}} g_{\Xi^{0}\Xi^{-}\pi^+} g_{\Xi_c^{0}\Xi^{-}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{-}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{0}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{0}})f_{1}(m^{2}_{\pi^+}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{0}})g_{1}(m^{2}_{\pi^+})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $\tag{A14} \begin{aligned}[b] {\cal A}bs\,M_{f}(\pi^+;\Xi_c^{\prime 0};\Xi^-) = & \;{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cd}^{*}V_{ud}a_{2}f_{\pi^+} \frac{F^{2}(t,m_{\Xi^{-}})}{t-m_{\Xi^{-}}^{2}+{\rm i}m_{\Xi^{-}}\Gamma_{\Xi^{-}}} g_{\Xi^{0}\Xi^{-}\pi^+} g_{\Xi_c^{\prime 0}\Xi^{-}D_s^+}\\ &\times\overline{u}(p_{5},s^{\prime}_{z})\gamma_{5}(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{-}}) \gamma_{5} (/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{\prime 0}}) \\ &\times\left[(m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime 0}})f_{1}(m^{2}_{\pi^+}) +(m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime 0}})g_{1}(m^{2}_{\pi^+})\gamma_{5}\right]u(p_{1},s_{z}). \end{aligned} $

      $\tag{A15} \begin{aligned}[b] {\cal A}bs\,M_{f}(\rho^+;\Xi_c^0;\Xi^-) = & -{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cd}^{*}V_{ud}a_{2}f_{\rho^+} \frac{F^{2}(t,m_{\Xi^{-}})}{t-m_{\Xi^{-}}^{2}+{\rm i}m_{\Xi^{-}}\Gamma_{\Xi^{-}}} g_{\Xi_c^{0}\Xi^-D_s^{+}}\\ &\times\overline{u}(p_{5},s^{\prime}_{z}) \left[ f_{1\Xi^0\Xi^-\rho^+}\gamma_{\mu} +\frac{f_{2\Xi^{0}\Xi^{-}\rho^+}}{m_{\Xi^{0}}+m_{\Xi^{-}}}\sigma_{\mu\nu}(-{\rm i}p_{2}^{\mu}) \right]\\ &\times(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{-}})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{0}}) \left(-g^{\alpha\mu}+\frac{p_{2}^{\alpha}p_{2}^{\mu}}{m_{\rho^+}^{2}}\right) \left(-g^{\alpha\nu}+\frac{p_{2}^{\alpha}p_{2}^{\nu}}{m_{\rho^+}^{2}}\right)\\ &\times\left[ \left(f_{1}(m^2_{\rho^+}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{0}}}{m_{\Omega_{cc}^{+}}}{f_{2}(m^2_{\rho^+})}\right)\gamma_{\alpha}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{\rho^+})}p_{3\alpha}\\ &\left.-\left (g_{1}(m^2_{\rho^+})+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{0}}}{m_{\Omega_{cc}^{+}}}{g_{2}(m^2_{\rho^+})}\right) \gamma_{\alpha}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}(m^2_{\rho^+})}p_{3\alpha}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} $

      $ \tag{A16}\begin{aligned}[b] {\cal A}bs\,M_{f}(\rho^+;\Xi_c^{\prime 0};\Xi^-) = & \;-{\rm i}\int\frac{|\vec{p_2}|{\rm sin}\theta {\rm d}\theta {\rm d}\varphi}{32\pi^{2}m_{\Omega_{cc}^{+}}} \frac{G_{\rm F}}{\sqrt{2}}V_{cd}^{*}V_{ud}a_{2}f_{\rho^+} \frac{F^{2}(t,m_{\Xi^{-}})}{t-m_{\Xi^{-}}^{2}+{\rm i}m_{\Xi^{-}}\Gamma_{\Xi^{-}}} g_{\Xi_c^{\prime 0}\Xi^-D_s^{+}}\\ &\times\overline{u}(p_{5},s^{\prime}_{z}) \left[ f_{1\Xi^0\Xi^-\rho^+}\gamma_{\mu} +\frac{f_{2\Xi^{0}\Xi^{-}\rho^+}}{m_{\Xi^{0}}+m_{\Xi^{-}}}\sigma_{\mu\nu}(-{\rm i}p_{2}^{\mu}) \right]\\ &\times(/\kern-0.57 em {{p_{4}}}+m_{\Xi^{-}})\gamma_{5}(/\kern-0.57 em {{p_{3}}}+m_{\Xi_c^{\prime 0}}) \left(-g^{\alpha\mu}+\frac{p_{2}^{\alpha}p_{2}^{\mu}}{m_{\rho^+}^{2}}\right) \left(-g^{\alpha\nu}+\frac{p_{2}^{\alpha}p_{2}^{\nu}}{m_{\rho^+}^{2}}\right)\\ &\times\left[ \left(f_{1}(m^2_{\rho^+}) -\frac{m_{\Omega_{cc}^{+}}+m_{\Xi_{c}^{\prime 0}}}{m_{\Omega_{cc}^{+}}}{f_{2}(m^2_{\rho^+})}\right)\gamma_{\alpha}\right. +\frac{2}{m_{\Omega_{cc}^+}}{f_{2}(m^2_{\rho^+})}p_{3\alpha}\\ &\left.-\left (g_{1}(m^2_{\rho^+})+\frac{m_{\Omega_{cc}^{+}}-m_{\Xi_{c}^{\prime 0}}}{m_{\Omega_{cc}^{+}}}{g_{2}(m^2_{\rho^+})}\right) \gamma_{\alpha}\gamma_{5}\right. \left.-\frac{2}{m_{\Omega_{cc}^+}}{g_{2}(m^2_{\rho^+})}p_{3\alpha}\gamma_{5} \right] u(p_{1},s_{z}). \end{aligned} $

    APPENDIX B.   EXPRESSIONS OF AMPLITUDES
    • The expressions of amplitudes for all the $ {\cal B}_{cc}\to{\cal B} D^{(*)} $ decays are collected in this section. In order to make the expressions simpler, we define a function $ {\cal M}(P1, P2,P3, P4,P5,P6) $ to represent the absorptive part of a triangle diagram shown in Fig. 4. The absorptive part in Eq. (14) is related to this function by

      $\tag{B1} {\cal A}bs\,M_{a}(K^+;\Omega_c^0;D^{*0}) = {\cal M}(\Omega_{cc}^{+}, K^+,\Omega_c^0,D^{*0},\Xi^0,D_s^{+}). $

      Amplitudes of all $ {\cal B}_{cc}\to{\cal B} D^{(*)} $ decays are given as follows with this function.

      $\tag{B2} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\to\Sigma^{+}D^{+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, D^{*0}, D^+, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, D^{*0}, D^+, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, D^{0}, D^+, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, D^0, D^+, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \bar K^{0}, \Sigma_c^{++}, D_s^{*+}, D^+, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \bar K^{*0}, \Sigma_c^{++}, D_s^{+}, D^+, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, \Sigma^0, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, \Lambda, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, \Sigma^0, \Sigma^{+}, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, \Lambda, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, \Sigma^0, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, \Lambda, \Sigma^{+}, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, \Sigma^0, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, \Lambda, \Sigma^{+}, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \bar K^{0}, \Sigma_c^{++}, p, \Sigma^{+}, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \bar K^{*0}, \Sigma_c^{++}, p, \Sigma^{+}, D^+ ) ], \end{aligned} $

      $\tag{B3} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\to\Sigma^{+}D^{*+}) = &\;{\rm i} [ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, D^{0}, D^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, D^{0}, D^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, D^{*0}, D^{*+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, D^{*0}, D^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \bar K^{0}, \Sigma_c^{++}, D_s^{+}, D^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \bar K^{*0}, \Sigma_c^{++}, D_s^{*+}, D^{*+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, \Sigma^0, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^+, \Lambda, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, \Sigma^0, \Sigma^{+}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Xi_c^{\prime +}, \Lambda, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, \Sigma^0, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^+, \Lambda, \Sigma^{+}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, \Sigma^0, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Xi_c^{\prime +}, \Lambda, \Sigma^{+}, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \bar K^{0}, \Sigma_c^{++}, p, \Sigma^{+}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \bar K^{*0}, \Sigma_c^{++}, p, \Sigma^{+}, D^{*+} ) ], \end{aligned} $

      $\tag{B4} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{+}_{s}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, D^{*0}, D_s^{+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, k^+, \Xi_c^{\prime +}, D^{*0}, D_s^{+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, D^{0}, D_s^{+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, D^{0}, D_s^{+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \phi, \Sigma_c^{++}, D_s^{+}, D_s^{+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, D_s^{*+}, D_s^{+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, D_s^{*+}, D_s^{+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Xi^0, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Xi^0, \Sigma^{+}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Xi^0, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Xi^0, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \phi, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^{+}, \Lambda, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^{+}, \Lambda, \Sigma^{+}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^{+}, \Lambda, \Sigma^{+}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^{+}, \Lambda, \Sigma^{+}, D_s^{+} ) ], \end{aligned} $

      $\tag{B5} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}_{s}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, D^{0}, D_s^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, D^{0}, D_s^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, D^{*0}, D_s^{*+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, D^{*0}, D_s^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \phi, \Sigma_c^{++}, D_s^{*+}, D_s^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, D_s^{+}, D_s^{*+}, \Sigma^{+}) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, D_s^{+}, D_s^{*+}, \Sigma^{+}) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Xi^0, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Xi^0, \Sigma^{+}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Xi^0, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Xi^0, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \phi, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, \Sigma^{+}, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^{+}, \Lambda, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^{+}, \Lambda, \Sigma^{+}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^{+}, \Lambda, \Sigma^{+}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^{+}, \Sigma^{0}, \Sigma^{+}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^{+}, \Lambda, \Sigma^{+}, D_s^{*+} ) ], \end{aligned} $

      $\tag{B6} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow p D^{+}) = &\;{\rm i} [ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^+, D^{*0}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^+, D^{*0}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^+, D^{0}, D^{+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^+, D^{0}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \rho^0, \Sigma_c^{++}, D^{+}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \omega, \Sigma_c^{++}, D^{+}, D^{+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^0, \Sigma_c^{++}, D^{*+}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, D^{*+}, D^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, D^{*+}, D^{+}, p )\\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^+, n, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^+, n, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^+, n, p, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^+, n, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \rho^0, \Sigma_c^{++}, p, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \pi^0, \Sigma_c^{++}, p, p, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, p, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, p, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Sigma^0, p, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Lambda, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Sigma^0, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Lambda, p, D^+ )\\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Sigma^0, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Lambda, p, D^+ ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Sigma^0, p, D^+ ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Lambda, p, D^+ ) ], \end{aligned} $

      $\tag{B7} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow p D^{*+}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^+, D^{0}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^+, D^{0}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^+, D^{*0}, D^{*+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^+, D^{*0}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \rho^0, \Sigma_c^{++}, D^{*+}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \omega, \Sigma_c^{++}, D^{*+}, D^{*+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^0, \Sigma_c^{++}, D^{+}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, D^{+}, D^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, D^{+}, D^{*+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \pi^+, \Lambda_c^+, n, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^+, \Sigma_c^+, n, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^+, \Lambda_c^+, n, p, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \rho^+, \Sigma_c^+, n, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \rho^0, \Sigma_c^{++}, p, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \pi^0, \Sigma_c^{++}, p, p, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, \eta_1, \Sigma_c^{++}, p, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, \eta_8, \Sigma_c^{++}, p, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Sigma^0, p, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^+, \Lambda, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Sigma^0, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Xi_c^{\prime +}, \Lambda, p, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Sigma^0, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^{\prime +}, \Lambda, p, D^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Sigma^0, p, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Xi_c^+, \Lambda, p, D^{*+} ) ], \end{aligned} $

      $\tag{B8} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow p D^{+}_{s}) = &\;{\rm i} [ {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, D^{*0}, D_s^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, D^{*0}, D_s^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, D^{0}, D_s^{+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, D^{0}, D_s^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, \Sigma^0, p, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, \Lambda, p, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, \Sigma^0, p, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, \Lambda, p, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, \Sigma^0, p, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, \Lambda, p, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, \Sigma^0, p, D_s^{+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, \Lambda, p, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^0, \Sigma_c^{++}, D^{*+}, D_s^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^{*0}, \Sigma_c^{++}, D^{+}, D_s^{+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^0, \Sigma_c^{++}, \Sigma^+, p, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*0}, \Sigma_c^{++}, \Sigma^+, p, D_s^{+} ) ], \end{aligned} $

      $\tag{B9} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{++}\rightarrow p D^{*+}_{s} ) = &\;{\rm i} [ {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, D^{0}, D_s^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, D^{0}, D_s^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, D^{*0}, D_s^{*+}, p ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, D^{*0}, D_s^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, \Sigma^0, p, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Lambda_c^+, \Lambda, p, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, \Sigma^0, p, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^+, \Sigma_c^+, \Lambda, p, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, \Sigma^0, p, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Lambda_c^+, \Lambda, p, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, \Sigma^0, p, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{++}, K^{*+}, \Sigma_c^+, \Lambda, p, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^0, \Sigma_c^{++}, D^{+}, D_s^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^{*0}, \Sigma_c^{++}, D^{*+}, D_s^{*+}, p ) + {\cal M}(\Xi_{cc}^{++}, K^0, \Sigma_c^{++}, \Sigma^+, p, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{++}, K^{*0}, \Sigma_c^{++}, \Sigma^+, p, D_s^{*+} ) ], \end{aligned} $

      $\tag{B10} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, D^{*0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, D^{0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Sigma^{0}, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Sigma^{0}, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0}, D^{0}, D^{+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Sigma^{0}, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Sigma^{0}, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, D_{s}^{*+}, D^{+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, D_{s}^{+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, D_{s}^{*+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, D_{s}^{+}, D^{+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, n, \Sigma^{0}, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, n, \Sigma^{0}, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, n, \Sigma^{0}, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, n, \Sigma^{0}, D^{+} ) ], \end{aligned} $

      $\tag{B11} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Lambda D^{+}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, D^{*0}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, D^{0}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Lambda, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Lambda, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, D_{s}^{*+}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, D_{s}^{+}, D^{+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, D_{s}^{*+}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, D_{s}^{+}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, n, \Lambda, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, n, \Lambda, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, n, \Lambda, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, n, \Lambda, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0}, D^{0}, D^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Lambda, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Lambda, D^{+} ) ], \end{aligned} $

      $\tag{B12} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+} ) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, D^{0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, D^{*0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Sigma^{0}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, D_{s}^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, D_{s}^{*+}, D^{*+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, D_{s}^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, D_{s}^{*+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, n, \Sigma^{0}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, n, \Sigma^{0}, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, n, \Sigma^{0}, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, n, \Sigma^{0}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Sigma^{0}, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Sigma^{0}, D^{*+} ) ], \end{aligned} $

      $\tag{B13} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) = & \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, D^{0}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, D^{*0}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Lambda, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{ 0}, \Sigma^{-}, \Lambda, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, D_{s}^{+}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, D_{s}^{*+}, D^{*+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, D_{s}^{+}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, D_{s}^{*+}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{+}, n, \Lambda, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{+}, n, \Lambda, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{+}, n, \Lambda, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{+}, n, \Lambda, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{0}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Lambda, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Xi_c^{\prime 0},\Sigma^{-}, \Lambda, D^{*+} ) ], \end{aligned} $

      $\tag{B14} \begin{aligned}[b] {\cal A}( \Xi_{cc}^{+}\rightarrow\Lambda D_{s}^{+} ) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, D^{*0}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, D^{0}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Xi^{-}, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Xi^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, D_s^{+}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, D_s^{+}, D_s^{+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D_s^{*+}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, D_s^{*+}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D_s^{*+}, D_s^{+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, D_s^{*+}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^+, \Sigma_{c}^{0}, \Sigma^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_{c}^{0}, \Sigma^{-}, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Lambda_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Sigma_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{0}, D_s^{+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0},\Xi^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0},\Xi^{-}, \Lambda, D_s^{+} ) ], \end{aligned} $

      $\tag{B15} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{+}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, D^{*0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, D^{0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Xi^{-}, \Sigma^{0}, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Xi^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, D_s^{+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, D_s^{+}, D_s^{+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D_s^{*+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, D_s^{*+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D_s^{*+}, D_s^{+}, \Sigma^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, D_s^{*+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^+, \Sigma_{c}^{0}, \Sigma^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_{c}^{0}, \Sigma^{-}, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Lambda_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Sigma_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{0}, D_s^{+}, \Sigma^{0} ) \\ & + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0},\Xi^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0},\Xi^{-}, \Sigma^{0}, D_s^{+} ) ], \end{aligned} $

      $\tag{B16} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{*+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, D^{0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, D^{*0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, D_s^{*+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, D_s^{*+}, D_s^{*+}, \Sigma^{0} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D_s^{+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, D_s^{+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D_s^{+}, D_s^{*+}, \Sigma^{0} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, D_s^{+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^+, \Sigma_{c}^{0}, \Sigma^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_{c}^{0}, \Sigma^{-}, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Lambda_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Sigma_{c}^{+}, \Lambda, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) \\ & + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{*+}, \Sigma^{0} ) \\ & + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) ], \end{aligned} $

      $\tag{B17} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Lambda D_{s}^{*+}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, D^{0}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, D^{*0}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Xi^{-}, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Xi^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, D_s^{*+}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, D_s^{*+}, D_s^{*+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D_s^{+}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, D_s^{+}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D_s^{+}, D_s^{*+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, D_s^{+}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \phi, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^+, \Sigma_{c}^{0}, \Sigma^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_{c}^{0}, \Sigma^{-}, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Lambda_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^0, \Sigma_{c}^{+}, \Sigma^{0}, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_{c}^{+}, \Lambda, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{0}, D_s^{*+}, \Lambda ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{*+}, \Lambda ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{*+} ) ], \end{aligned} $

      $\tag{B18} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow n D_{s}^{+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Sigma_c^{0}, D^{*0}, D_s^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Sigma_c^{0}, D^{0}, D_s^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Sigma_c^{0}, \Sigma^{-}, n, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Sigma_c^{0}, \Sigma^{-}, n, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, D^{*+}, D_s^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, D^{*+}, D_s^{+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, D^{+}, D_s^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, D^{+}, D_s^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, \Sigma^{0}, n, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, \Lambda, n, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, \Sigma^{0}, n, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, \Lambda, n, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, \Sigma^{0}, n, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, \Lambda, n, D_s^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, \Sigma^{0}, n, D_s^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, \Lambda, n, D_s^{+} ) ], \end{aligned} $

      $\tag{B19} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow n D_{s}^{*+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Sigma_c^{0}, D^{0}, D_s^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Sigma_c^{0}, D^{*0}, D_s^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Sigma_c^{0}, \Sigma^{-}, n, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Sigma_c^{0}, \Sigma^{-}, n, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, D^{+}, D_s^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, D^{+}, D_s^{*+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, D^{*+}, D_s^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, D^{*+}, D_s^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, \Sigma^{0}, n, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{0}, \Lambda_{c}^{+}, \Lambda, n, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, \Sigma^{0}, n, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{0}, \Sigma_c^{+}, \Lambda, n, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, \Sigma^{0}, n, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Lambda_{c}^{+}, \Lambda, n, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, \Sigma^{0}, n, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*0}, \Sigma_c^{+}, \Lambda, n, D_s^{*+} ) ], \end{aligned} $

      $\tag{B20} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow n D^{+}) =& {\rm i}\; [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Sigma_c^{ 0}, D^{*0}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Sigma_c^{ 0}, D^{0}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Lambda_{c}^{+}, D^{+}, D^{+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Sigma_c^{ +}, D^{+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, D^{+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_c^{ +}, D^{+}, D^{+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_{c}^{+}, D^{*+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, D^{*+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D^{*+}, D^{+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D^{*+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, D^{*+}, D^{+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, D^{*+}, D^{+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Lambda_{c}^{+}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Sigma_c^{ +}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_{c}^{+}, n, n, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, n, n, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, n, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^+, \Xi_c^{ 0}, \Sigma^-, n, D^{+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Sigma^-, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^+, \Xi_c^{\prime 0}, \Sigma^-, n, D^{+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Sigma^-, n, D^{+} ) ], \end{aligned} $

      $\tag{B21} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow n D^{*+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Sigma_c^{ 0}, D^{0}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \rho^{+}, \Sigma_c^{ 0}, D^{*0}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Lambda_{c}^{+}, D^{*+}, D^{*+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Sigma_c^{ +}, D^{*+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Lambda_{c}^{+}, D^{*+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \omega, \Sigma_c^{ +}, D^{*+}, D^{*+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_{c}^{+}, D^{+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, D^{+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, D^{+}, D^{*+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, D^{+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, D^{+}, D^{*+}, n ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, D^{+}, D^{*+}, n ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Lambda_{c}^{+}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^{0}, \Sigma_c^{ +}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_{c}^{+}, n, n, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_{c}^{+}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_{c}^{+}, n, n, D^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, n, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^+, \Xi_c^{ 0}, \Sigma^-, n, D^{*+} )\\ &+ {\cal M}(\Xi_{cc}^{+}, K^+, \Xi_c^{\prime 0}, \Sigma^-, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Sigma^-, n, D^{*+} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Sigma^-, n, D^{*+} ) ], \end{aligned} $

      $\tag{B22} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow p D^{0}) = & \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Lambda, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Sigma^{0}, p, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Lambda, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Lambda, p, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Lambda, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Sigma_c^{ 0}, n, p, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_c^{ 0}, n, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_c^{ +}, p, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, p, p, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, p, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, p, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_c^{ +}, p, p, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_c^{ +}, p, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_c^{ +}, p, p, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_c^{ +}, p, p, D^{0} ) ], \end{aligned} $

      $\tag{B23} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow p D^{*0}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{ 0}, \Lambda, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Sigma^{0}, p, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Lambda, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{ 0}, \Lambda, p, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Lambda, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Sigma_c^{ 0}, n, p, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^+, \Sigma_c^{ 0}, n, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Sigma_c^{ +}, p, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Sigma_c^{ +}, p, p, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \eta_1, \Sigma_c^{ +}, p, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Sigma_c^{ +}, p, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^0, \Lambda_c^{ +}, p, p, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{0}, \Lambda_c^{ +}, p, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_1, \Lambda_c^{ +}, p, p, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \eta_8, \Lambda_c^{ +}, p, p, D^{*0} ) ], \end{aligned} $

      $\tag{B24} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{+} D^{0}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{0}, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Lambda, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Sigma^{0}, \Sigma^{ +}, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Lambda, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Sigma^{0}, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Lambda, \Sigma^{ +}, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Sigma^{0}, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Lambda, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, p, \Sigma^{ +}, D^{0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, p, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, p, \Sigma^{ +}, D^{0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, p, \Sigma^{ +}, D^{0} ) ], \end{aligned} $

      $\tag{B25} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Sigma^{+} D^{*0}) =& \;{\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Sigma^{0}, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Lambda, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Sigma^{0}, \Sigma^{ +}, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Lambda, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Sigma^{0}, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Lambda, \Sigma^{ +}, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Sigma^{0}, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Lambda, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, p, \Sigma^{ +}, D^{*0} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, p, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, p, \Sigma^{ +}, D^{*0} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, p, \Sigma^{ +}, D^{*0} ) ], \end{aligned} $

      $\tag{B26} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Xi^{-}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Xi^{-}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^+ ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, \Lambda, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, \Lambda, \Xi^{0}, D_s^+ ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Xi^{-}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^+ ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, \Lambda, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^+ ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, \Lambda, \Xi^{0}, D_s^+ ) ], \end{aligned} $

      $\tag{B27} \begin{aligned}[b] {\cal A}(\Xi_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{*+}) =&\; {\rm i} [ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{ 0}, \Xi^{-}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{ 0}, \Xi^{-}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Sigma_c^{ +}, \Lambda, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Sigma_c^{ +}, \Lambda, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Xi^{-}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Xi_{cc}^{+}, \bar K^{0}, \Lambda_c^{ +}, \Lambda, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, \Sigma^{0}, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Xi_{cc}^{+}, \bar K^{*0}, \Lambda_c^{ +}, \Lambda, \Xi^{0}, D_s^{*+} )], \end{aligned} $

      $\tag{B28} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Omega_{c}^{0}, D^{*0}, D^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Omega_{c}^{0}, D^{0}, D^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Omega_{c}^{0}, \Xi^-, \Xi^{0}, D^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Omega_{c}^{0}, \Xi^-, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, \Sigma^{ 0}, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, \Lambda, \Xi^{0}, D^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, \Sigma^{ 0}, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, \Lambda, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, \Sigma^{ 0}, \Xi^{0}, D^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, \Lambda, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, \Sigma^{ 0}, \Xi^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, \Lambda, \Xi^{0}, D^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, D_s^{*+}, D^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, D_s^{*+}, D^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, D_s^{+}, D^{+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, D_s^{+}, D^{+}, \Xi^{0} ) ], \end{aligned} $

      $\tag{B29} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{*+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Omega_{c}^{0}, D^{0}, D^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Omega_{c}^{0}, D^{*0}, D^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Omega_{c}^{0}, \Xi^-, \Xi^{0}, D^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Omega_{c}^{0}, \Xi^-, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, \Sigma^{ 0}, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, \Lambda, \Xi^{0}, D^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, \Sigma^{ 0}, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, \Lambda, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, \Sigma^{ 0}, \Xi^{0}, D^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, \Lambda, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, \Sigma^{ 0}, \Xi^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, \Lambda, \Xi^{0}, D^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{ +}, D_s^{+}, D^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{0}, \Xi_c^{\prime +}, D_s^{+}, D^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{ +}, D_s^{*+}, D^{*+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \bar K^{*0},\Xi_c^{\prime +}, D_s^{*+}, D^{*+}, \Xi^{0} ) ], \end{aligned} $

      $\tag{B30} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{+}) =& \;{\rm i}[ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Omega_{c}^{0}, D^{*0}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, D^{0}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^+, D_s^{+}, D_s^{+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^{\prime +}, D_s^{+}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{ +}, D_s^{*+}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{\prime +}, D_s^{*+}, D_s^{+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{ +}, D_s^{*+}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{\prime +}, D_s^{*+}, D_s^{+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_c^0, \Xi^-, \Xi^{0}, D_s^{+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^0, \Xi^-, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_c^{\prime 0}, \Xi^-, \Xi^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Xi^-, \Xi^{0}, D_s^{+} ) ], \end{aligned} $

      $\tag{B31} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D_{s}^{*+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Omega_{c}^{0}, D^{0}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, D^{*0}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^+, D_s^{*+}, D_s^{*+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^{\prime +}, D_s^{*+}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{ +}, D_s^{+}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{\prime +}, D_s^{+}, D_s^{*+}, \Xi^{0} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{ +}, D_s^{+}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{\prime +}, D_s^{+}, D_s^{*+}, \Xi^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^+, \Xi^0, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_c^{\prime +}, \Xi^0, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_c^0, \Xi^-, \Xi^{0}, D_s^{*+} ) \\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^0, \Xi^-, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_c^{\prime 0}, \Xi^-, \Xi^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, \Xi^-, \Xi^{0}, D_s^{*+} ) ], \end{aligned} $

      $\tag{B32} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{+}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, D^{*0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, D^{0}, D_s^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{0}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, \Xi^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, \Xi^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, \Xi^{0}, \Sigma^{0}, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, \Xi^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, \Xi^{0}, \Sigma^{0}, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, \Xi^{0}, \Sigma^{0}, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, D^{*+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, D^{*+}, D_s^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, D^{+}, D_s^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, D^{+}, D_s^{+}, \Sigma^{0} ) ], \end{aligned} $

      $\tag{B33} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Lambda D_{s}^{+}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, D^{*0}, D_s^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, D^{0}, D_s^{+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{0}, D_s^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, \Xi^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, \Xi^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, \Xi^{0}, \Lambda, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, \Xi^{0}, \Lambda, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, \Xi^{0}, \Lambda, D_s^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, \Xi^{0}, \Lambda, D_s^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, D^{*+}, D_s^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, D^{*+}, D_s^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, D^{+}, D_s^{+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, D^{+}, D_s^{+}, \Lambda ) ], \end{aligned} $

      $\tag{B34} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D_{s}^{*+}) = & \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, D^{0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, D^{*0}, D_s^{*+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, \Xi^{0}, \Sigma^{0}, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, \Xi^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, \Xi^{0}, \Sigma^{0}, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, \Xi^{0}, \Sigma^{0}, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, D^{+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, D^{+}, D_s^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, D^{*+}, D_s^{*+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, D^{*+}, D_s^{*+}, \Sigma^{0} ) ], \end{aligned} $

      $\tag{B35} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Lambda D_{s}^{*+}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, D^{0}, D_s^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, D^{0}, D_s^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, D^{*0}, D_s^{*+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, D^{*0}, D_s^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^0, \Xi^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^0, \Xi^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_c^{\prime 0}, \Xi^{-}, \Lambda, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, \Xi^{0}, \Lambda, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, \Xi^{0}, \Lambda, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, \Xi^{0}, \Lambda, D_s^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, \Xi^{0}, \Lambda, D_s^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^+, D^{+}, D_s^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_c^{\prime +}, D^{+}, D_s^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^+, D^{*+}, D_s^{*+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_c^{\prime +}, D^{*+}, D_s^{*+}, \Lambda ) ], \end{aligned} $

      $\tag{B36} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{+}) = &\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, D^{*0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, D^{*0}, D^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, \Sigma^-, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{\prime 0}, \Sigma^-, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^-, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^-, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, D^{+}, D^{+}, \Sigma^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, D^{+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, D^{*+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, D^{*+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, D^{*+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, D^{+}, D^{+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, D^{+}, D^{+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, \Lambda, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, \Lambda, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, \Lambda, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, \Lambda, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^+, \Omega_{c}^{0}, \Xi^-, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^-, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{+} ) ], \end{aligned} $

      $\tag{B37} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Lambda D^{+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, D^{*0}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, D^{*0}, D^{+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, D^{*0}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, \Sigma^-, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{\prime 0}, \Sigma^-, \Lambda, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^-, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^-, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, D^{+}, D^{+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, D^{+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, D^{*+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, D^{*+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, D^{*+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, D^{*+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, D^{+}, D^{+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, D^{+}, D^{+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, \Lambda, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, \Lambda, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, \Lambda, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, \Lambda, \Lambda, D^{+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^+, \Omega_{c}^{0}, \Xi^-, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^-, \Lambda, D^{+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{+} ) ], \end{aligned} $

      $\tag{B38} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, D^{0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, D^{*0}, D^{*+}, \Sigma^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, D^{*0}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, \Sigma^-, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{\prime 0}, \Sigma^-, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^-, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^-, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, D^{*+}, D^{*+}, \Sigma^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, D^{*+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, D^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Sigma^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, D^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, D^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Sigma^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, D^{*+}, D^{*+}, \Sigma^{0} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, D^{*+}, D^{*+}, \Sigma^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, \Lambda, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, \Lambda, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, \Lambda, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, \Lambda, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^+, \Omega_{c}^{0}, \Xi^-, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^-, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Sigma^{0}, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Sigma^{0}, D^{*+} ) ], \end{aligned} $

      $\tag{B39} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Lambda D^{*+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, D^{0}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_c^{\prime 0}, D^{0}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, D^{*0}, D^{*+}, \Lambda )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_c^{\prime 0}, D^{*0}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{0}, \Sigma^-, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{+}, \Xi_{c}^{\prime 0}, \Sigma^-, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^-, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^-, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, D^{*+}, D^{*+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, D^{*+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, D^{+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, D^{+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, D^{+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, D^{+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, D^{*+}, D^{*+}, \Lambda ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, D^{*+}, D^{*+}, \Lambda )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{+}, \Lambda, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \rho^0, \Xi_{c}^{\prime +}, \Lambda, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \omega, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{+}, \Lambda, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \pi^{0}, \Xi_{c}^{\prime +}, \Lambda, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^+, \Omega_{c}^{0}, \Xi^-, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^-, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{0}, \Lambda, D^{*+} )\\ & + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime +}, \Sigma^{0}, \Lambda, D^{*+} ) ], \end{aligned} $

      $\tag{B40} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{+} D^{0}) = &\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Omega_{c}^{0}, \Xi^{0}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^{0}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{0}, \Sigma^{0}, \Sigma^{+}, D^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{\prime 0}, \Sigma^{0}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{0}, \Lambda, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{\prime 0}, \Lambda, \Sigma^{+}, D^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^{0}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^{0}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Lambda, \Sigma^{+}, D^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Lambda, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{0} )\\ & + {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{0} ) ], \end{aligned} $

      $\tag{B41} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow\Sigma^{+} D^{*0}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Omega_{c}^{0}, \Xi^{0}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Omega_{c}^{0}, \Xi^{0}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{0}, \Sigma^{0}, \Sigma^{+}, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{\prime 0}, \Sigma^{0}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{0}, \Lambda, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \pi^+, \Xi_{c}^{\prime 0}, \Lambda, \Sigma^{+}, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Sigma^{0}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Sigma^{0}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{0}, \Lambda, \Sigma^{+}, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \rho^+, \Xi_{c}^{\prime 0}, \Lambda, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{+}, \Sigma^{+}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \phi, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, \eta_1, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, \eta_8, \Xi_{c}^{\prime 0}, \Sigma^{+}, \Sigma^{+}, D^{*0} ) ], \end{aligned} $

      $\tag{B42} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow p D^{0}) =& {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Lambda, p, D^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Lambda, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Sigma^{0}, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Sigma^{0}, p, D^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Lambda, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Lambda, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Sigma^{+}, p, D^{0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Sigma^{+}, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Sigma^{+}, p, D^{0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Sigma^{+}, p, D^{0} ) ], \end{aligned} $

      $\tag{B43} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow p D^{*0}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Lambda, p, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Lambda, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Sigma^{0}, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Sigma^{0}, p, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Lambda, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Lambda, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Sigma^{+}, p, D^{*0} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Sigma^{+}, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Sigma^{+}, p, D^{*0} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Sigma^{+}, p, D^{*0} ) ], \end{aligned} $

      $\tag{B44} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow n D^{+}) =&\; {\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Lambda, n, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Lambda, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{+} ) ], \end{aligned} $

      $\tag{B45} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow n D^{*+}) =& \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Lambda, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Lambda, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{*+} ) ], \end{aligned} $

      $\tag{B46} \begin{aligned}[b] {\cal A}(\Omega_{cc}^{+}\rightarrow n D^{*+}) = & \;{\rm i} [ {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{0}, \Sigma^{-}, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*+}, \Xi_{c}^{\prime 0}, \Sigma^{-}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{+}, \Lambda, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Sigma^{0}, n, D^{*+} )\\ &+ {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{+}, \Lambda, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Sigma^{0}, n, D^{*+} ) + {\cal M}(\Omega_{cc}^{+}, K^{*0}, \Xi_{c}^{\prime +}, \Lambda, n, D^{*+} ) ]. \end{aligned} $

    APPENDIX C.   STRONG COUPLING CONSTANTS
    • In this section we list all the strong coupling constants used in our calculation. Some of these values are taken from Refs. [35, 41-47]. For those that can not be found directly in the literatures, we calculate them under the assumption of $ SU(3)_F $ symmetry.

      According to which $ SU(3)_F $ multiplets do the particles belong to, the vertices in this paper can be divided into $ {\cal B}{\cal B}V $ , $ {\cal B}{\cal B}P $ , $ DD^*P $ , $ DDV $ , $ D^*D^*V $ , $ {\cal B}_c{\cal B} D $ and $ {\cal B}_c {\cal B} D^* $ . P denotes a light pseudoscalar meson, V represents a light vector meson, and $ {\cal B}_c $ is a singly charmed baryon. With these label-definitions one can know the meaning of our symbols for each vertices whose coupling constants are collected in Tables 5, 6, 7, 8.

      vertex $ f_{1} $ $ f_{2} $ vertex $ f_{1} $ $ f_{2} $ vertex $ f_{1} $ $ f_{2} $
      $ p\rightarrow\ n\rho^{+} $ −2.40 32.95 $ \Lambda\rightarrow\Sigma^{-}\rho^{+} $ 2.00 12.30 $ \Sigma^{0}\rightarrow\Sigma^{+}\rho^{+} $ 7.20 −25.00
      $ \Sigma^{+}\rightarrow\Lambda\rho^{+} $ 2.00 12.30 $ \Sigma^{+}\rightarrow p\overline{K}^{*0} $ 5.66 −1.70 $ \Sigma^{+}\rightarrow\Xi^{0}K^{*+} $ −2.26 37.05
      $ \Sigma^{+}\rightarrow\Sigma^{+}\phi $ −6.00 2.50 $ p\rightarrow\Sigma^{0}K^{*+} $ 4.00 −1.20 $ p\rightarrow\Lambda K^{*+} $ 5.10 −28.00
      $ p\rightarrow\Sigma^{+}K^{*0} $ 5.66 −1.70 $ \Sigma^{0}\rightarrow\Sigma^{-}\rho^{+} $ −7.20 25.00 $ \Sigma^{0}\rightarrow n\overline{K}^{*0} $ −4.00 1.20
      $ \Lambda\rightarrow n\overline{K}^{*0} $ 5.10 −28.00 $ \Sigma^{0}\rightarrow\Xi^{-}K^{*+} $ −1.60 26.20 $ \Sigma^{0}\rightarrow\Sigma^{0}\phi $ −6.00 2.50
      $ \Sigma^{0}\rightarrow\Sigma^{0}\omega $ 4.30 −1.10 $ \Lambda\rightarrow\Sigma^{0}\rho^{0} $ 1.90 11.90 $ p\rightarrow p\rho^{0} $ −2.50 22.20
      $ \Lambda\rightarrow\Xi^{0}K^{*0} $ −6.00 17.10 $ \Lambda\rightarrow\Xi^{-}K^{*+} $ −6.00 17.10 $ \Lambda\rightarrow\Lambda\phi $ −5.30 24.60
      $ n\rightarrow\Sigma^{0}K^{*0} $ −4.00 1.20 $ \Lambda\rightarrow\Lambda\omega $ −7.10 8.70 $ n\rightarrow\Sigma^{-}K^{*+} $ 5.66 −1.70
      $ n\rightarrow\Lambda K^{*0} $ 5.10 −28.00 $ \Xi^{-}\rightarrow\Sigma^{+}\overline{K}^{*0} $ −2.26 37.05 $ n\rightarrow n\rho^{0} $ 2.50 −22.20
      $ \Xi^{0}\rightarrow\Lambda\overline{K}^{*0} $ 4.45 −27.54 $ \Xi^{0}\rightarrow\Xi^{-}\rho^{+} $ 6.08 −1.56 $ \Xi^{0}\rightarrow\Sigma^{0}\overline{K}^{*0} $ 1.60 −26.20
      $ \Xi^{0}\rightarrow\Xi^{0}\phi $ −9.50 32.30 $ \Sigma^{0}\rightarrow\Xi^{0}K^{*0} $ 1.60 −26.20

      Table 5.  Strong coupling constants of $ {\cal B}{\cal B}V $ vertices.

      vertex g vertex g vertex g
      $ p\rightarrow n\pi^{+} $ 21.20 $ \Lambda\rightarrow\Sigma^{-}\pi^{+} $ 10.00 $ \Sigma^{0}\rightarrow\Sigma^{+}\pi^{+} $ −10.70
      $ \Sigma^{+}\rightarrow\Lambda\pi^{+} $ 10.00 $ \Sigma^{+}\rightarrow p\overline{K}^{0} $ 5.75 $ \Sigma^{+}\rightarrow\Xi^{0}K^{+} $ 19.80
      $ p\rightarrow\Sigma^{0}K^{+} $ 4.25 $ p\rightarrow\Lambda K^{+} $ −13.50 $ p\rightarrow\Sigma^{+} K^{0} $ 5.75
      $ \Sigma^{-}\rightarrow\Sigma^{0}\pi^{+} $ 10.70 $ \Sigma^{0}\rightarrow n\overline{K}^{0} $ −4.25 $ \Xi^{-}\rightarrow\Sigma^{+}\overline{K}^{0} $ 19.80
      $ \Sigma^{0}\rightarrow\Xi^{-}K^{+} $ 14.00 $ \Lambda\rightarrow\Xi^{-}K^{+} $ 4.25 $ \Lambda\rightarrow n\overline{K}^{0} $ −13.50
      $ p\rightarrow p\eta_8 $ 4.25 $ n\rightarrow\Sigma^{-} K^{+} $ 4.70 $ p\rightarrow p\pi^{0} $ 14.90
      $ p\rightarrow p\eta_1 $ 14.14 $ n\rightarrow n\pi^{0} $ −14.90 $ n\rightarrow\Sigma^{0} K^{0} $ −4.25
      $ n\rightarrow\Lambda K^{0} $ −13.50 $ \Xi^{0}\rightarrow\Sigma^{0}\overline{K}^{0} $ −14.00 $ n\rightarrow n\eta_8 $ 4.25
      $ \Xi^{0}\rightarrow\Xi^{-}\pi^{+} $ 4.70 $ \Lambda\rightarrow\Xi^{0}K^{0} $ 4.25 $ n\rightarrow n\eta_1 $ 14.14
      $ \Sigma^{0}\rightarrow\Xi^{0}K^{0} $ −14.00 $ \Sigma^{0}\rightarrow\Sigma^{0}\eta_8 $ 10.00 $ \Xi^{0}\rightarrow\Lambda\overline{K}^{0} $ 4.25
      $ \Lambda\rightarrow\Sigma^{0}\pi^{0} $ 10.00 $ \Sigma^{0}\rightarrow\Sigma^{0}\eta_1 $ 14.14 $ \Xi^{0}\rightarrow\Xi^{0}\eta_8 $ −13.50
      $ \Lambda\rightarrow\Lambda\eta_8 $ −10.00 $ \Sigma^{+}\rightarrow\Sigma^{+}\eta_8 $ 10.00 $ \Xi^{0}\rightarrow\Xi^{0}\eta_1 $ 14.14
      $ \Lambda\rightarrow\Lambda\eta_1 $ −14.14 $ \Sigma^{+}\rightarrow\Sigma^{+}\eta_1 $ 14.14

      Table 6.  Strong coupling constants of $ {\cal B}{\cal B}P $ vertices.

      vertex g vertex g vertex g f
      $ {D}^{*}\rightarrow D\pi $ 17.90 $ D\rightarrow D\rho $ 3.69 $ {D}^{*}\rightarrow{D}^{*}\rho $ 3.69 4.61

      Table 7.  Strong coupling constants of $ D D^{*}P $ , $ D DV $ and $ D^{*} D^{*}V $ vertices.

      vertex g vertex g f
      $ \Lambda_{c}\rightarrow N{D}_{q} $ 4.82 $ \Lambda_{c}\rightarrow N{D}_{q}^{*} $ -5.80 3.60
      $ \Sigma_{c}\rightarrow N{D}_{q} $ 3.78 $ \Sigma_{c}\rightarrow N{D}_{q}^{*} $ 11.21 4.64

      Table 8.  Strong coupling constants of $ {\cal B}_{c}{\cal B}D $ and $ {\cal B}_{c}{\cal B}{ D}^{*} $ vertices.

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