D-wave excited ${\boldsymbol{ cs}\bar{\boldsymbol c}\bar{\boldsymbol s}} $ tetraquark states with ${ \boldsymbol{J^{PC}}=\bf 1^{\bf ++}} $ and ${\bf 1^{\bf +-}} $

$ \begin{aligned}[b]& (\mathbf{3}\otimes\mathbf{3})_{[cs]}\otimes(\bar{\mathbf{3}}\otimes\bar{\mathbf{3}})_{[\bar{c}\bar{s}]}\\=&(\mathbf{6}\oplus\bar{\mathbf{3}})_{[cs]}\otimes(\mathbf{3}\oplus\bar{\mathbf{6}})_{[\bar{c}\bar{s}]}\\ =&(\mathbf{6}\otimes\bar{\mathbf{6}})\oplus(\bar{\mathbf{3}}\otimes\mathbf{3})\oplus(\mathbf{6}\otimes\mathbf{3})\oplus(\bar{\mathbf{3}}\otimes\bar{\mathbf{6}})\\ =&(\mathbf{1}\oplus\mathbf{8}\oplus\mathbf{27})\oplus(\mathbf{1}\oplus\mathbf{8})\oplus(\mathbf{8}\oplus{\mathbf{10}})\oplus(\mathbf{8}\oplus\overline{\mathbf{10}})\, , \end{aligned} $

$ \begin{align} \mathcal{O}_{P,\,\mu}=c^T_{a}\mathbb{C}\gamma_{5}D_{\mu}s_{b}\, , \end{align} $

$ \begin{align} \mathcal{O}_{D,\,\mu\nu}=c^T_{a}\mathbb{C}\gamma_{5}D_{\mu}D_{\nu}s_{b}\, , \end{align} $

$ \begin{aligned}[b] \bar{\mathcal{O}}_S=&\bar{c}_{a}\mathbb{C}\gamma_5\bar{s}^T_{b},\\ \bar{\mathcal{O}}_{P,\, \mu}=&\bar{c}_{a}\mathbb{C}\gamma_5 D_\mu \bar{s}^T_{b},\\ \bar{\mathcal{O}}_{D,\, \mu\nu}=&\bar{c}_{a}\mathbb{C}\gamma_5 D_\mu D_\nu\bar{s}^T_{b}. \end{aligned} $

$ \begin{aligned} L_\lambda=0&:\qquad \mathcal{O}_S\bar{\mathcal{O}}_S,\\ L_\lambda=1&:\qquad \mathcal{O}_SD_{\mu}\bar{\mathcal{O}}_S,\\ L_\lambda=2&:\qquad \mathcal{O}_SD_\mu D_\nu\bar{\mathcal{O}}_S.\\ \end{aligned} $

$\begin{aligned}[b]\\[-5pt] J_{1,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\{D_\mu,D_\nu\}\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\{D_\mu,D_\nu\}\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{1,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\{D_\mu,D_\nu\}\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\{D_\mu,D_\nu\}\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{2,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5D_\mu s_b]\;D_\nu\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\;D_\nu\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right), \\ J_{2,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5D_\mu s_b]\;D_\nu\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\;D_\nu\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right), \\ J_{3,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\;D_\mu\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\;D_\mu\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{3,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\;D_\mu\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\;D_\mu\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{4,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}D_\mu\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{4,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}D_\mu\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{5,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{5,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{6,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_a]\right), \\ J_{6,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_a^T]\right)+[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_a]\right),\\ \end{aligned} $

$ \begin{aligned}[b] J_{7,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\{D_\mu,D_\nu\}\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\{D_\mu,D_\nu\}\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{7,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\{D_\mu,D_\nu\}\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\{D_\mu,D_\nu\}\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{8,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5D_\mu s_b]\;D_\nu\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\;D_\nu\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right), \\ J_{8,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5D_\mu s_b]\;D_\nu\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\;D_\nu\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right), \\ J_{9,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\;D_\mu\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\;D_\mu\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{9,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\;D_\mu\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\;D_\mu\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{10,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}D_\mu\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{10,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}D_\mu\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\nu\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\nu\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\nu s_a]\right), \\ J_{11,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5s_b]-[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{11,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]\left([\bar{c}_a\mathbb{C}\gamma_5\bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5\bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5s_b]+[c_b^T\mathbb{C}\gamma_5s_a]\right),\\ J_{12,\, \mu\nu}^{A}=&[c_a^T\mathbb{C}\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_b^T]-[\bar{c}_b\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]-[c_b^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_a]\right), \\ J_{12,\, \mu\nu}^{S}=&[c_a^T\mathbb{C}\gamma_5s_b]\left([\bar{c}_a\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_b^T]+[\bar{c}_b\mathbb{C}\gamma_5D_\mu\;D_\nu \bar{s}_a^T]\right)-[\bar{c}_a\mathbb{C}\gamma_5\bar{s}^T_b]\left([c_a^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_b]+[c_b^T\mathbb{C}\gamma_5D_\mu\;D_\nu s_a]\right), \end{aligned} $

$ \begin{aligned}[b] \Pi_{\mu\nu,\,\rho\sigma}(q^2)&={\rm i}\int {\rm d}^4x {\rm e}^{{\rm i} q\cdot x}\langle 0|T\left[J_{\mu\nu}(x)J^{\dagger}_{\rho\sigma}(0)\right]|0\rangle\\ &=T^+_{\mu\nu\rho\sigma}\Pi_1(q^2)+\cdots \, , \end{aligned} $

$ \begin{aligned}[b] T^\pm_{\mu\nu\rho\sigma}&=\left(\frac{q_\mu q_\nu}{q^2}\eta_{\nu\sigma}\pm(\mu\leftrightarrow\nu)\right)\pm(\rho\leftrightarrow\sigma),\\ \eta_{\mu\nu}&=\frac{q_{\mu} q_{\nu}}{q^{2}}-g_{\mu \nu}, \end{aligned} $

$ \begin{aligned}[b] \langle0|J_{\mu\nu}(x)|1^{\mathbb{P}\mathbb{C}}(\overrightarrow{\mathbf{p}},r)\rangle&=Z\epsilon^{\mu\nu\alpha\beta}\in_\alpha(\overrightarrow{\mathbf{p}},r)p_\beta,\\ \langle0|J_{\mu\nu}(x)|1^{(-\mathbb{P})\mathbb{C}}(\overrightarrow{\mathbf{p}},r)\rangle&=Z_+(\in^\mu(\overrightarrow{\mathbf{p}},r)p^\nu+\in^\nu(\overrightarrow{\mathbf{p}},r)p^\mu)\\ &+Z_-(\in^\mu(\overrightarrow{\mathbf{p}},r)p^\nu-\in^\nu(\overrightarrow{\mathbf{p}},r)p^\mu), \end{aligned} $

$ \begin{equation} \Pi(q^2)=\frac{1}{\pi}\int^{\infty}_{s_<}\frac{\mathrm{Im}\Pi(s)}{s-q^2-{\rm i}\epsilon}{\rm d}s, \end{equation} $

$ \begin{aligned}[b] \rho(s)\equiv\frac{1}{\pi}\mathrm{Im}\Pi(s)&=\sum_n\delta(s-M^2_n)\langle 0|\eta|n\rangle\langle n|\eta^\dagger|0\rangle\\ &=f^2_X\delta(s-m^2_X)+\mathrm{continuum}, \end{aligned} $

$ \begin{equation} \mathcal{L}_k(s_0,M_{\rm B}^2)=f^2_Xm^{2k}_{H}{\rm e}^{-m^2_H/M_{\rm B}^2}=\int^{s_0}_{4m_c^2}{\rm d} s\,{\rm e}^{-s/M_{\rm B}^2}\rho(s)s^k, \end{equation} $

$ \begin{equation} m_X(s_0,M_{\rm B}^2)=\sqrt{\frac{\mathcal{L}_1(s_0,M_{\rm B}^2)}{\mathcal{L}_0(s_0,M_{\rm B}^2)}}, \end{equation} $

$ \begin{aligned}[b] {\rm i} S_{c}^{a b}(p)=&\frac{{\rm i} \delta^{a b}}{\hat{p}-m_{c}} +\frac{{\rm i}}{4} g_{s} \frac{\lambda_{a b}^{n}}{2} G_{\mu \nu}^{n} \frac{\sigma^{\mu \nu}\left(\hat{p}+m_{c}\right)+\left(\hat{p}+m_{c}\right) \sigma^{\mu \nu}}{12} \\ &+\frac{{\rm i} \delta^{a b}}{12}\langle g_{s}^{2} G G\rangle m_{c} \frac{p^{2}+m_{c} \hat{p}}{(p^{2}-m_{c}^{2})^{4}}\, , \\ {\rm i} S_{s}^{ab}(x)=&\frac{{\rm i}\delta^{ab}}{2\pi^2x^4}\hat{x}-\frac{\delta^{ab}}{12}\langle\bar{s}s\rangle+\frac{{\rm i}}{32\pi^2}\frac{\lambda^n_{ab}}{2}g_sG^n_{\mu\nu}\frac{1}{x^2}(\sigma^{\mu\nu}\hat{x}+\hat{x}\sigma^{\mu\nu})\\ &+\frac{\delta^{ab}x^2}{192}\langle\bar{s}g_s\sigma\cdot Gs\rangle-\frac{m_s\delta^{ab}}{4\pi^2x^2}+\frac{{\rm i}\delta^{ab}m_s\langle\bar{s}s\rangle}{48}\hat{x}\\&-\frac{{\rm i} m_s\langle\bar{s}g_s\sigma\cdot Gs\rangle\delta^{ab}x^2\hat{x}}{1152}\, , \end{aligned} $

$ \begin{aligned}[b] &m_c(m_c)=1.27\pm0.02\;\mathrm{GeV},\\ &m_c/m_s=11.76^{+0.05}_{-0.10} \, , \\ &\langle \bar{q}q\rangle=-(0.24\pm0.03)^3\;\mathrm{GeV}^3,\\ &\langle \bar{q}g_s\sigma\cdot Gq\rangle=-M_0^2\langle \bar{q}q\rangle,\\ &\langle \bar{q}q\bar{q}q\rangle=\langle \bar{q}q\rangle^2\,,\\ &M_0^2=(0.8\pm0.2)\;\mathrm{GeV}^2,\\ &\langle \bar{s}s\rangle/\langle \bar{q}q\rangle=0.8\pm0.1,\\ &\langle g_s^2GG\rangle=(0.48\pm0.14)\;\mathrm{GeV}^4,\\ \end{aligned} $

$ \begin{equation} \mathrm{PC}(s_0,M_{\rm B}^2)=\frac{\mathcal{L}_0(s_0,M_{\rm B}^2)}{\mathcal{L}_0(\infty,M_{\rm B}^2)}, \end{equation} $

$ \begin{equation} m_{J_{5}^A}=5.16_{-0.13}^{+0.12} \; \text{GeV}\,, \end{equation} $

$ \bar{m}_X(s_0)=\sum\limits^N_{i=1}\frac{m_X(s_0,M_{{\rm B},i}^2)}{N}, $

$ \chi^2(s_0)=\sum\limits^N_{i=1}\left[\frac{m_X(s_0,M_{{\rm B},i}^2)}{\bar{m}_X(s_0)}-1\right]^2, $

$ \begin{equation} m_{J_{1}^S}=4.91_{-0.12}^{+0.11} \; \text{GeV}. \end{equation} $

$ \begin{aligned}[b] \rho_{i;A(S)}(s) =& \rho^{\rm pert}_{i;A(S)}(s)+\langle \bar{s}s\rangle\rho^{\langle \bar{s}s\rangle}_{i;A(S)}(s)+m_s\langle\bar{s}s\rangle\rho^{m_s\langle \bar{s}s\rangle}_{i;A(S)}(s)+\langle g_s^2G^2\rangle\rho^{\langle g_s^2G^2\rangle}_{i;A(S)}(s)+\langle \bar{s}\sigma\cdot G s\rangle\rho^{\langle \bar{s}\sigma\cdot G s\rangle}_{i;A(S)}(s)+m_s\langle \bar{s}\sigma\cdot G s\rangle\rho^{m_s\langle \bar{s}\sigma\cdot G s\rangle}_{i;A(S)}(s)\\ & +\langle \bar{s}s \bar{s}s\rangle\rho^{\langle \bar{s}s \bar{s}s\rangle}_{i;A(S)}(s)+\langle \bar{s}s\rangle\langle \bar{s}\sigma\cdot G s\rangle\rho^{\langle \bar{s}s\rangle\langle \bar{s}\sigma\cdot G s\rangle}_{i;A(S)}(s)+\langle g_s^2G^2\rangle\langle \bar{s}s\rangle\rho^{\langle g_s^2G^2\rangle\langle \bar{s}s\rangle}_{i;A(S)}(s)+m_s\langle g_s^2G^2\rangle\langle \bar{s}s\rangle\rho^{m_s\langle g_s^2G^2\rangle\langle \bar{s}s\rangle}_{i;A(S)}(s)\\ & +\langle g_s^2G^2\rangle^2\rho^{\langle g_s^2G^2\rangle^2}_{i;A(S)}(s)+\langle g_s^2G^2\rangle\langle \bar{s}\sigma\cdot G s\rangle\rho^{\langle g_s^2G^2\rangle\langle \bar{s}\sigma\cdot G s\rangle}_{i;A(S)}(s)+m_s\langle g_s^2G^2\rangle\langle \bar{s}\sigma\cdot G s\rangle\rho^{m_s\langle g_s^2G^2\rangle\langle \bar{s}\sigma\cdot G s\rangle}_{i;A(S)}(s). \\\end{aligned} $

$ \begin{aligned}[b]\rho^{\rm pert}_{1,7;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{x}{1612800 \pi ^5 (y-1)^5} F\left(s,x,y\right){}^3 c_1 \left(2 (x-1) \left(10 ((x (5 (13 x-42) x+273)-140) x\right.\right.\\ & \left.\left. +35)y^2-28 \left(39 x^2-45 x+20\right) y-21 x (2 x+5)+\left(10 ((x (2 (x-35) x+189)-140) x+35) y^2+28 (x ((15 x\right.\right.\right.\\ & \left.\left.\left.-74)x+70)-20) y+21 ((23 x-30) x+10)\right) c_p+210\right) x^2 y F\left(s,x,y\right){}^3+42 x \left((x-1) (y-1) \left(10 ((x (5 (13 x\right.\right.\right.\\ & \left.\left.-42) x+273)-140) x+35) y^4-((x (50 x+923)-1165) x+590) y^3+2 ((32 x-165) x+190) y^2+60 (x)\right.\right.\\ & \left.\left. -2) y+10s x+\left(-4 ((x ((59 x-184) x+195)-90) x+15) x y^3+((x (58 (x-3) x+195)-120) x+30) y^2\right.\right.\right.\\& \left.\left.\left.+2 (3 (16 x-45)x+110) x y-60 y+5 (3 x-8) x+30\right) m_c m_s+c_p \left((x-1) (y-1) \left(10 ((x (2 (x-35) x+189)\right.\right.\right.\right.\\& \left.\left.\left.\left.-140) x+35) y^2+((450 x-2183) x+2065) x y-590 y+24 (23 x-30) x+240\right) s x y^2+\left(-4 (x (4 (x-5) x\right.\right.\right.\right.\\ & +35)-15) (x-1) x y^3+(((4 (64-13 x) x-245) x+20) x+30) y^2-2 \left(37 x^3-60 x+30\right) y+55 x^2-80 x\\ & \left.\left.\left.\left.\left.+30\right) m_c m_s\right)\right)\right. F\left(s,x,y\right){}^2+15 (y-1) \left((x-1) (y-1) \left(50 ((x (5 (13 x-42) x+273)-140) x+35) y^4\right.\right.\right.\\ & \left.\left.\left.-14 ((x (10 x+361)-455) x+230) y^3+7 ((79 x-310) x+330) y^2+420 (x-2) y+70\right) s^2 y x^2+14 m_c m_s\right.\right.\\ & \left(\left(-11 ((x ((59 x-184) x+195)\right.\right.-90) x+15) x y^4+((x (2 (96 x-325) x+765)-440) x+105) y^3+(x ((153 x\\ & \left.\left.\left.\left.-485) x+430)-150) y^2+5 ((7 x-12) x+12) y+5 (x-3)\right) s x+\left(6 (4 (2 x ((2 x-5) x+5)-5) x+5) y^2\right.\right.\right.\right.\\ \end{aligned} $

$ \begin{aligned}[b] & \left.\left.\left.\left.+5 (7 (x-4) x+30) x y-60 y+10 (x-3) x+30\right) m_c m_s\right)+c_p \left((x-1) (y-1) \left(50 ((x (2 (x-35) x+189)\right.\right.\right.\right.\\ & \left.-140) x+35) y^2+14 (x ((180 x-851) x+805)-230) y+147 ((23 x-30) x+10)\right) s^2 x^2 y^3+7 m_c m_s \left(\left(-22\right.\right.\\ & (x (4 (x-5) x+35)-15) (x-1) x y^3-2 (x (((143 x-680) x+595) x+20)-105) y^2-((x (359 x+240)\\ & \left.-930) x+420) y+35 ((11 x-16) x+6)\right) s x y+2 \left(2 (4 (2 x ((x-5) x+10)-15) x+15) y^2+5 (11 (x-4) x\right. \\ & \left.\left.\left.\left.\left.+42) x y-60 y+10 (7 x-9) x+30\right) m_c m_s\right)\right)\right)F\left(s,x,y\right)+60 (y-1)^2 s \left((x-1) (y-1) \left(4 ((x (5 (13 x-42) x\right.\right.\right.\\& \left.\left.\left.+273)-140) x+35) y^3-56 (2 (4 x-5) x+5) y^2+21 ((3 x-10) x+10) y+35 (x-2)\right) s^2 x^2 y^3+2 \left((x-1) \right.\right.\right.\\ & \left.(y-1) \left(2 ((x (2 (x-35) x+189)-140) x+35) y^2\right.+14 (x ((8 x-37) x+35)-10) y+7 (23 x-30) x+70\right)\\ & \left. s^2 x^2 y^3+7 \left(2 \left(2 (4 (2 x ((x-5) x+10)-15) x+15) y^2\right.\right.+5 (11 (x-4) x+42) x y-60 y+10 (7 x-9) x+30\right)\\ & \left.\left. m_c m_s-s x y (x y-1) \left(55 x^2-80 x+2 (x (4 (x-5) x+35)\right. -15)(x-1) y^2+2 (x ((17 x-80) x+90)-30) y\right.\right.\\ & \left.\left.\left.+30\right)\right) m_c m_s\right) c_p y+7 m_c m_s \left(\left(-4 ((x ((59 x-184) x+195)\right.\right.-90) x+15) x y^4+4 ((x-2) ((17 x-25) x+25) x\\ & \left.\left.\left.\left.+15) y^3+(x ((53 x-210) x+250)-120) y^2+5 ((7 x-20) x+18) y+20 x-30\right) s x y+2 \left(12 (4 (2 x ((2 x-5)\right.\right.\right.\right.\\ & \left.\left.\left.\left. x+5)-5) x+5) y^3+10 (x (5 (x-4) x+24)-12) y^2+30 ((x-3) x+3) y+15 (x-2)\right) m_c m_s\right)\right)\right),\\ \rho^{\langle\bar{s}s\rangle}_{1,7;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y \frac{c_1 x m_c}{96 \pi ^3 (y-1)^4} F\left(s,x,y\right){}^2 \left(2 s (y-1) \left((x-1) y^2 \left((x (26 x-1)-14) c_p-22 x^2+50 x\right.\right.\right.\\ & \left.\left.-10\Big)+11 x y^4 \left(x^3 \left(c_p-23\right)-2 x \left(c_p+5\right)+c_p+7 x^4+24 x^2+1\right)-y^3 \left((x (x (11 x+37)-19)-7) (x-1)\right.\right.\right.\\ & \left.\left.\left. c_p-2 ((21 x-40) x+28) x+7\right)-(x-1) y \left(7 (x-1) c_p+10 x-4\right)-x+1\right) F\left(s,x,y\right)+\left((x-1) (y-1) c_p\right.\right. \\ & \left.\left.\left.\left(2 \left(x^2+x-1\right)\right.x y^2+x (2-5 x) y+x+y-1\right)+2 ((x ((7 x-23) x+24)-10) x+1) x y^3+(x ((5 x-9) x\right.\right.\\& \left.\left.+7)-1) y^2-(x-1)((5 x-9) x+2) y-(x-1)^2\right) F\left(s,x,y\right){}^2+6 s^2 (y-1)^2 y \left(-2 y^3 \left((x (x+2)-4) x^2 c_p\right.\right.\right.\\ & \left.\left.\left.+c_p-2 (2 (x-2) x+3) x+1\right)+(x-1) y^2 \left(2 \left(2 x^2+x-2\right) c_p+x (11-4 x)-4\right)+2 x y^4 \left(x^3 \left(c_p-23\right)\right.\right.\right.\\ & \left.\left.-2 x \left(c_p+5\right)+c_p+7 x^4+24 x^2+1\Big)-(x-1)^2 y \left(2 c_p+3\right)-x+1\right)\right),\\ \rho^{\langle m_s\bar{s}s\rangle}_{1,7;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1}{96 \pi ^3 (y-1)^3} F\left(s,x,y\right) \left(-2 F\left(s,x,y\right){}^2 \left(m_c^2 \left(5 x^2 c_p+y^2 \left(x^4 \left(c_p+9\right)-4 x^3 \left(c_p+5\right)\right.\right.\right.\right.\\ & \left.+2 x^2 \left(5 c_p+9\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)+2 y \left((x ((x-7) x+7)-2) c_p+((x-5) x+5) x-2\right)-6 x c_p\\ & \left.\left.\left.+2 c_p+x^2-2 x+2\right)-s (x-1) x (y-1) \left(35 y^4 \left(((x ((x-4) x+10)-8) x+2) c_p+(3 x ((x-4) x+6)-8) x\right.\right.\right.\right.\\ & \left.\left.\left.+2\Big)+y^3 \left(59 (x ((x-7) x+7)-2) c_p+(233-x (81 x+233)) x-118\right)+2 y^2 \left(12 ((5 x-6) x+2) c_p+(14 x\right.\right.\right.\right.\\ & \left.\left.\left.\left.-33) x+38\right)+12 (x-2) y+2\right)\right)-3 s (y-1) F\left(s,x,y\right) \left(2 m_c^2 \left(2 y^3 \left(x^4 \left(c_p+9\right)-4 x^3 \left(c_p+5\right)+2 x^2 \left(5 c_p\right.\right.\right.\right.\right.\\& \left.+9\Big)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)+4 y^2 \left((x ((x-7) x+7)-2) c_p+x (x-2)^2-2\right)+x y \Big(2 (5 x-6) c_p+3 (x\\ & \left.\left.\left.-2)\Big)+y \left(4 c_p+6\right)+x-2\right)-s (x-1) x (y-1) y \left(25 y^4 \left(((x ((x-4) x+10)-8) x+2) c_p+(3 x ((x-4) x\right.\right.\right.\right.\\ & \left.\left.\left.+6)-8) x+2\Big)+2 y^3 \left(23 (x ((x-7) x+7)-2) c_p+(91-x (27 x+91)) x-46\right)+y^2 \left(21 ((5 x-6) x+2) c_p\right.\right.\right.\right.\\ & \left.\left.\left.+(29 x-62) x+66\Big)+12 (x-2) y+2\right)\right)+(x-1) x y \left(5 y^2 \Big(((x ((x-4) x+10)-8) x+2) c_p+(3 x ((x-4) x\right.\right.\\ & \left.\left.+6)-8) x+2\Big)+4 y \left(2 (x ((x-7) x+7)-2) c_p-3 (x (x+3)-3) x-4\right)+3 ((5 x-6) x+2) c_p-3 x+6\right)\right.\\ & \left. F\left(s,x,y\right){}^3+6 s^3 (x-1) x (y-1)^3 y^3 \left(2 y^3 \left(((x ((x-4) x+10)-8) x+2) c_p+(3 x ((x-4) x+6)-8) x+2\right)\right.\right.\\ & \left.\left.\left.+4 y^2 \left((x ((x\right.-7) x+7)-2) c_p-(x (x+4)-4) x-2\right)+x y \left(2 (5 x-6) c_p+3 (x-2)\right)+y \left(4 c_p+6\right)+x-2\right)\right),\\ \rho^{\langle g_sG^2\rangle}_{1,7;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{max}}_{y_{\min}}{\rm d}y \frac{x^2 c_1 m_c}{1935360 \pi ^5 (x-1)^3 (y-1)^5} \left(-2 (x-1) \left(2 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(10 \left(\left(2 c_p\right.\right.\right.\right.\right.\\ & \left.\left.\left.\left.+65\Big) x^4-70 \left(c_p+3\right) x^3+21 \left(9 c_p+13\right) x^2-140 \left(c_p+1\right) x+35 \left(c_p+1\right)\right) y^2+28 \left(-39 x^2+45 x+(x\right.\right.\right.\right.\\ & \left.\left.\left.\left.((15 x-74) x+70)-20) c_p-20\right) y+21 \left((2 x+5) (-x)+((23 x-30) x+10) c_p+10\right)\right) x y m_c+21 \left(-4\right.\right.\right.\\ \end{aligned} $

$ \begin{aligned}[b] & \left.\Big(\left(\left(x \left(4 x^2\right.\right.\right.\right.-34 x+105\Big)-125\Big) x+45\Big) c_p (x-1)^2+(x ((x ((59 x-327) x+762)-949) x+660)-255) x\\ & +45\Big) x y^5+\left(3 (x (2 ((-7 (x-8) x-116) x+61) x+65)-120) x+(150-x ((4 (x (23 (x-8) x+494)-554) x\right.\\ & \left.+805) x+220)) c_p+150\right) y^4-2 \left((3 x ((-5 (x-13) x-218) x+300)-650) x+((x ((5 (17 x-59) x+141) x\right.\\ & \left.+535)-660) x+210) c_p+210\right) y^3+2 \left((x ((50 x-279) x+570)-540) x+((x (4 (5 x-61) x+725)-690)\right.\\ & x+210)c_p+210\Big) y^2+6 \left(((11 x-45) x+60) x+2 (x (8 (x-5) x+45)-15) c_p-30\right) y+5 \left((3 x-8) x\right.\\ & \left.\left.\left.\left.+((11 x-16) x+6) c_p+6\right)\right) m_s\right) F\left(s,x,y\right){}^3+21 \left(2 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(4 \left((x ((59 x-184)\right.\right.\right.\right.\\ & \left.x+195)-90) x+(x (4 (x-5) x+35)-15) (x-1) c_p+15\right) x y^3+\left(((-58 (x-3) x-195) x+120) x+(x\right.\\ & \left.(x (4 (13 x-64) x+245)-20)-30) c_p-30\right) y^2+2 \left((3 (45-16 x) x-110) x+\left(37 x^3-60 x+30\right) c_p+30\right)\\& \left.\left.\left.y-30 \left(c_p+1\right)-5 x^2 \left(11 c_p\right.+3\Big)+40 \left(2 c_p+1\right) x\right) m_s m_c^2-2 s (x-1) x (y-1) (y ((x ((x-3) x+3) y-3) y\right.\right. \\ & \left.+3)-1) \left(10 \left(\left(2 c_p+65\right) x^4-70\right.\right.\left(c_p+3\right) x^3+21 \left(9 c_p+13\right) x^2-140 \left(c_p+1\right) x+35 \left(c_p+1\right)\right) y^4\\ & \left.\left.\left.+\left(50 \left(9 c_p-1\right) x^3-\left(2183 c_p+923\right) x^2\right.+5 \left(413 c_p+233\right) x-590 \left(c_p+1\right)\right) y^3+\left(8 \left(69 c_p+8\right) x^2\right.\right.\right.\\& \left.\left.\left.\left.-30 \left(24 c_p+11\right) x+240 c_p+380\right) y^2+60 (x-2) y+10\right) m_c+3 (x-1) (y-1) \left(22 \left(4 c_p+59\right) y^6 x^7\right.\right.\right.\\ & \left.\left.\left.\left.+2 \left(-33 \left(14 c_p+109\right) y+253 c_p+83\right) y^5 x^6+\left(66 \left(59 c_p\right.\right.+254\Big) y^2-16 \left(253 c_p+83\right) y+935 c_p+10\right) y^4\right.\right.\right.\\ & \left.\left.\left. x^5-y^3 \left(2 (11 y (949 y-109)-670) y+11 \left(\left(738 y^2-988 y\right.\right.\right.+295\Big) y+20\Big) c_p+470\Big) x^4+\left(6 ((20 y (121 y\right.\right.\right.\right.\\ & -2)-913) y+408) y+(y ((20 (440 y-607) y+1407) y+2828)-576) c_p-286\Big) y^2 x^3-5 y \left(2 (y ((y (561 y\right.\\ & \left.+205)-794) y+513)-147) y+((y (2 (y (473 y-427)-644) y+1739)-609) y+77) c_p+30\right) x^2+10\\ & \left. \left(y \left((y ((11 y (9 y+20)-630) y+560)-251) y+(y ((y (99 y+235)\right.\right.-548) y+292)-56) (y-1) c_p+52\right)\\ & \left.\left.\left.\left.\left.-4\right) x-30 (y-1) \left(\left(((29 y-50) y+39) y+(y-1) ((29 y-25) y+7) c_p\right.\right.-14\right) y+2\right)\right) s m_s\right)F\left(s,x,y\right){}^2 \\ & +6 (y-1) s \left(7 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(22 \left(4 c_p+59\right) y^4 x^5\right.\right.-2 y^3 \Big(88 \left(3 c_p+23\right) y-143 c_p\\ & \left.\left.\left.+192\Big) x^4+\left(110 \left(11 c_p+39\right) y^2+20 \left(65-68 c_p\right) y+359 c_p-306\right) y^2 x^3-5 y \Big(44 \left(5 c_p+9\right) y^3+34\right.\right.\right.\\ & \left(9-7 c_p\right) y^2-2 \left(24 c_p+97\right) y+77 c_p+14\Big) x^2+10 \Big(y \Big(33 \left(c_p+1\right) y^3+4 \Big(c_p+22\Big) y^2-\left(93 c_p+86\right) y\\ & \left.\left. +56 c_p+12\Big)-1\Big) x-30 (y-1) \left(\left(7 \left(c_p+1\right) y-7 c_p-3\right) y+1\right)\Big) m_s m_c^2-s (x-1)x (y-1) y (y ((x ((x-3) x\right.\right.\\ & \left.\left.\left.\left.+3) y-3) y+3)-1) \left(\left(50 \left(2 c_p+65\right) y^3 x^4-140 y^2 \left(25 \left(c_p+3\right) y-18 c_p+1\right) x^3\right.\right.+7 \Big(150 \left(9 c_p+13\right) y^2\right.\right.\right.\right.\\ & \left.\left.\left.\left.\left.\left.-2 \left(851 c_p+361\right) y+483 c_p+79\Big) y x^2+70 \left(\left(-100 \left(c_p+1\right) y^2+7 \left(23 c_p+13\right) y\right.\right.-63 c_p-31\right) y+6\right) x\right.\right.\right.\right.\\ & \left.\left.\left.\left.\left.+70 (y-1) \left((25 y-21) \left(c_p+1\right) y+12\right)\right) y+70\right) m_c+21 (x-1) (y-1) \left(4 \left(4 c_p+59\right)\right.y^6 x^7+4 \Big(-327 y\right.\right.\right.\\ & \left.\left.\left.+(23-42 y) c_p+8\Big) y^5 x^6+\left(8 (381 y-32) y+2 \left(354 y^2-368 y+85\right) c_p+15\right) y^4 x^5-y^3 \Big((4 y (949 y\right.\right.\right.\\ & \left.-119)-195) y+2 \left(\left(738 y^2-988 y+295\right) y+20\right) c_p+90\Big) x^4+\left(3 ((4 y (220 y-7)-323) y\right.+168) y\right.\\ & \left.+2 (y ((4 (200 y-273) y+93) y+292)-64) c_p-68\right) y^2 x^3-5 y \left((y (4 (y (51 y+19)-78) y+231)-75) y\right.\\ & \left.+2 ((y (2 (y (43 y-35)-72) y+193)-75) y+11) c_p+9\right) x^2+10 \left(y \left((y ((2 y (9 y+22)-135) y+136)\right.\right.\\ & \left.\left.-70) y+2 (y ((y (9 y+25)-60) y+36)-8) (y-1) c_p+18\right)-2\right) x-30 (y-1) (3 (y-1) y+1) \left(2 (y-1)\right.\\ & \left.\left.\left.\left. \left(c_p+1\right) y+1\right)\right) s y m_s\right) F\left(s,x,y\right)+6 (y ((x ((x-3) x+3) y-3) y+3)-1) (y-1)^2 \left(7 \left(4 \left(4 c_p+59\right) y^4 x^5-4\right.\right.\right.\\ & \left.\left.\left. y^3 \left(8 \left(3 c_p+23\right) y-13 c_p+17\right) x^4+\left(4 (195 y+59) y+(4 (55 y-56) y+42) c_p-53\right) y^2 x^3-5 y \left(6 (2 y (6 y\right.\right.\right.\right.\\ & \left.+5)-7) y+(4 (y (10 y-7)-8) y+22) c_p+7\right) x^2+10 \left(6 \left(c_p+1\right) y^4+4 \left(2 c_p+5\right) y^3-5 \left(6 c_p+5\right) y^2+2 \right.\\ & \left.\left.\left.\left.\left(8 c_p+5\right) y-2\right) x-30 (y-1) \left(2 (y-1) \left(c_p+1\right) y+1\right)\right) m_c m_s-s (x-1) x (y-1) y^2 \left(4 \left(2 c_p+65\right) y^3 x^4\right.\right.\right.\\ & -56 y^2 \left(5 y \left(c_p+3\right)-4 c_p\right) x^3+7 \left(12 \left(9 c_p+13\right) y^2-4 \left(37 c_p+16\right) y+46 c_p+9\right) y x^2+35 \left(1-2 y\right.\\ \end{aligned} $

$ \begin{aligned}[b] &\left.\left.\left.\left.\left. \left(8 (y-1) y\right.+2 (4 y-3) (y-1) c_p+3\right)\right) x+70 (y-1) \left(2 (y-1) \left(c_p+1\right) y+1\right)\right)\right) s^2 y m_c\right),\\ \rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{1,7;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{ \frac{c_1 m_c}{192 \pi ^3 (y-1)^3} F\left(s,x,y\right) \left(3 s (y-1) \left(y \left(x^2 \left(7 c_p-38\right)-7 c_p+44 x-4\right)+11 x y^4 \left(9 x^3\right.\right.\right. \\ & \left.\left.\left.\left(c_p-7\right)-12 x^2 \left(c_p-5\right)+2 x \left(c_p-11\right)+c_p+19 x^4+1\right)+y^3 \left(-(x-1) (x (11 x (9 x+5)-59)-7) c_p\right.\right.\right.\\ & \left.\left.\left.+2 ((12 x (x+4)-97) x+68) x-7\right)+(x-1) y^2 \left((11 x (8 x-5)-14) c_p-2 (6 (5 x-12) x+5)\right)-3 x+1\right)\right.\\ & \left. F\left(s,x,y\right)+2 \left((x-1) (y-1) c_p (x (y (2 x ((9 x-3) y-8)-2 y+9)-1)+y-1)+y \left(x \left(2 ((x ((19 x-63) x\right.\right.\right.\right.\\ & \left.\left.\left.\left.+60)-22) x+1) y^2+((2 x (x+7)-21) x+16) y-10 (x-3) x-22\right)-y\right)+x (4-3 x)+2 y-1\right) F(s,x,y)^2\right.\\ & \left.+6 s^2 (y-1)^2 y \left(2 x y^4 \left(9 x^3 \left(c_p-7\right)-12 x^2 \left(c_p-5\right)+2 x \left(c_p-11\right)+c_p+19 x^4+1\right)-2 y^3 \left((x (9 x-4)-1)\right.\right.\right. \\ & \left.(x-1) (x+1) c_p-2 ((x (x+5)-10) x+7) x+1\right)+(x-1) y^2 \left(2 (x (8 x-5)-2) c_p+x (31-12 x)-4\right)\\ & \left.\left.+2 x y \left(x \left(c_p-5\right)+7\right)-y \left(2 c_p+3\right)-2 x+1\right)\right)+\frac{c_2 x m_c}{128 \pi ^3 (x-1) (y-1)^4} F\left(s,x,y\right) \left(3 s (y-1) \left(-2 y^4 \left(\left(55 x^2\right.\right.\right.\right.\\ & \left.\left.-75 x+31\right) (x-1)^2 c_p+(x ((10 x-83) x+134)-103) x+31\right)+11 y^5 \left(((5 x-6) x+2) (x-1)^2 c_p\right.\\ & \left.\left.\left.+(x ((x ((7 x-30) x+51)-48) x+27)-10) x+2\right)+y^3 \left(((55 x-102) x+65) (x-1)^2 c_p-2 x ((2 x (x+17)\right.\right.\right.\\ & \left.\left.\left.-95) x+102)+75\right)+2 (x-1) y^2 \left((9 x-16) (x-1) c_p+(9 x-32) x+24\right)+x y \left(7 (x-2) c_p+11 x-26\right)\right.\right.\\ & \left.\left.+y \left(7 c_p+15\right)+2 x-2\right) F\left(s,x,y\right)+2 \left((x-1)^2 (y-1)^2 c_p (y (x (2 (5 x-6) y+3)+4 y-3)+1)+2 ((x ((x\right.\right. \\ & ((7 x-30) x+51)-48) x+27)-10) x+2) y^4+(x (((37-6 x) x-55) x+39)-11) y^3+(11-x ((2 x (x+4)\\ & \left.\left.-27) x+30)) y^2+(3 x-5) (x-1)^2 y+(x-1)^2\right) F\left(s,x,y\right){}^2+6 s^2 (y-1)^2 y \left(2 y^5 \left(((5 x-6) x+2) (x-1)^2 c_p\right.\right.\right.\\ & \left.+(x ((x ((7 x-30) x+51)-48) x+27)-10) x+2\right)-4 y^4 \left(((5 x-7) x+3) (x-1)^2 c_p+(x ((x-8) x+13)\right.\\ & -10) x+3\Big)+2 y^3 \left((5 (x-2) x+7) (x-1)^2 c_p+((21-8 x) x-22) x+8\right)+(x-1) y^2 \left(4 (x-2) (x-1) c_p\right.\\ & \left.\left.\left.+(4 x-15) x+12\right)+x y \left(2 (x-2) c_p+3 x-8\right)+y \left(2 c_p+5\right)+x-1\right)\right)\Bigg\},\\ \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{1,7;A(S)}(s) = &-\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1}{288 \pi ^3 (y-1)^2} \left(3 s (y-1) y F(s,x,y) \left(s (x-1) (y-1) \left(25 y^4 \left(x^4 \left(5 c_p-1\right)-4 x^3\right.\right.\right.\right.\\ & \left. \left(c_p+3\right)+6 x^2 \left(c_p+5\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)-2 y^3 \left(((x (42 x+115)-161) x+46) c_p+(x (152 x\right.\\ & \left.+185)-91) x+46\Big)+y^2 \left(21 ((7 x-6) x+2) c_p+(95 x-62) x+66\right)+12 (x-2) y+2\right)-6 x m_c^2 \left(2 c_p (y (x (4\right.\\ & \left.\left.\left. y-5)-2 y+2)+1)+2 y (4 (2 x-3) x y+x+6 y-4)+3\right)\right)+3 F\left(s,x,y\right){}^2 \left(s (x-1) (y-1) \left(35 y^4 \left(x^4 \Big(5 c_p\right.\right.\right.\right.\\ & \left.-1\Big)-4 x^3 \Big(c_p+3\Big)+6 x^2 \left(c_p+5\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)-y^3 \left(((x (96 x+295)-413) x+118) c_p+(x \right.\\ & \left.\left.(436 x+475)-233) x+118\right)+2 y^2 \left(12 ((7 x-6) x+2) c_p+(52 x-33) x+38\right)+12 (x-2) y+2\right)-3 x m_c^2\\ & \left.\left.\left. \left(2 y^2 \left(2 x \left(c_p-3\right)\right.\right.-c_p+4 x^2+3\right)-y \left((5 x-2) c_p+x+2\right)+c_p+1\right)\right)+2 (x-1) y \left(-4 y \left((x (x+4)-2)\right.\right.\\ & \left. (3 x-2) c_p+3 (6 x+5) x^2-9 x+4\right)+5 y^2 \Big(x^4 \left(5 c_p-1\right)-4 x^3 \left(c_p+3\right)+6 x^2 \left(c_p+5\right)-8 x \left(c_p+1\right)+2 \\ & \left.\left.\left(c_p+1\right)\Big)+3 ((7 x-6) x+2) c_p+6 x^2-3 x+6\right) F\left(s,x,y\right){}^3+3 s^3 (x-1) (y-1)^3 y^3 \left(2 x^4 y^3 \left(5 c_p-1\right)-8 x^3 \right.\right.\\ & y^2 (y+1) \left(c_p+3\right)+x^2 y \Big(12 y^2\left(c_p+5\right)-4 y \left(5 c_p+8\right)+14 c_p+9\Big)+2 x y \Big(-8 y^2 \left(c_p+1\right)+2 y \left(7 c_p+4\right)\\ & \left.\left. \left.-6 c_p-3\Big)+2 (y-1) \left(2 (y-1) y \Big(c_p\right.+1\Big)+1\right)+x\right)\right)+\frac{c_2}{128 \pi ^3 (y-1)^3} \left(-3 F(s,x,y)^2 \left(m_c^2 \left((y-1) c_p (x y-1)\right.\right.\right.\\ & \left. \left(\left(x^2+x-1\right) y-x+1\right)+y \left(x \left(\left(-x^2+x-3\right) y+(x ((8 x-15) x+9)-1) y^2-2 x+5\right)+y\right)-x-2 y+1\right)\\ & -s x (y-1) \left(y \left(35 x y^4\right.\right.\left(\left(x^3-2 x+1\right) c_p+(3 x ((x-5) x+8)-10) x+1\right)-y^3 \left((x (x (35 x+72)-13)-35)\right.\\ & \left.(x-1) c_p+(x ((11 x+115) x+275)-202) x+35\right)+y^2 \Big((x (37 x+46)-59) (x-1) c_p+5 (x (12 x+47)\\ & \left.\left.\left.-45) x+59\Big)-2 (x-1)^2 y \left(12 c_p+19\right)-11 x+12\right)-1\right)\right)+3 s (y-1) F(s,x,y) \left(s x (y-1) y \left(y \left(25 x y^4 \right.\right.\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.\left(\left(x^3-2 x+1\right) c_p+(3 x ((x\right.-5) x+8)-10) x+1\right)-y^3 \Big((x (x (25 x+63)-17)-25) (x-1) c_p+2 (x (x\\& \left.\left.\left.\left.+20) (2 x+5)-74) x+25\Big)+y^2 \left((x (38 x+29)-46) (x-1) c_p+(x (46 x+179)-175) x+46\right)-3 (x-1)^2\right.\right.\right.\right.\\ & \left.\left.\left. y \left(7 c_p+11\right)-11 x+12\right)-1\Big)-2 m_c^2 \left(y \left(2 (y-1) c_p (x y-1) \left(\left(x^2+x-1\right) y-x+1\right)+y \left(x \left(2 (x ((8 x-15)\right.\right.\right.\right.\right.\right.\\ & \left.\left.\left.\left.\left. x+9)-1) y^2-2 ((x-3) x+5) y-4 x+11\right)+2 y\right)-3 x-4 y+3\right)-1\right)\right)+2 x y \left((x-1) (y-1) c_p \left(x \Big(5 \Big(x^2\right.\right.\\ & \left.+x-1\Big) y^2-4 (x+1) y+3\Big)+5 y-3\right)+5 ((3 x ((x-5) x+8)-10) x+1) x y^3-(2 (x ((x+10) x+15)-12) x\\ & \left.\left.+5) y^2+((x (7 x+33)-30)x+8) y-3 (x-1)^2\right) F(s,x,y)^3+3 s^3 x (y-1)^3 y^3 \left(2 x y^4 \left(\left(x^3-2 x+1\right) c_p+(3 x\right.\right.\right.\\ & \left. ((x-5) x+8)-10) x+1\right)-2 y^3 \left((x (x+2)-4) x^2 c_p+c_p+2 (2 x (x+2)-3) x+1\right)+y^2 \left(2 \left(2 x^2+x-2\right)\right.\\ & \left.\left.\left. (x-1) c_p+(x (4 x+15)-15) x+4\right)-(x-1)^2 y \left(2 c_p+3\right)-x+1\right)\right)\Bigg\},\\ \rho^{\langle\bar{s}s\bar{s}s\rangle}_{1,7;A(S)}(s) =&- \int^{z_{\max}}_{z_{\min}}{\rm d}z \frac{c_1}{24 \pi } \left(m_c m_s \left(s (z-1) \left(z \left(-14 c_p+22 z-5\right)+2\right) G(s,z)+\left(-2 c_p+4 z-3\right) G(s,z)^2+2 s^2 (z-1)^2 z\right.\right.\\ & \left.\left. \left(z \left(-2 c_p+2 z-1\right)+1\right)\right)+m_s^2 \left(-2 s \left(z \left(z \left((35 z-24) (z-1) c_p+(35 z-59) z+38\right)-12\right)+1\right) G(s,z)\right.\right.\\ & \left.\left.-2 z (5 z-3) \left(c_p+1\right) G(s,z)^2+s^2 (-(z-1)) z \left((z-1) z \left((25 z-21) z \left(c_p+1\right)+12\right)+1\right)\right)+2 m_c^2 G(s,z)\right.\\& \left. \left(c_p G(s,z)+G(s,z)+4 s (z-1) z \left(c_p+1\right)+2 s\right)\right)+\int^{1}_{0}{\rm d}z \frac{c_1}{24 \pi }s^3 (z-1)^3 z^3 m_s^2 \left(2 (z-1) z \left(c_p+1\right)+1\right),\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{1,7;A(S)}(s) =& - \int^{z_{\max}}_{z_{\min}}{\rm d}z\Bigg\{\frac{ c_1}{288 \pi } \left(12 m_c^2 \left(\left(\left(8 z^2-4 z-2\right) c_p+8 z^2-4 z+2\right) G(s,z)+2 s (z (11 z-7)-2) (z-1) z c_p\right.\right.\\ & \left.\left.+2 s (z ((11 z-18) z+14)-5) z+s\right)+m_c m_s \left(s \left(-4 (z-1) (10 z (12 z-7)-21) z c_p+((5 ((10 z-59) z+9) z\right.\right.\right.\\ & \left.\left.\left.+51) z+45) z-12\right)-8 \left((z (15 z-7)-3) c_p+3 (5 z-2) z+3\right) G(s,z)\right)-4 z m_s^2 \left(2 \left(2 (2 (5 (3 z-4) z+4) z\right.\right.\right.\\ & \left.+3) c_p+4 (5 (3 z-4) z+9) z-9\right) G(s,z)+s (z-1) \left(((2 (z (130 z-77)-115) z+127) z+8) c_p+2 (z ((130 z\right.\\ & \left.\left.\left.-77) z+11)-10) z\right)\right)\right)+\frac{c_2 }{64 \pi }\left(4 m_c^2 \left(\left(c_p+1\right) G(s,z)+2 s (z-1) z c_p+2 s (z-1) z+s\right)+m_c m_s \left(\Big(-4 c_p\right.\right.\\ & \left.\left.+8 z-6\Big) G(s,z)+s (z-1) \left(-14 z c_p+(22 z-5) z+2\right)\right)-2 m_s^2 \left(2 (5 z-3) z \left(c_p+1\right) G(s,z)+s z \Big(z \Big((35 z\right.\right.\\ & \left.\left.-24) (z-1) c_p+(35 z-59) z+38\Big)-12\Big)+s\right)\right)\Bigg\}+\int^{1}_{0}{\rm d}z\Bigg\{\frac{c_1 s^2 (z-1) z}{144 \pi } \left(m_c m_s \left(z \left(3 (z (35 z-27)-4)\right.\right.\right.\\ & \left.\left.+\left(z-1) c_p(60 z^2-58 z+15\right) z-4\right)-2\right)+2 (z-1) z m_s^2 \Big((((2 z (73 z-77)-39) z+37) z+12) c_p\\ & \left.+(z (2 (73 z-77) z+79)-26) z-4\Big)-12 (z-1) z m_c^2 \left(2 (z-1) z \left(c_p+1\right)+1\right)\right)-\frac{{\rm i} c_2 s^2 (z-1)^2 z}{32 \pi } m_c m_s\\ & \left(z \left(-2 c_p+2 z-1\right)+1\right)\Bigg\},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{1,7;A(S)}(s) = & \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{x c_1}{576 \pi ^3 (x-1)^3 (y-1)^4} m_c \left(-3 (x-1) \left(2 ((x ((x ((7 x-37) x+81)-95) x+61)-21) x\right.\right.\\ & +3) x y^5-((x ((6 (x-4) x+13) x+9)-15) x+5) y^4+((x ((-2 (x-4) x-43) x+66)-49) x+14) y^3\\ & +(x ((17 x-42) x+41)-14) y^2-3 (x-2) (x-1)^2 y-(x-1)^2+(y ((y (-2 x+2 (4 x-3) (x-1) y+7)-3) x\\ & \left.-5 y+4)-1) (x-1)^2 (y-1)^2 c_p\right) F(s,x,y)^2+\left(-2 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(2 ((x ((7 x-23) x\right.\right.\\ & +24)-10) x+1) x y^3+(x ((5 x-9) x+7)-1) y^2-(x-1) ((5 x-9) x+2) y-(x-1)^2+(x-1) \\ & \left.\left(2 \left(x^2+x-1\right) x y^2+x (2-5 x) y+y+x-1\right) (y-1) c_p\right) m_c^2-3 s (x-1) (y-1) \left(11 \left((4 x-3) c_p (x-1)^3\right.\right.\\ & \left.+(x ((x ((7 x-37) x+81)-95) x+61)-21) x+3\right) x y^6+\Big(-(11 x (8 x-5)-29) c_p (x-1)^3+2 ((2 x (2\\ & -5 (x-4) x)-53) x+50) x-29\Big) y^5+\Big(((11 x (4 x-5)-65) x+83) c_p (x-1)^2-4 x ((x ((x-4) x+48)\\ & -83) x+66)+79\Big) y^4+\left(-((11 x-76) x+86) c_p (x-1)^2+2 (9 (5 x-13) x+122) x-89\right) y^3-(x-1) \\ \end{aligned} $

$ \begin{aligned}[b] & \left.\left.\left((17 x-64) x+3 (6 x-13) (x-1) c_p+53\right) y^2-\left(7 c_p+16\right) y+\left(-10 x-7 (x-2) c_p+26\right) x y-2 x+2\right)\right)\\ & F(s,x,y)-s (y-1) \left((y ((x ((x-3) x+3) y-3) y+3)-1) \left(11 \left(7 x^4+\left(c_p-23\right) x^3+24 x^2-2 \left(c_p+5\right) x\right.\right.\right.\\ & \left.+c_p+1\right) x y^4-\left(-2 ((21 x-40) x+28) x+(x (x (11 x+37)-19)-7) (x-1) c_p+7\right) y^3+\left(-22 x^2+50 x\right.\\ & \left.\left.+(x (26 x-1)-14) c_p-10\right) (x-1) y^2-(x-1) \left(10 x+7 (x-1) c_p-4\right) y-x+1\right) m_c^2+3 (x-1) (y-1)\\& \left(2 \left((4 x-3) c_p (x-1)^3+(x ((x ((7 x-37) x+81)-95) x+61)-21) x+3\right) x y^6-2 \left((8 x+3) c_p (x-1)^4\right.\right.\\ & \left.+2 \left(x^4-4 x^3+5 x-5\right) x+3\right) y^5+\left(2 ((x (4 x-5)-7) x+9) c_p (x-1)^2-3 x (11 (x-2) x+19)+18\right) y^4\\ & +\left(-2 ((x-8) x+10) c_p (x-1)^2+((19 x-54) x+60) x-23\right) y^3-(x-1) \left((4 x-17) x+2 (2 x-5) (x-1)\right.\\ & \left.\left.\left.\left. c_p+16\right) y^2-2 \left(c_p+3\right) y+\left(-3 x-2 (x-2) c_p+9\right) x y-x+1\right) s y\right)\right)\Bigg\}\\ & -\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s^2 x y}{576 \pi ^3 (x-1)^3 (y-1)^2} m_c^3 (y (y (x ((x-3) x+3) y-3)+3)-1) \left(-2 y^3 \left((x (x+2)-4) x^2 c_p\right.\right.\\ & \left.\left.+c_p-2 (2 (x-2) x+3) x+1\right)+(x-1) y^2 \left(2 \left(2 x^2+x-2\right) c_p+x (11-4 x)-4\right)+2 x y^4 \left(x^3 \left(c_p-23\right)\right.\right.\\ & \left.\left.-2 x \left(c_p+5\right)+c_p+7 x^4+24 x^2+1\right)-(x-1)^2 y \left(2 c_p+3\right)-x+1\right),\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{1,7;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1}{576 \pi ^3 (x-1)^3 (y-1)^3} m_c^2 \left(-(y ((x ((x-3) x+3) y-3) y+3)-1) \left(5 c_p x^2+x^2-6 c_p\right.\right.\\ & x-2 x+\left(\left(c_p+9\right) x^4-4 \left(c_p+5\right) x^3+2 \left(5 c_p+9\right) x^2-8 \left(c_p+1\right) x+2 \left(c_p+1\right)\right) y^2+2 \left(((x-5) x+5) x\right.\\ & \left.\left.+(x ((x-7) x+7)-2) c_p-2\right) y+2 c_p+2\right) m_c^2+(x-1) (y-1) \left(35 \left((3 x ((x-4) x+6)-8) x+((x ((x-4)\right.\right.\\ & \left. x+10)-8) x+2) c_p+2\right) ((x-3) x+3) x^2 y^7+\left(((x (x (x (10-81 x)+374)-256)-837) x+486) x\right.\\ & \left.+(x (((x (59 (x-10) x+1724)-2176) x+543) x+486)-210) c_p-210\right) x y^6+\left(((x (((393-26 x) x\right.\\ & \left.-1115) x+2667)-1635) x+684) x+3 (x ((x (((38 x-121) x+41) x+643)-721) x+228)-8) c_p-24\right)\\ &y^5+\Big((x (1537-3 x ((35 x-99) x+571))-892) x+((x (((437-47 x) x-2273) x+2431)-880) x+72) c_p\\ & +72\Big) y^4+\left(((x (20 x+491)-737) x+634) x+(x (((917-95 x) x-1217) x+574)-84) c_p-96\right) y^3\\ & +\left(((180-43 x) x-256) x-12 (x-1) ((11 x-13) x+4) c_p+72\right) y^2-6 \left(2 c_p+5\right) y+3 \Big(-7 x+2 (6-5 x)\\& \left. c_p+18\Big) x y-5 x+6\right) s+(x-1) \left(10 \left((3 x ((x-4) x+6)-8) x+((x ((x-4) x+10)-8) x+2) c_p+2\right)\right.\\ & ((x-3) x+3) x^2 y^6+2 \left(\left(72-x \left(\left(12 x^3-63 x+52\right) x+114\right)\right) x+(x (((x (8 (x-10) x+233)-292) x+66)\right.\\ & \left. x+72)-30) c_p-30\right) x y^5+3 \left(((3 x (((22-3 x) x-54) x+106)-194) x+72) x+(x ((x ((x (9 x-26)-6) x\right.\\ & \left.+200)-218) x+72)-4) c_p-4\right) y^4+2 \left((x (277-3 x (6 (x-4) x+103))-142) x+2 ((x (((37-4 x) x\right.\\ & \left.-172) x+191)-77) x+9) c_p+18\right) y^3-2 \left((3 x ((x-26) x+38)-88) x+((x ((17 x-137) x+203)-112)\right.\\ & \left.x+21) c_p+21\right) y^2-6 \left(((x-7) x+9) x+(3 x (2 (x-3) x+5)-4) c_p-4\right) y-3 \left((x-2) x+((5 x-6) x+2)\right.\\ & \left.\left.\left. c_p+2\right)\right) F(s,x,y)\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{ c_1 s}{1152 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1)\\ & \left(2 m_c^2 \left(2 y^3 \left(x^4 \left(c_p+9\right)-4 x^3 \left(c_p+5\right)+2 x^2 \left(5 c_p+9\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)+4 y^2 \left((x ((x-7) x+7)\right.\right.\right.\\ & \left.\left.\left.-2) c_p+x (x-2)^2-2\right)+x y \left(2 (5 x-6) c_p+3 (x-2)\right)+y \left(4 c_p+6\right)+x-2\right)-s (x-1) x (y-1) y \left(25 y^4\right.\right.\\ & \left(((x ((x-4) x+10)-8) x+2) c_p+(3 x ((x-4) x+6)-8) x+2\right)+2 y^3 \Big(23 (x ((x-7) x+7)-2) c_p+(91\\ & \left.\left.-x (27 x+91)) x-46\Big)+y^2 \left(21 ((5 x-6) x+2) c_p+(29 x-62) x+66\right)+12 (x-2) y+2\right)\right)\Bigg\},\\ \rho^{\langle g_sG^2\rangle^2}_{1,7;A(S)}(s) = &-\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^3 y^4}{5806080 \pi ^5 (x-1)^2 (y-1)^2} m_c^4 \left(28 y \Big((x ((15 x-74) x+70)-20) c_p-39 x^2+45 x\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.-20\Big)+10 y^2 \left(x^4 \left(2 c_p+65\right)-70 x^3 \left(c_p+3\right)+21 x^2 \left(9 c_p+13\right)-140 x \left(c_p+1\right)+35 \left(c_p+1\right)\right)+21 \Big(((23 x\right.\\& \left.-30) x+10) c_p-(2 x+5) x+10\Big)\right)-\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s x^3 y^3}{1658880 \pi ^5 (x-1)^2 (y-1)} m_c^4 \Big(y^2 \left(8 x^2 \left(69 c_p+8\right)\right.\\ & \left.-30 x \left(24 c_p+11\right)+240 c_p+380\right)+y^3 \left(50 x^3 \left(9 c_p-1\right)-x^2 \left(2183 c_p+923\right)+5 x \left(413 c_p+233\right)\right.\\ & \left.-590 \left(c_p+1\right)\right)+10 y^4 \left(x^4 \left(2 c_p+65\right)-70 x^3 \left(c_p+3\right)+21 x^2 \left(9 c_p+13\right)-140 x \left(c_p+1\right)+35 \left(c_p+1\right)\right)\\ & +60 (x-2) y+10\Big),\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{1,7;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1}{2304 \pi ^3 (x-1)^3 (y-1)^3} m_c \left(6 (x-1) \left(y^4 \left(\left(2 \left(8 x^3-15 x+6\right) x+5\right) (x-1)^2 c_p\right.\right.\right.\\ & \left.+(x (2 (3 x ((x-2) x-4)-7) x+33)-24) x+5\right)-2 x y^5 \left(\left(8 x^2-3\right) (x-1)^3 c_p+(x ((x ((19 x-97) x+201)\right.\\ & \left.-219) x+121)-33) x+3\right)+2 y^3 \left(-(x-1) (x (((8 x-19) x+12) x+5)-7) c_p+\left(\left(2 x \left(x^2+x+19\right)-53\right)\right.\right.\\& \left.\left.\left.\left. x+33\right) x-7\right)+2 y^2 \left((x ((x-3) x+6)-7) (x-1) c_p-((x (4 x+13)-33) x+28) x+7\right)+6 (x-1) y \Big(c_p\right.\right.\\ & \left.+(x-3) x+1\Big)+(1-x) \left(x \left(c_p-3\right)+c_p+1\right)\right) F(s,x,y)-2 m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \Big((x\\ & -1)(y-1) c_p (x (y (2 x ((9 x-3) y-8)-2 y+9)-1)+y-1)+y \left(x \left(2 ((x ((19 x-63) x+60)-22) x+1) y^2\right.\right.\\ & \left.\left.+((2 x (x+7)-21) x+16) y-10 (x-3) x-22\right)-y\right)+x (4-3 x)+2 y-1\Big)+3 s (x-1) (y-1) \left(y^5 \Big(\Big(11\right.\\ & \left(8 x^3-15 x+6\right) x+29\Big) (x-1)^2 c_p+2 (x ((x (10 (x-2) x-53)-100) x+156)-90) x+29\Big)-11 x y^6\\& \left(\left(8 x^2-3\right) (x-1)^3 c_p+(x ((x ((19 x-97) x+201)-219) x+121)-33) x+3\right)+y^4 \left(-(x-1) (x (11 ((8 x\right.\\ & \left.-19) x+12) x+58)-83) c_p+2 ((x (4 (x+8) x+213)-340) x+213) x-79\right)+y^3 \left((11 x ((x-3) x+6)\right.\\ & \left.-86) (x-1) c_p-2 (9 (2 x (x+6)-29) x+208) x+89\right)+y^2 \Big(3 (x-1) (x+13) c_p+((51 x-209) x+217) x\\ & \left.\left.-53\Big)+x y \left(x \left(30-7 c_p\right)-52\right)+y \left(7 c_p+16\right)+4 x-2\right)\right)-\frac{c_2 x y^2}{768 \pi ^3 (x-1)^2 (y-1)^2} m_c^3 \Big(y \Big(((x (x+21)\\ & -21) x+5) c_p+\left(x^2+x-1\right) x+5\Big)-2 \left((1-2 x)^2 c_p-x^2+x+1\right)+2 x y^3 \left((x-1) ((x-4) x+6) x c_p+c_p\right.\\ & \left.+(3 (x-2) x+2) x+1\right)+y^2 \left(3 (x (((x-4) x-2) x+4)-1) c_p+(((20-11 x) x-12) x+2) x-3\right)\Big)\Bigg\}\\ & +\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s }{2304 \pi ^3 (x-1)^3 (y-1)^2}m_c \left(m_c^2 (-(y (y (x ((x-3) x+3) y-3)+3)-1)) \left(y \left(x^2 \left(7 c_p-38\right)\right.\right.\right.\\ & \left.-7 c_p+44 x-4\right)+11 x y^4 \left(9 x^3 \left(c_p-7\right)-12 x^2 \left(c_p-5\right)+2 x \left(c_p-11\right)+c_p+19 x^4+1\right)+y^3 \left(-(x-1)\right. \\& \left.(x (11 x (9 x+5)-59)-7) c_p+2 ((12 x (x+4)-97) x+68) x-7\right)+(x-1) y^2 \left((11 x (8 x-5)-14) c_p\right.\\ & \left.\left.-2 (6 (5 x-12) x+5)\right)-3 x+1\right)-3 s (x-1) (y-1) y \left(2 y^5 \left(-\left(\left(8 x^3-15 x+6\right) x+3\right) (x-1)^2 c_p+2 ((x (x\right.\right.\\ & \left.\left. (5-(x-2) x)+9)-15) x+9) x-3\right)+2 x y^6 \left(\left(8 x^2-3\right) (x-1)^3 c_p+(x ((x ((19 x-97) x+201)-219) x\right.\right.\\ & \left.+121)-33) x+3\right)+y^4 \left(2 (x (((8 x-19) x+12) x+6)-9) (x-1) c_p-3 ((x (6 x+25)-46) x+31) x+18\right)\\ & +y^3 \left(-2 (x-1) (x ((x-3) x+6)-10) c_p+((x (7 x+46)-123) x+104) x-23\right)+y^2 \left(-2 (x-1) (x+5) c_p\right.\\ & \left.\left.\left.-(x-2) (12 x-31) x+16\right)+x y \left(x \left(2 c_p-9\right)+18\right)-2 y \left(c_p+3\right)-2 x+1\right)\right)-\frac{c_2 s x y }{1536 \pi ^3 (x-1)^2 (y-1)}\\ & m_c^3 \left(y \left(-y \left(11 (1-2 x)^2 c_p-6 x^2+8 x+24\right)+11 x y^4 \left((x-1) ((x-4) x+6) x c_p+c_p+(3 (x-2) x+2) x+1\right)\right.\right.\\ & +y^3 \left(3 (2 x ((3 (x-4) x-4) x+10)-5) c_p-(((59 x-104) x+44) x+8) x-15\right)+y^2 \left(((x (7 x+111)-111)\right.\\ & \left.\left.\left. x+26) c_p+2 ((5 x-7) x+7) x+30\right)+9\right)-1\right)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{1,7;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 }{3456 \pi ^3 (x-1)^2 (y-1)^2}m_c^2 \left(10 ((x-3) x+3) x y^6 \left(x^4 \left(5 c_p-1\right)-4 x^3 \left(c_p+3\right)+6 x^2\right.\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left. \left(c_p+5\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)-2 y^5 \left(12 x^6 \left(c_p+6\right)+4 x^5 \left(c_p-39\right)-5 x^4 \left(13 c_p+3\right)+4 x^3 \Big(61 c_p\right.\\ & \left.+31\Big)+42 x^2 \left(7-3 c_p\right)-72 x \left(c_p+1\right)+30 \left(c_p+1\right)\right)+6 y^4 \left(((x (((7 x-8) x+48) x+28)-84) x+26) c_p\right.\\ & \left.+(x (255-2 x (5 (x-3) x+23))-88) x+26\right)-y^3 \left(((x (5 (x+28) x+228)-452) x+152) c_p+(x (x (168\right.\\ & \left.-19 x)+930)-458) x+152\right)+y^2 \left(((x (15 x+98)-184) x+68) c_p+3 (x (21 x+88)-66) x+68\right)\\ & \left.+3 y \left((x (x+12)-4) c_p-(x-14) x-4\right)-9 x \left(c_p+1\right)\right)+\frac{c_2 y}{1536 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \left(3 y \left((x ((7 x-17) x\right.\right.\\ & \left.+11)-2) c_p+\left(-3 x^2+x+3\right) x-2\right)+10 x y^5 \left(((x ((x ((x-6) x+15)-20) x+19)-10) x+2) c_p\right.\\ & \left.+(x ((9 x-19) x+8)-2) (x-1)\right)+4 x y^4 \left((4 x ((x ((x-5) x+10)-19) x+14)-13) c_p+(46-x ((x (5 x\right.\\ & \left.+17)-90) x+106)) x-13\right)+x y^3 \Big(3 ((x ((x-3) x+66)-66) x+17) c_p+(x ((33 x-145) x+216)-112)\\ & x+51\Big)+y^2 \left((3-2 x ((x (3 x+44)-56) x+20)) c_p+2 (x ((7 x-18) x+12)-14) x+3\right)\\ & \left.+3 \left((1-2 x)^2 c_p+1\right)\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{c_1 }{3456 \pi ^3 (x-1)^3 (y-1)^2}m_c^2 \left(s (x-1) (y-1) \left(y \Big(35 ((x-3) x\right.\right.\\ & +3) x y^6 \left(x^4 \left(5 c_p-1\right)-4 x^3 \left(c_p+3\right)+6 x^2 \left(c_p+5\right)-8 x \left(c_p+1\right)+2 \left(c_p+1\right)\right)-y^5 \left(4 x^6 \left(24 c_p+109\right)\right.\\ & +7 x^5 \left(c_p-119\right)-5 x^4 \left(97 c_p+91\right)+2 x^3 \left(911 c_p+491\right)+9 x^2 \left(233-107 c_p\right)-486 x \left(c_p+1\right)+210\\ & \left. \left(c_p+1\right)\right)+y^4 \left(3 ((x (((56 x-65) x+344) x+241)-621) x+188) c_p+(x (((21-40 x) x-194) x+4797)\right.\\ & \left.-1527) x+564\right)-y^3 \left(((x ((85 x+364) x+1203)-1807) x+568) c_p+(x (x (552-29 x)+3291)-1465)\right.\\ & \left.x+652\right)+y^2 \left(((x (78 x+583)-773) x+262) c_p+(x (267 x+1087)-767) x+418\right)-2 y \left(3 ((13 x-24)\right.\\ & \left.\left.x+8) c_p+(61 x-114) x+77\right)-3 x \left(6 c_p+13\right)+30\Big)-2\right)-3 x m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1)\\ & \left.\left(2 y^2 \left(2 x \left(c_p-3\right)-c_p+4 x^2+3\right)-y \left((5 x-2) c_p+x+2\right)+c_p+1\right)\right)+\frac{c_2 y}{1536 \pi ^3 (x-1)^3 (y-1)^2} m_c^2\\ & \left(m_c^2 \left(4 x^2 c_p+y^4 \left(((x ((x ((x-6) x+15)-20) x+19)-10) x+2) c_p+(x ((x ((x-6) x+23)-36) x+27)\right.\right.\right.\\ & \left.-10) x+2\right)+2 y^3 \left((x ((x ((x-5) x+10)-18) x+13)-3) c_p+((x ((x-13) x+26)-24) x+11) x-3\right)\\ & +y^2 \left(((x ((x-4) x+30)-28) x+7) c_p+(x ((9 x-20) x+26)-16) x+7\right)-4 y \Big((1-2 x)^2 c_p+(x-1) x\\ & \left.+1\Big)-4 x c_p+c_p+1\right)-s (x-1) (y-1) \left(35 x y^6 \left(((x ((x ((x-6) x+15)-20) x+19)-10) x+2) c_p\right.\right.\\ & \left.+(x ((9 x-19) x+8)-2) (x-1)\right)+x y^5 \left((x ((59 x ((x-5) x+10)-1106) x+811)-188) c_p+(631\right.\\ & \left.-x ((x (70 x+247)-1290) x+1486)) x-188\right)+x y^4 \left(3 (2 (x ((3 x-11) x+132)-128) x+65) c_p\right.\\ & \left.+(x ((137 x-568) x+786)-406) x+223\right)+y^3 \left((6-x (4 (x (3 x+95)-107) x+131)) c_p+(x ((37 x\right.\\& \left.-120) x+84)-147) x+6\right)+y^2 \left(6 (3 x-2) (5 (x-1) x+1) c_p+(x (23-18 x)+49) x-12\right)\\ & \left.\left.\left. +x y \left(24 (x-1)\right.c_p-3 x-8\right)+y \left(6 c_p+9\right)+x-3\right)\right)\Bigg\},\\ \end{aligned} $

$\begin{aligned}[b]\rho^{\rm pert}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{x^2 }{51609600 \pi ^5 (y-1)^5}F(s,x,y)^3 c_1 \left((x-1) x \left((350 (4 y-3) y+(231-8 y (-266 x+5 ((x\right.\right.\\ & -14) x+42) y+147)) x y+35) x+(x (140 (4 y-1) y+(8 (5 x (20 x y+21)-28 (5 y+4)) y+483) x y-105)\\& \left.-70 (y-1)) c_p\right) F(s,x,y)^3+42 x \left((x-1) (y-1) s \left(\left(\left(\left(-20 ((x-14) x+42) y^2+6 (141 x-32) y-29\right) x\right.\right.\right.\right.\\ & \left.\left.+500 y-410\right) y+105\right) x y+\left(-20 (y-1) y+2 \Big(55 (2 y-1) y+\left(\left(115 x+40 \left(5 x^2-7\right) y-96\right) y+143\right) x y\right.\\ & \left.\left.-15\Big) x y-5\right) c_p\right)+\left(50 (y-1)+\left(-10 (3 y+10) y+((8 (7 x-8) y x-183 x+166) y+140) x y+2 (y (x (y (11 x\right.\right.\\ & \left.\left.\left.+8 ((x-9) x+5) y+68)-20)-40 y)+5) c_p+15\right) x\right) m_c m_s\right) F(s,x,y)^2+30 (y-1) \Big((x-1) (y-1) \\ & \left(50 \left(-(x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^3+14 \left((131 x+3) x+4 ((5 x+2) x+5) c_p+75\right) y^2+7 \left((82 x-30)\right.\right.\\ & \left.\left. c_p-35 (x+4)\right) y+385\right) s^2 x^2 y^2+14 \left(30 (y-1)+\left(\left(-2 \left(7 c_p+17\right) y x^2+5 \left(8 c_p y+12 y-2 c_p+3\right) x-20 y\right.\right.\right.\\ & \left.\left.\left. \left(c_p+2\right)-10\right) y+5\right) x\right) m_c^2 m_s^2+7 \left(10 (y+1) y+(-30 (y+4) y+((22 (7 x-8) y x-419 x+330) y+346) x y\right.\\ & \left.-125) x y+2 (y ((((2 y (34 x+11 ((x-9) x+5) y+75)-107) x-110 y+30) y+30) x+10 y)-5) c_p+20\right) s x\\ & \left.m_c m_s\Big) F(s,x,y)+120 (y-1)^2 s \left((x-1) (y-1) \left(\left(4 \left(-(x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^2+14 \left(\Big(9 x+4 c_p\right.\right.\right.\right.\right.\\ & \left.\left.\left.+3\Big) x+5\right) y+7 \left(4 c_p-5\right) x-70\right) y+35\right) s^2 x^2 y^3+7 \left(10 (y-1) y+\left(y (x ((4 (7 x-8) y x-77 x+82) y+44)\right.\right.\\ & \left.\left.-30 y)+2 (2 y (9 x+2 ((x-9) x+5) y-5)-5) (x y-1) c_p-25\right) x y+10\right) s x m_c m_s y+14 \left(\left(-4 \left((17 x-30) x\right.\right.\right.\\ & \left.\left.\left.\left.\left.+((7 x-20) x+10) c_p+20\right) x y^2+5 \left(\left(x+(4-8 x) c_p+6\right) x+6\right) y+10 \left(c_p-2\right) x-30\right) y+15\right) m_c^2 m_s^2\right)\right),\\ \rho^{\langle\bar{s}s\rangle}_{2,8;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 (x-1) x^2}{3072 \pi ^3 (y-1)^3} m_c F(s,x,y)^2 \Big(4 s (y-1) y (11 x y-5) (2 x y-1) F(s,x,y)+(x y-1)\\& (8 x y+1) F(s,x,y)^2+12 s^2 (y-1)^2 y^2 (x y (4 x y-3)+1)\Big),\\ \rho^{\langle m_s\bar{s}s\rangle}_{2,8;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x}{6144 \pi ^3 (y-1)^3} F(s,x,y) \left(12 s (y-1) F(s,x,y) \left(2 m_c^2 \Big(x y \left(-4 ((x-2) x+2) y^2+6 y-3\right)\right.\right.\\ & \left.+2 (y-1) y+1\Big)+s (x-1) x (y-1) y^2 \left(y \left(50 ((x-2) x+2) x y^2-2 (x+15) (2 x+1) y+29 x+28\right)-11\right)\right)\\ & +4 F(s,x,y)^2 \left(4 m_c^2 (y (-((x-2) x+2) x y+x+1)-1)+s (x-1) x (y-1) y (y (x (2 y (70 ((x-2) x+2) y-11 x\right.\\ & \left.-68)+57)-100 y+82)-21)\right)+(x-1) c_p \left((x (y (-8 ((x-4) x+2) y-15 x+4)+3)+2 (y-1)) F(s,x,y)^2\right.\\& -4 s (y-1) (2 y (x (y (11 ((x-4) x+2) y+25 x-11)-3)-2 y+2)-1) F(s,x,y)-24 s^2 x (y-1)^2 y^3 (2 ((x-4) x\\ & \left.+2) y+5 x-3)\right) F(s,x,y)+(x-1) x \left(40 ((x-2) x+2) x y^3-8 ((x+3) x+5) y^2+3 (x+10) y-1\right) F(s,x,y)^3\\ & \left.+24 s^3 (x-1) x (y-1)^3 y^3 \left(y \left(x \left(4 ((x-2) x+2) y^2-6 y+3\right)-2 y+2\right)-1\right)\right),\\ \rho^{\langle g_sG^2\rangle}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{x^2 c_1}{30965760 \pi ^5 (x-1)^3 (y-1)^5} m_c \left((x-1) x \left((-350 (4 y-3) y+(8 y (-266 x+5 ((x-14) x\right.\right.\\ & +42) y+147)-231) x y-35) (x y-1) ((x+((x-3) x+3) y-3) y+1) (-x) m_c+21 \left(8 ((x ((7 x-41) x+101)\right.\\& -108) x+40) x^2 y^5+(x (((23-31 x) x-469) x+1056)-610) x y^4+(((x (25 x+541)-1020) x+320) x\\ & \left.+310) y^3+(13 x (x (5-14 x)+35)-600) y^2+5 ((23 x-65) x+74) y+45 x-80\right) m_s+c_p \left((x y-1) ((x+((x\right.\\ & -3) x+3) y-3) y+1) (x (140 (4 y-1) y+(8 (5 x (20 x y+21)-28 (5 y+4)) y+483) x y-105)-70 (y-1)) m_c\\ & +42 \left(8 ((x ((x-13) x+38)-44) x+15) x^2 y^5+(x ((x (27 x-71)-7) x+278)-140) x y^4+((((103-15 x) x\right.\\ & \left.\left.\left.-330) x+100) x+20) y^3+(x (x (95-16 x)+35)-30) y^2-5 (x (x+7)-2) y+5 x\right) m_s\right)\right) F(s,x,y)^3\\ & +21 \left((y ((x ((x-3) x+3) y-3) y+3)-1) \left(50 (y-1)+\left(-10 (3 y+10) y+((8 (7 x-8) y x-183 x+166) y\right.\right.\right.\\ & \left.\left.+140) x y+2 (y (x (y (11 x+8 ((x-9) x+5) y+68)-20)-40 y)+5) c_p+15\right) x\right) x m_s m_c^2+(x-1) (y-1)\\ & \left(s x (y ((x ((x-3) x+3) y-3) y+3)-1) \left(\Big(\left(\left(-20 ((x-14) x+42) y^2+6 (141 x-32) y-29\right) x+500 y-410\right) y\right.\right.\\ & \left.+105\Big) x y+\left(-20 (y-1) y+2 \left(55 (2 y-1) y+\left(\left(115 x+40 \left(5 x^2-7\right) y-96\right) y+143\right) x y-15\right) x y-5\right) c_p\right)\\ \end{aligned} $

$ \begin{aligned}[b] & -6 ((((x-2) x+2) y-2) y+1) \left(x \Big(y \left(2 \left(7 c_p+17\right) y x^2-5 \left(8 c_p y+12 y-2 c_p+3\right) x+20 \left(c_p+2\right) y+10\right)\right.\\ & \left.\left.-5\Big)-30 (y-1)\right) m_s^2\right) m_c+3 (x-1) (y-1) \left(22 \left((x ((7 x-41) x+101)-108) x+2 ((x ((x-13) x+38)-44)\right.\right.\\ & \left.x+15) c_p+40\right) x^2 y^6+\left((x ((x+367) x+377)-2040) (-x)+4 (x (2 (28 x-61) (x-1) x+305)-185) c_p\right.\\ & \left.-1370\right) x y^5+\left(3 ((11 x (5 x+33)-864) x+440) x+(2 (((287-45 x) x-1041) x+400) x+100) c_p+470\right) y^4\\ & -\left(((558 x-757) x+5) x+2 (((49 x-421) x+20) x+80) c_p+900\right) y^3+\left((181 x-315) x-2 (62 x+105) c_p x\right.\\ & \left.\left.\left.+70 c_p+620\right) y^2+5 \left(3 x+2 (7 x+1) c_p\right) y-170 y-10 c_p+20\right) s x m_s\right) F(s,x,y)^2-6 (y-1) \left(14 (y ((x ((x\right.\\ & -3) x+3) y-3) y+3)-1) \left(x \left(y \left(2 \left(7 c_p+17\right) y x^2-5 \left(8 c_p y+12 y-2 c_p+3\right) x+20 \left(c_p+2\right) y+10\right)-5\right)\right.\\ & \left.-30 (y-1)\right) m_s^2 m_c^3-7 s x (y ((x ((x-3) x+3) y-3) y+3)-1) \left(10 (y+1) y+(-30 (y+4) y+((22 (7 x-8) y x\right.\\ & -419 x+330) y+346) x y-125) x y+2 (y ((((2 y (34 x+11 ((x-9) x+5) y+75)-107) x-110 y+30) y\\ & \left.+30) x+10 y)-5) c_p+20\right) m_s m_c^2-s (x-1) (y-1) \left(s x^2 y^2 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(50 \left(-(x\right.\right.\right.\\ & \left.-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^3+14 \left((131 x+3) x+4 ((5 x+2) x+5) c_p+75\right) y^2+7 \left((82 x-30) c_p\right.\\ & \left.\left.-35 (x+4)\right) y+385\right)-42 ((((x-2) x+2) y-2) y+1) \left(y \left(4 \left((17 x-30) x+((7 x-20) x+10) c_p+20\right) x y^2\right.\right.\\ & \left.\left.\left.+5 \left(x \left(-x+(8 x-4) c_p-6\right)-6\right) y-10 x \left(c_p-2\right)+30\right)-15\right) m_s^2\right) m_c-21 s^2 (x-1) x (y-1) y \left(\left(4 \left((x ((7 x\right.\right.\right.\\ & \left.-41) x+101)-108) x+2 ((x ((x-13) x+38)-44) x+15) c_p+40\right) x^2 y^5+\left((x ((x+67) x+51)-352)\right.\\ & \left. (-x)+4 (x (((11 x-38) x+36) x+43)-30) c_p-250\right) x y^4+\left(\left((x (35 x+163)-468) x+2 (((39-5 x) x\right.\right.\\ & \left.\left. -189) x+90) c_p+300\right) x+70\right) y^3-\left(\left(16 \left(c_p+6\right) x^2-\left(188 c_p+193\right) x+70 c_p+125\right) x+140\right) y^2\\ & \left. \left.\left.+\left(\left(9 x-2 (18 x+5) c_p+5\right) x+120\right) y+5 \left(2 c_p-1\right) x-50\right) y+10\right) m_s\right) F(s,x,y)+6 (y ((x ((x-3) x+3) y\\ & -3) y+3)-1) (y-1)^2 s m_c \left((x-1) (y-1) \left(\left(4 \left(-(x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^2+14 \left(\left(9 x+4 c_p+3\right)\right.\right.\right.\right.\\ & \left.\left. \left.x+5\right) y+7 \left(4 c_p-5\right) x-70\right) y+35\right) s^2 x^2 y^3+7 \left(10 (y-1) y+\left(y (x ((4 (7 x-8) y x-77 x+82) y+44)\right.\right.\\ & \left.\left.-30 y)+2 (2 y (9 x+2 ((x-9) x+5) y-5)-5) (x y-1) c_p-25\right) x y+10\right) s x m_c m_s y+14 \left(\left(-4 \left((17 x-30) x\right.\right.\right.\\ & \left.\left.\left.\left.\left.+((7 x-20) x+10) c_p+20\right) x y^2+5 \left(\left(x+(4-8 x) c_p+6\right) x+6\right) y+10 \left(c_p-2\right) x-30\right) y+15\right) m_c^2 m_s^2\right)\right)\\ & +\frac{c_3}{23592960 \pi ^5 (y-1)^3} (x-1) x^2 \left(c_p+1\right) F(s,x,y)^2 \Big(8 s (y-1) y ((393 x-200) y+73) F(s,x,y)+((477 x\\ & -230) y+43) F(s,x,y)^2+24 s^2 (y-1)^2 y^2 ((64 x-30) y+15)\Big)\Bigg\},\\ \rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Big\{-\frac{c_1 x }{3072 \pi ^3 (y-1)^3}m_c F(s,x,y) \left(3 s (y-1) \left(y c_p \left(x \left(2 y \left(22 (x-1) x y^2-4 (x-1) (3 x+5)y\right.\right.\right.\right.\right.\\ & \left.\left.\left.\left.+13 x-9\right)-7\right)-2 y\right)+c_p+y (x (y (x (y (66 (x-1) y-41 x-23)+42)+69 y-28)-15)-21 y+19)-2\right)\\ & F(s,x,y)+\Big(x \left(y \left(2 (x-1) c_p (y (8 x y-2 x-7)+1)+x (y (24 (x-1) y-9 x-13)+7)+25 y-12\right)+2\right)-y\\ & +1\Big) F(s,x,y)^2+6 s^2 (y-1)^2 y \left(y \left(x \left(2 c_p (x y-1) (2 (x-1) (2 y-1) y+1)+y (x (y (12 (x-1) y-7 x-3)+6)\right.\right.\right.\\ & \left.\left.\left.\left.+11 y-2)-4\right)-5 y+5\right)-1\right)\right)-\frac{c_2 x^2}{2048 \pi ^3 (y-1)^3} m_c F(s,x,y) \left(3 s (y-1) y \left(x y \left(44 (x-1) y^2+(26-39 x) y\right.\right.\right.\\ & \left.\left.+11\right)+18 (y-1) y+2\right) F(s,x,y)+(x y (y (16 (x-1) y-13 x+6)+4)+10 (y-1) y+3) F(s,x,y)^2+6 s^2\\& \left.(y-1)^2 y^3 \left(8 (x-1) x y^2+(x (6-7 x)+2) y+x-2\right)\right)\Bigg\},\\ \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1}{9216 \pi ^3 (y-1)^2} \left(c_p \left(12 s x (y-1) y F(s,x,y) \left(6 m_c^2 (2 y (((x-4) x+2) y+2 x-1)-1)\right.\right.\right.\\ & \left.+s (x-1) (y-1) y^2 \left(x \left(50 \left(x^2-2\right) y^2+8 (x+7) y+11\right)-4 y+3\right)\right)+3 F(s,x,y)^2 \left(12 x y m_c^2 (((x-4) x+2) y\right.\\ & \left.+x)+s (x-1) (y-1) \left(2 x y \left(y \left(7 x \left(y \left(20 \left(x^2-2\right) y+7 x+24\right)-1\right)-22 y+11\right)+3\right)+4 (y-1) y+1\right)\right)\\ \end{aligned} $

$ \begin{aligned}[b] & +(x-1) \left(x \left(y \left(x \left(8 y \left(10 \left(x^2-2\right) y+9 x+8\right)-21\right)-16 y+4\right)+3\right)+2 (y-1)\right) F(s,x,y)^3+24 s^3 (x-1) x^2\\ & \left. (y-1)^3 y^4 \left(2 y \left(\left(x^2-2\right) y+1\right)+1\right)\right)+x \left(-6 s (y-1) y F(s,x,y) \left(6 m_c^2 (y (x+8 y-12)+5)-s (x-1) (y-1)\right.\right.\\& \left. y (y (x (2 y (25 (5 (x-2) x+6) y+119 x-183)+139)-30 y+28)-11)\right)+3 F(s,x,y)^2 \left(s (x-1) (y-1) y (y \right.\\ & \left.(x (14 y (x (50 (x-2) y+51)+60 y-72)+313)-100 y+82)-21)-6 m_c^2 (y (3 x+4 y-8)+1)\right)+(x-1)\\ & (y (x (8 y (5 (5 (x-2) x+6) y+32 x-39)+51)-40 y+30)-1) F(s,x,y)^3+6 s^3 (x-1) (y-1)^3 y^3 \Big(y \Big(x \Big(4 (5\\ & \left.\left. (x-2) x+6) y^2+6 (3 x-5) y+13\Big)-2 y+2\Big)-1\Big)\right)\right)-\frac{c_2}{8192 \pi ^3 (y-1)^3} x \left(2 \left(6 s (y-1)^2 y F(s,x,y) \left(m_c^2 (2 x y\right.\right.\right.\\ & \left. (3-4 x y)-2)+s x y^2 (x (x y (5 y (10 (x-1) y-10 x+3)+36)+7 (5 y-4) y-8)-9 y+9)\right)+3 (y-1)\\ & F(s,x,y)^2 \left(s x y (y (x (5 x y (2 y (14 (x-1) y-14 x+5)+19)+90 (y-1) y-7)-10 y+14)-2)-2 m_c^2 (x y-1)\right.\\ & \left. (2 x y+1)\right)+x (y (x (y (x (20 y (2 x (y-1)-2 y+1)+23)+20 y-34)+8)+8 y-2)-3) F(s,x,y)^3+6 s^3\\ & \left. (x-1) x (y-1)^4 y^4 (x y (4 x y-3)+1)\right)+c_p \left(3 s (y-1) \left(y \left(x \left(2 y \Big(22 (x-1) x y^2-6 (x-1) (2 x+5) y+23 x\right.\right.\right.\right.\\ & \left.\left.\left.-24\Big)+3\right)-4 y+4\right)-1\right) F(s,x,y)+2 (x-1) (x y (y (8 x y-2 x-13)+7)+y-1) F(s,x,y)^2+12 s^2 x (y-1)^2\\ & \left.\left. y^2 \left(y \left(4 (x-1) x y^2-2 (x-1) (x+3) y+5 x-6\right)+1\right)\right) F(s,x,y)\right)\Bigg\},\\ \rho^{\langle\bar{s}s\bar{s}s\rangle}_{2,8;A(S)}(s) =& \int^{z_{max}}_{z_{min}}{\rm d}z\frac{c_1 c_p}{768 \pi } m_s^2 G(s,z) \left(G(s,z)+s (1-2 z)^2\right),\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{2,8;A(S)}(s) =& \int^{z_{\max}}_{z_{\min}}{\rm d}z\Bigg\{-\frac{c_1}{2304 \pi } \left(m_c m_s \left(s \left(z^2 \left(-\left(6 c_p+23\right)\right)+3 \left(c_p-2\right)+17 z\right)-11 G(s,z)\right)+m_s^2 \left(\left(-8 z^2 \left(3 c_p+5\right)\right.\right.\right.\\ & \left.\left.+2 z \left(7 c_p+15\right)+c_p-1\right) G(s,z)-s (z-1) z \left(6 (11 z-8) z c_p+c_p+2 (50 z-41) z+21\right)\right)+6 m_c^2 (2 G(s,z)\\ & \left.+2 s (z-1) z+s)\right)+\frac{c_2 c_p}{2048 \pi } m_s^2 \left(2 G(s,z)+s (1-2 z)^2\right)\Bigg\}+\int^{1}_{0}{\rm d}z\Bigg\{\frac{c_1 s^2 (z-1) z}{2304 \pi } m_s \left((z-1) z m_s \left((2 (6 z-5) z\right.\right.\\ & \left.\left.+1) c_p+30 z^2-28 z+11\right)+(7 (z-1) z+3) m_c\right)\Bigg\},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{2,8;A(S)}(s) =& \int^{x_{max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^2}{18432 \pi ^3 (x-1)^2 (y-1)^3} m_c \left(2 F(s,x,y) \left(m_c^2 (x y-1)^2 (y (((x-3) x+3) y+x-3)+1)\right.\right.\\ & \left. (8 x y+1)+3 s (x-1) (y-1) y (x y (y (x (y (22 (x-1) y-17 x-19)+29)+41 y-28)-4)-13 (y-1) y-2)\right)\\ & +3 (x-1) (x y-1) (x (8 y-5) y ((x-1) y-1)+11 (y-1) y+3) F(s,x,y)^2+2 s (y-1) y \left(m_c^2 (11 x y-5) (x y-1)\right.\\ & (2 x y-1) (y (((x-3) x+3) y+x-3)+1)+3 s (x-1) (y-1) y^2 \left(y \left(x \Big(x \left(4 (x-1) y^2-3 (x+1) y+5\right)+7 y\right.\right.\\ & \left.\left.\left.\left.-6\Big)-1\right)+1\right)\right)\right)\Bigg\}-\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s^2 x^2 y^2}{9216 \pi ^3 (x-1)^2 (y-1)} m_c^3 (x y-1) (x y (4 x y-3)+1) (y (((x-3) x+3) y\\ & +x-3)+1),\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x}{18432 \pi ^3 (x-1)^3 (y-1)^3} m_c^2 \left((x-1) \left(c_p (x y-1) (y (((x-3) x+3) y+x-3)+1) (x (y (8\right.\right.\\& ((x-4) x+2) y+15 x-4)-3)-2 y+2)-40 x^3 ((x-3) x+3) ((x-2) x+2) y^6+8 \Big(\left(x^3+14 x-36\right) x\\ & +45\Big) x^2 y^5+3 (x (x (3 (x-21) x+131)-166)-24) x y^4+(x (((41 x-95) x+224) x+162)-24) y^3+((x (4 x\\ & \left.-45)-109) x+48) y^2+3 (x (x+7)-12) y-x+12\right) F(s,x,y)+4 m_c^2 (x y-1) (y (((x-3) x+3) y+x-3)\\ & +1) \left(((x-2) x+2) x y^2-(x+1) y+1\right)+s (x-1) (y-1) \left(c_p (2 y (x (y (11 ((x-4) x+2) y+25 x-11)-3)\right.\\ & -2 y+2)-1) (x y-1) (y (((x-3) x+3) y+x-3)+1)+y \left(-140 x^3 ((x-3) x+3) ((x-2) x+2) y^6+2 ((x\right.\\ & ((11 x+35) x+89)-366) x+570) x^2 y^5-x (((x (33 x+427)-1041) x+1686) x+204) y^4+(x (((161 x\\ \end{aligned} $

$ \begin{aligned}[b] & \left.\left.\left.-361) x+1078) x+402)-24) y^3+((x (20 x-379)-277) x+48) y^2+17 (3 x+5) x y-3 x-48 y+24\right)-6\right)\right)\Bigg\}\\ &+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Big\{\frac{c_1 s x}{18432 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \left(2 m_c^2 \left(y \left(x \left(4 ((x-2) x\right.\right.\right.\right.\\ & \left.\left.\left.+2) y^2-6 y+3\right)-2 y+2\right)-1\right)-s (x-1) x (y-1) y^2 \left(y \left(-2 c_p (2 ((x-4) x+2) y+5 x-3)+50 ((x-2) x\right.\right.\\ & \left.\left.\left.+2) x y^2-2 (x+15) (2 x+1) y+29 x+28\right)-11\right)\right)\Big\},\\ \rho^{\langle g_sG^2\rangle^2}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^3 y^3}{371589120 \pi ^5 (x-1)^2 (y-1)^2} m_c^4 \Big(c_p (x (x y (8 y (5 x (20 x y+21)-28 (5 y+4))+483)\\ & +140 (4 y-1) y-105)-70 (y-1))+x (x y (8 y (7 (38 x-21)-5 ((x-14) x+42) y)+231)+350 (4 y-3) y\\ & +35)\Big)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x^3 y^3 }{53084160 \pi ^5 (x-1)^2 (y-1)}m_c^4 \left(c_p \left(2 x y \left(x y \left(y \left(40 \left(5 x^2-7\right) y+115 x-96\right)+143\right)\right.\right.\right.\\ & \left.\left.+55 (2 y-1) y-15\right)-20 (y-1) y-5\right)+x y \left(y \Big(x \left(-20 ((x-14) x+42) y^2+6 (141 x-32) y-29\right)+500 y\right.\\ & \left.\left.-410\Big)+105\right)\right)\Bigg\},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{2,8;A(S)}(s) =& \int^{x_{max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x}{36864 \pi ^3 (x-1)^3 (y-1)^3} m_c \left(3 (x-1) \left(8 (2 x-3) (x-1) x^2 y^5 \left(2 (x-1) c_p+x+1\right)+y^3\right.\right.\\ & \left(2 (x (2 x-27)-2) (x-1)^2 c_p+\left(\left(22 x^2-30 x-111\right) x+94\right) x+13\right)-x y^4 \left(10 (2 (x-1) x-5) (x-1)^2 c_p\right.\\ & \left.+((x (x+58)-149) x+50) x+37\right)+y^2 \left(2 (8 x+3) (x-1)^2 c_p+((92-13 x) x-33) x-28\right)-y \Big(2 (x-1)^2 c_p\\ & \left.+(15 x+16) x-19\Big)+7 x-4\right) F(s,x,y)+m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \left(x \left(y \left(2 (x-1) c_p (y (x (8 y\right.\right.\right.\\ & \left.\left.\left.-2)-7)+1)+x (y (24 (x-1) y-9 x-13)+7)+25 y-12\right)+2\right)-y+1\right)+3 s (x-1) (y-1) \Big(22 (2 x-3)\\ & (x-1) x^2 y^6 \left(2 (x-1) c_p+x+1\right)-x y^5 \left(4 (x (17 x-4)-17) (x-2) (x-1) c_p+((x (19 x+98)-329) x\right.\\ & \left.+118) x+89\right)+y^4 \left(2 (x (x ((7 x-89) x+177)-87)-5) c_p+((x (67 x-104)-231) x+246) x+5\right)+y^3\\ & \left((((45 x-127) x+47) x+16) c_p+((205-36 x) x-132) x-14\right)+y^2 \left((4 x (3 x+4)-7) c_p+5 x (2-5 x)-2\right)\\ & \left.-y \left(8 x c_p+c_p+x-9\right)+c_p-2\Big)\right)-\frac{c_2 x^2 y}{24576 \pi ^3 (x-1)^2 (y-1)^2} m_c^3 (x y-1) \Big(y (x (y (8 ((x-3) x+3) y+6 x\\& -15)+3)-9 y+9)-2\Big)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{c_1 s x}{36864 \pi ^3 (x-1)^3 (y-1)^2} m_c \left(m_c^2 (y (y (x ((x-3) x+3) y-3)\right.\\ & +3)-1) \left(y c_p \left(x \left(2 y \left(22 (x-1) x y^2-4 (x-1) (3 x+5) y+13 x-9\right)-7\right)-2 y\right)+c_p+y (x (y (x (y (66 (x-1) y\right.\\ & \left.-41 x-23)+42)+69 y-28)-15)-21 y+19)-2\right)+3 s (x-1) (y-1) y \left(y \left(4 (2 x-3) (x-1) x^2 y^5 \Big(2 (x\right.\right.\\& -1) c_p+x+1\Big)-x y^4 \left(4 (x (3 x-1)-3) (x-2) (x-1) c_p+(3 x (x+8)-11) (x-2) x+15\right)+y^3 \left(2 (x ((x-15)\right.\\ & \left.x+33)-18) x c_p+(x (11 x-6)-48) (x-1) x-3\right)+y^2 \left(x \left(2 (2 (2 x-7) x+7) c_p+x (37-6 x)-33\right)+6\right)\\ & \left.\left.\left. y \left((4 x+2) c_p-5 x+9\right)-2 x \left(c_p+1\right)-8 y+5\right)-1\right)\right)-\frac{c_2 s x^2 y^2}{24576 \pi ^3 (x-1)^2 (y-1)} m_c^3 \Big(x y (y (x (y (22 ((x\\ & -3) x+3) y-4 x+17)-2)-83 y+60)-17)+23 (y-1) y+7\Big)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{2,8;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1}{110592 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \left(8 x^2 y^5 \left((((x (9 x-19)-29) x+30) x+54) c_p+(((32 x\right.\right.\\ & \left.-135) x+133) x+48) x-105\right)+40 ((x-3) x+3) x^3 y^6 \left(2 \left(x^2-2\right) c_p+5 (x-2) x+6\right)+x y^4 \left((x ((15 x+91)\right.\\ & \left.x+143)-1098) x c_p+198 c_p+3 ((x (17 x+159)-659) x+630) x-24\right)+y^3 \left((x (x (x (61-41 x)+790)\right.\\ & \left.-210)-6) c_p+(((1423-255 x) x-1728) x+222) x\right)+y^2 \left(((91-x (36 x+343)) x+12) c_p+((609-274 x)\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.\left.x-263) x\right)+y \left((x (57 x+5)-8) c_p+21 x (7-5 x)\right)-3 x c_p+2 c_p-17 x\right)+\frac{c_2 x y}{49152 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \Big(y^2 \\ & \left(x^3 \left(-\left(c_p+3\right)\right)+x^2 \left(94-33 c_p\right)+3 x \left(c_p+7\right)+4 c_p\right)+4 x y^4 \left(2 ((x ((x-4) x+6)-6) x+2) c_p+(((2 x-11)\right. \\ & \left.x+21) x+16) x+10\right)+y^3 \left((x (x ((5 x-14) x+54)-18)-2) c_p+(3 x (x+1) (8 x-31)-70) x\right)+y \left((2 x (5 x\right.\\ & \left.+2)-3) c_p+7 x (1-3 x)+6\right)-2 x c_p+c_p-40 x^2 ((x-2) ((x-2) x+2) x+2) y^5-2 x-6\Big)\Bigg\}\\ & +\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1}{110592 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(c_p \left(-12 x y m_c^2 (x y-1) (((x-4) x+2) y+x) (y (((x-3) x+3) y\right.\right.\\ & +x-3)+1)-s (x-1) (y-1) \left(y \left(2 (((7 x (7 x+3)-799) x+570) x+774) x^2 y^5+280 \left(x^2-2\right) ((x-3) x+3)\right.\right.\\ & x^3 y^6+2 ((x ((29 x+236) x+233)-1749) x+216) x y^4-2 (((x (65 x+116)-1324) x+321) x+6) y^3\\ & \left.\left.\left.+((311-x (61 x+885)) x+24) y^2+(2 x (79 x-2)-19) y-42 x+7\right)-1\right)\right)+x \left(6 m_c^2 (x y-1) (y (3 x+4 y-8)\right.\\ & +1) (y (((x-3) x+3) y+x-3)+1)-s (x-1) (y-1) y \left(y \left(140 ((x-3) x+3) (5 (x-2) x+6) x^2 y^5+2 (x ((21\right.\right.\\ & (17 x-75) x+1483) x+738)-1410) x y^4+(((x (313 x+1243)-5793) x+6078) x+12) y^3+(((3857\\& \left.\left.\left.\left.-739 x) x-5334) x+174) y^2+(3 (721-268 x) x-347) y-331 x+251\right)-69\right)\right)\right)\\ & -\frac{c_2 x y}{98304 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(s (x-1) (y-1) \left(y c_p \left(-44 x ((x ((x-4) x+6)-6) x+2) y^4+4 ((((23-8 x) x\right.\right.\right.\\ & \left.-82) x+31) x+2) y^3-2 (((x-112) x+28) x+8) y^2+(14-x (67 x+14)) y+14 x-6\right)+c_p+2 \left(x y \left(y \Big(140\right.\right.\\ & ((x-2) ((x-2) x+2) x+2) x y^4-2 ((((11 x-58) x+108) x+158) x+50) y^3+((5 x (23-8 x)+519) x\\ & \left.\left.\left.+182) y^2+(2 (x-182) x-135) y+73 x+57\Big)-5\right)-18 (y-1) y-6\right)\right)-4 m_c^2 \left(2 ((x-2) ((x-2) x+2) x+2)\right.\\ & \left.\left.x y^4+((x-4) x (x+1)-2) y^3+(x (6-(x-3) x)+4) y^2-(5 x+3) y+x+1\right)\right)\Bigg\},\\ \end{aligned} $

$ \begin{aligned}[b] \rho^{pert}_{3,9;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{{\rm i} x^2}{51609600 \pi ^5 (y-1)^5} F(s,x,y)^3 c_1 \left((x-1) x \left(-40 \left((27 x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x^2\right.\right.\\ & y^3-56 x \left(7 (12 x-7) x+((3 x-4) x+10) c_p+25\right) y^2+7 \left(x (140-57 x)+(x (50-99 x)+10) c_p\right) y\\ & \left.+35 \left(x+(3 x-2) c_p\right)\right) F(s,x,y)^3+42 x \left(\left(-20 c_p (y-1)-110 (y-1)-75 x+((y (443 x-8 ((27 x-88) x\right.\right.\\ & +40) y-1026)-120) x+470 y+140) x y+2 (y ((50-y (41 x+8 ((x-9) x+5) y+38)) x+40 y-20)-15) x\\ & \left. c_p\right) m_c m_s-s (x-1) (y-1) y \left((100 (5 y-4) y+(2 (909 x+10 (x (27 x-14)-42) y-364) y+127) x y+95) x\right.\\ & \left.\left.+2 \left(x \left(y \left(\left(\left(3 x+40 \left(5 x^2-7\right) y+16\right) y+144\right) x+110 y-80\right)-15\right)-10 (y-1)\right) c_p\right)\right) F(s,x,y)^2+30 (y-1)\\& \left((x-1) (y-1) \left(50 \left((27 x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^3-14 \left(-303 x^2+93 x+4 (2 x-5) (3 x+1) c_p-75\right)\right.\right.\\ & \left.y^2+7 \left(37 x+20 (3 x-2) c_p-130\right) y+315\right) \left(-s^2\right) x^2 y^2+14 \left(x \left(y \left(-75 x+2 \left((37 x-50) x+((7 x-20) x\right.\right.\right.\right.\\ & \left.\left.\left.\left.+10) c_p+20\right) y+5 (6 x-4) c_p+70\right)-5\right)-30 (y-1)\right) m_c^2 m_s^2-7 s x \left(\left((-10 (115 y+12) y+((-719 x+22 ((27 \right.\right.\\ & x-88) x+40) y+2190) y+26) x y+95) x+350 y+4 (10 (y-1)+(((y (59 x+11 ((x-9) x+5) y+50)-71) x\\ & \left.\left.\left.-55 y+35) y+15) x) c_p-270\right) y+60\right) m_c m_s\right) F(s,x,y)-120 s (y-1)^2 \left((x-1) (y-1) \left(70 (y-1) y+\left(4 \Big((27 x\right.\right.\right.\\ & \left.\left.-14) x+4 \left(5 x^2-7\right) c_p-42\Big) y^2-14 \left(-23 x+4 (x-2) c_p+5\right) y+21\right) x y+35\right) s^2 x^2 y^3+7 \left(50 (y-1) y\right.\\ & +\Big(\left((y (-97 x+4 ((27 x-88) x+40) y+342)-16) x-190 y+8 (7 x+((x-9) x+5) y-5) (x y-1) c_p+20\right) y\\ & \left.+5\Big) x y+20\right) s x m_c m_s y+14 \left(30 (y-1) y+\left(-4 \left(\left(7 c_p+37\right) x^2-10 \left(2 c_p+5\right) x+10 \left(c_p+2\right)\right) y^2-5 (3 x-2)\right.\right.\\ & \left.\left.\left.\left. \left(4 c_p-3\right) y+10\right) x y+15\right) m_c^2 m_s^2\right)\right), \end{aligned} $

$ \begin{aligned}[b] \rho^{\langle\bar{s}s\rangle}_{3,9;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^2}{3072 \pi ^3 (y-1)^4} m_c F(s,x,y)^2 \left(4 s (y-1) (y (x (y (x (y (22 (x-3) (2 x-1) y-34 x+153)\right.\\ & -12)-75 y-4)+9)+19 y-15)+3) F(s,x,y)+(x y-1) (x (y (8 (x-3) (2 x-1) y-8 x+13)-5)-5 y+5)\\ & \left. F(s,x,y)^2+12 s^2 (y-1)^2 y (y (x y (x (y (4 (x-3) (2 x-1) y-4 x+25)-4)-13 y+2)+x+3 (y-1))+1)\right),\\ \rho^{\langle m_s\bar{s}s\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x}{6144 \pi ^3 (y-1)^3} F(s,x,y) \left(12 s (y-1) F(s,x,y) \left(2 m_c^2 (y (x (2 y (2 ((5 x-6) x+2) y-2 x+1)\right.\right.\\ & \left.-1)-2 y+2)-1)+s (x-1) x (y-1) y^2 (y (x (2 y (25 (x (3 x-2)-2) y+130 x-21)+11)+30 y-26)+9)\right)\\ & +4 F(s,x,y)^2 \left(4 m_c^2 (y (x (((5 x-6) x+2) y-4 x+3)-1)+1)+s (x-1) x (y-1) y (x y (2 y (70 (x (3 x-2)-2) y\right.\\ &\left.+385 x-88)+35)+20 (5 y-4) y+19)\right)+(x-1) c_p \left(8 s (y-1) y (x (y (11 ((x-4) x+2) y+30 x-16)-3)\right.\\ & -2 y+2) F(s,x,y)+(x (y (8 ((x-4) x+2) y+21 x-10)-3)-2 y+2) F(s,x,y)^2+48 s^2 x (y-1)^2 y^3 (((x-4)\\ & \left. x+2) y+3 x-2)\right) F(s,x,y)+(x-1) x (y (x (8 y (5 (x (3 x-2)-2) y+35 x-13)+13)+40 y-28)-1)\\ & \left. F(s,x,y)^3+24 s^3 (x-1) x (y-1)^3 y^3 \left(y \left(4 (x (3 x-2)-2) x y^2+2 ((10 x-1) x+1) y+x-2\right)+1\right)\right), \end{aligned} $

$\begin{aligned} \rho^{\langle g_sG^2\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{x^2 c_1}{30965760 \pi ^5 (x-1)^3 (y-1)^5} m_c \left((x-1) x \left(\left(y \left(40 (x (27 x-14)-42) x y^2+56 (7 (12 x-7)\right.\right.\right.\right.\\ & \left.\left. x+25) y+399 x-980\right)-35\right) (x y-1) ((x+((x-3) x+3) y-3) y+1) x m_c+21 \left(8 ((x (3 (9 x-47) x+281)\right.\\ & -268) x+80) x^2 y^5+(x (((1743-451 x) x-2629) x+2836)-1050) x y^4+((((121-15 x) x-900) x+120) x\\ & \left.+370) y^3+(x ((38 x-175) x+695)-660) y^2+5 (3 (9 x-23) x+74) y+45 x-80\right) m_s+c_p \Big((x y-1)\\ & ((x+((x-3) x+3) y-3) y+1) \Big(x \left(70 (8 y-5) y+\left(8 y \left(7 (3 x-4)+20 \left(5 x^2-7\right) y\right)+693\right) x y-105\right)-70\\& (y-1)\Big) m_c+42 \Big(8 ((x ((x-13) x+38)-44) x+15) x^2 y^5+(x (((57 x-191) x+173) x+188)-140) x y^4\\ & +((((103-15 x) x-420) x+180) x+30) y^3-(((16 x-185) x+25) x+60) y^2-35 x (x+1) y+40 y+15 x\\ & \left.-10\Big) m_s\Big)\right) F(s,x,y)^3+21 \left((y ((x ((x-3) x+3) y-3) y+3)-1) x \left(110 (y-1)+(-10 (47 y+14) y+((-443 x\right.\right.\\ & +8 ((27 x-88) x+40) y+1026) y+120) x y+75) x+2 (10 (y-1)+(((y (41 x+8 ((x-9) x+5) y+38)-50)\\ & \left.x-40 y+20) y+15) x) c_p\right) m_s m_c^2+(x-1) (y-1) \left(s x y (y ((x ((x-3) x+3) y-3) y+3)-1) \left((100 (5 y-4) y\right.\right.\\ & +(2 (909 x+10 (x (27 x-14)-42) y-364) y+127) x y+95) x+2 \left(x \left(y \left(\left(\left(3 x+40 \left(5 x^2-7\right) y+16\right) y+144\right)\right.\right.\right. \\ & \left.\left.\left.\left.x+110 y-80\right)-15\right)-10 (y-1)\right) c_p\right)-6 ((((x-2) x+2) y-2) y+1) \left(x \left(y \left(-75 x+2 \left((37 x-50) x+((7 x\right.\right.\right.\right.\\ & \left.\left.\left.\left.\left.-20) x+10) c_p+20\right) y+5 (6 x-4) c_p+70\right)-5\right)-30 (y-1)\right) m_s^2\right) m_c+3 (x-1) (y-1) \Big(22 \left((x (3 (9 x-47)\right.\\ & \left.x+281)-268) x+2 ((x ((x-13) x+38)-44) x+15) c_p+80\right) x^2 y^6+\left((((2833-741 x) x-4217) x+5860)\right.\\ & \left.x+4 (x (((81 x-278) x+272) x+230)-185) c_p-2490\right) x y^5+\left((((109-15 x) x-2952) x+1200) x+4\right.\\ & \left.((((121-15 x) x-573) x+270) x+30) c_p+810\right) y^4-\left((x (18 x-877)-235) x+4 \Big(\left(22 x^2-278 x+85\right) x\right.\\ & \left.+60\Big) c_p+1460\right) y^3+\left((41 x-535) x-16 (x (14 x+5)-10) c_p+1160\right) y^2+5 \left(27 x+4 (3 x-2) c_p-86\right) y\\& \left.+60\Big) s x m_s\right) F(s,x,y)^2-6 (y-1) \left(14 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(x \left(y \left(-75 x+2 \left((37 x-50) x\right.\right.\right.\right.\right.\\ & \left.\left.\left.\left.+((7 x-20) x+10) c_p+20\right) y+5 (6 x-4) c_p+70\right)-5\right)-30 (y-1)\right) m_s^2 m_c^3-7 s x (y ((x ((x-3) x+3) y-3)\\ & y+3)-1) \left(\left((-10 (115 y+12) y+((-719 x+22 ((27 x-88) x+40) y+2190) y+26) x y+95) x+350 y+4\right.\right.\\ & \left.\left.(10 (y-1)+(((y (59 x+11 ((x-9) x+5) y+50)-71) x-55 y+35) y+15) x) c_p-270\right) y+60\right) m_s m_c^2\\ & -s (x-1) (y-1) \left(s x^2 y^2 (y ((x ((x-3) x+3) y-3) y+3)-1) \left(50 \left((27 x-14) x+4 \left(5 x^2-7\right) c_p-42\right) x y^3\right.\right.\\ & \left.-14 \left(-303 x^2+93 x+4 (2 x-5) (3 x+1) c_p-75\right) y^2+7 \left(37 x+20 (3 x-2) c_p-130\right) y+315\right)-42 ((((x-2)\\ & x+2) y-2) y+1) \left(4 \left(\left(7 c_p+37\right) x^2-10 \left(2 c_p+5\right) x+10 \left(c_p+2\right)\right) x y^3+5 \left(x (3 x-2) \left(4 c_p-3\right)-6\right) y^2\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.\left.-10 (x-3) y-15\right) m_s^2\right) m_c-21 s^2 (x-1) x (y-1) y \left(\left(4 \left((x (3 (9 x-47) x+281)-268) x+2 ((x ((x-13) x\right.\right.\right.\\& \left.+38)-44) x+15) c_p+80\right) x^2 y^5+\Big((((373-101 x) x-531) x+892) x+8 (x (((8 x-29) x+33) x+14)-15)\\& c_p-410\Big) x y^4+\left(\left(((23-5 x) x-588) x+24 ((2 x-17) x+10) c_p+320\right) x+110\right) y^3-\left(\left((6 x-223) x+8 ((2 x\right.\right.\\ & \left.\left.\left.\left.\left.-31) x+20) c_p+95\right) x+220\right) y^2-x \left(11 x+8 (7 x-5) c_p+35\right) y+210 y+15 x-100\right) y+20\right) m_s\right) F(s,x,y)\\ & -6 s (y-1)^2 (y ((x ((x-3) x+3) y-3) y+3)-1) m_c \left((x-1) (y-1) \left(70 (y-1) y+\left(4 \left((27 x-14) x+4 \left(5 x^2-7\right)\right.\right.\right.\right.\\ & \left.\left.\left. c_p-42\right) y^2-14 \left(-23 x+4 (x-2) c_p+5\right) y+21\right) x y+35\right) \left(-s^2\right) x^2 y^3-7 s x \left(50 (y-1) y+\left(\left((y (-97 x+4 ((27\right.\right.\right.\\ & \left.\left.\left. x-88) x+40) y+342)-16) x-190 y+8 (7 x+((x-9) x+5) y-5) (x y-1) c_p+20\right) y+5\right) x y+20\right) m_c m_s\\ & y+14 \left(4 \left((37 x-50) x+((7 x-20) x+10) c_p+20\right) x y^3+5 \left(x (3 x-2) \left(4 c_p-3\right)-6\right) y^2-10 (x-3) y-15\right)\\ & m_c^2 m_s^2\Big)\Big)\Bigg\}, \end{aligned} $

$\begin{aligned}[b]\rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x}{3072 \pi ^3 (y-1)^3} m_c F(s,x,y) \left(3 s (y-1) \left(y \left(4 (x-1) (y-1) c_p (x y (11 x y-10)+1)\right.\right.\right.\\ & \left.\left.+x (x y (y (22 ((6 x-25) x+9) y-73 x+517)-51)-7 (29 y+2) y+30)+41 y-33\right)+6\right) F(s,x,y)\\& +\left(2 (x-1) (y-1) c_p (x y (8 x y-7)+1)+x y (x (y (8 ((6 x-25) x+9) y-65 x+223)+11)-75 y-26)+12 x\right.\\ & \left.+9 y-9\right) F(s,x,y)^2+6 s^2 (y-1)^2 y \left(x y \left(y \left(8 (x-1) (y-1) c_p (x y-1)+x (y (4 ((6 x-25) x+9) y-7 x+89)\right.\right.\right.\\ & -17)-37 y+6\Big)+4\Big)+7 (y-1) y+2\Big)\Big)-\frac{c_2 x^2}{2048 \pi ^3 (x-1) (y-1)^4} m_c F(s,x,y) \left(3 s (y-1) \left(y \left(44 ((x-3) x+1)\right.\right.\right.\\ & ((x-1) x+1) x y^4+(x (((197-56 x) x-47) x+12)-18) y^3+((15-22 x (x+3)) x+32) y^2+3 (4 x+5) x y\\ & \left.\left.-9 x-36 y+18\right)-3\right) F(s,x,y)+\left(16 ((x-3) x+1) ((x-1) x+1) x y^4+(x (((103-32 x) x-53) x+24)\right.\\ & \left.-10) y^3-(x ((7 x+11) x+14)-16) y^2+9 (x-1) y-3 x+3\right) F(s,x,y)^2+6 s^2 (y-1)^2 y \left(y \left(\left(x \left(-8 x^3+29 x^2\right.\right.\right.\right.\\ & \left.\left.\left.+x-4\right)-2\right) y^3+8 ((x-3) x+1) ((x-1) x+1) x y^4+((9-4 x (x+4)) x+4) y^2+(x (4 x-1)-6) y-x+4\right)\\& -1\Big)\Big)\Bigg\}, \end{aligned} $

$\begin{aligned}[b] \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1}{9216 \pi ^3 (y-1)^2} \left(c_p \left(24 s x (y-1) y^2 F(s,x,y) \left(6 m_c^2 (((x-4) x+2) y+3 x-2)+s\right.\right.\right.\\& \left.(x-1) (y-1) y \left(x \left(25 \left(x^2-2\right) y^2+2 (25-9 x) y-3\right)-2 y+2\right)\right)+6 y F(s,x,y)^2 \left(6 x m_c^2 (((x-4) x+2) y+3 x\right.\\ & \left.-2)+s (x-1) (y-1) \left(x \left(y \left(x \left(7 y \left(20 \left(x^2-2\right) y-9 x+40\right)-36\right)-22 y+16\right)+3\right)+2 (y-1)\right)\right)+(x-1) \\ & \left(x \left(y \left(x \left(8 y \left(10 \left(x^2-2\right) y-3 x+20\right)-27\right)-16 y+10\right)+3\right)+2 (y-1)\right) F(s,x,y)^3+48 s^3 (x-1) x^2 (y-1)^3\\ & \left. y^5 \left(\left(x^2-2\right) y-x+2\right)\right)-x \left(6 s (y-1) y F(s,x,y) \left(6 m_c^2 \left(8 (1-2 x)^2 y^2-3 x y-1\right)+s (x-1) (y-1) y \left(y \left(x \Big(50\right.\right.\right.\right.\\ & \left.\left.\left.(5 x (3 x-2)-6) y^2+(954 x-66) y+29\Big)+30 y-26\right)+9\right)\right)+3 F(s,x,y)^2 \left(6 m_c^2 \Big(y \left(4 (1-2 x)^2 y-9 x+4\right)\right.\\& \left.+1\Big)+s (x-1) (y-1) y (x y (2 y (70 (5 x (3 x-2)-6) y+1401 x-164)+83)+20 (5 y-4) y+19)\right)+(x-1)\\ & (y (x (8 y (5 (5 x (3 x-2)-6) y+126 x-29)+21)+40 y-28)-1) F(s,x,y)^3+6 s^3 (x-1) (y-1)^3 y^3 (x y (2 y\\& \left.\left.(2 (5 x (3 x-2)-6) y+37 x-1)+3)+2 (y-1) y+1)\right)\right)+\frac{c_2 x}{4096 \pi ^3 (x-1) (y-1)^3} \left(6 s (y-1) F(s,x,y)\right.\\ & \left(2 m_c^2 (y (x y (x (y (4 (4 x-3) (x-1) y-12 x+25)-4)-13 y+2)+x+3 (y-1))+1)+s (x-1) x (y-1) y^2 (y (x\right.\\ & \left.(x y (y (50 (2 x-3) (x+1) y+62 x+65)-148)+5 (33 y-4) y-11)-37 y+33)-9)\right)+3 (x-1) F(s,x,y)^2\\ & \left(2 m_c^2 (y (2 (4 x-3) x y-2 x+1)-1) (x y-1)+s x (y-1) y (y (x (y (x (2 y (70 (2 x-3) (x+1) y+108 x+55)-415)\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.+470 y-26)-38)-108 y+92)-21)\right)-(x-1)^2 (y-1) c_p F(s,x,y) \left(6 s (y-1) y (x y (11 x y-10)+1) F(s,x,y)\right.\\ & \left.+(x y (8 x y-7)+1) F(s,x,y)^2+24 s^2 x (y-1)^2 y^3 (x y-1)\right)+(x-1) x (y (x (y (x (4 y (10 (2 x-3) (x+1) y+26 x\\ & -5)-139)+140 y+22)-20)-30 y+26)-3) F(s,x,y)^3+6 s^3 (x-1) x (y-1)^3 y^3 (y (x (y (x (y (4 (2 x-3)\\ & \left.(x+1) y+4 x+7)-12)+13 y-2)-1)-3 y+3)-1)\right)\Bigg\}, \end{aligned} $

$\begin{aligned}[b]\rho^{\langle\bar{s}s\bar{s}s\rangle}_{3,9;A(S)}(s) =& \int^{z_{\max}}_{z_{\min}}{\rm d}z\frac{c_1 c_p}{768 \pi } m_s^2 G(s,z) (G(s,z)+4 s (z-1) z),\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{3,9;A(S)}(s) =& \int^{z_{\max}}_{z_{\min}}{\rm d}z\Bigg\{-\frac{c_1}{2304 \pi } \left(m_s^2 \left(\left((4 z (5-6 z)+1) c_p+4 z (7-10 z)+1\right) G(s,z)-s (z-1) z \left(\left(66 z^2-58 z-2\right) c_p\right.\right.\right.\\ & \left.\left.+20 (5 z-4) z+19\right)\right)-m_c m_s \left(\left(6 c_p+13\right) G(s,z)+s \left(z \left(12 (z-1) c_p+29 z-21\right)+6\right)\right)+6 m_c^2 (2 G(s,z)\\ & +2 s (z-1) z+s)\Big)+\frac{c_2 c_p}{1024 \pi } m_s^2 (G(s,z)+2 s (z-1) z)\Bigg\}+\int^{1}_{0}dz\Bigg\{\frac{c_1}{2304 \pi } s^2 (z-1) z m_s \Big((z-1) z m_s \Big(12 (z-1) z\\\ & \left.\left.c_p+30 z^2-26 z+9\right)+(3 (z-1) z+2) m_c\right)\Bigg\}, \end{aligned} $

$\begin{aligned}[b] \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^2}{18432 \pi ^3 (x-1)^3 (y-1)^4} m_c \left(2 F(s,x,y) \left(m_c^2 (x y-1)^2 (y (((x-3) x+3) y+x-3)+1)\right.\right.\\ & (x (y (8 (x-3) (2 x-1) y-8 x+13)-5)-5 y+5)+3 s (x-1) (y-1) \left(y \left(22 ((x (2 (x-5) x+19)-18) x+5)\right.\right.\\ & x^2 y^5+(x (((209-56 x) x-234) x+350)-137) x y^4+(37-2 x (x (32 x+87)-36)) y^3+2 (x (x (11 x+40)\\ & \left.\left.\left.-2)-33) y^2-6 (2 x (x+2)-9) y+9 x-21\right)+3\right)\right)+3 (x-1) \left(8 ((x (2 (x-5) x+19)-18) x+5) x^2 y^5\right.\\ & +(x (((119-32 x) x-146) x+162)-55) x y^4+((x+2) ((x-26) x+4) x+15) y^3+2 (x ((5 x+2) x+14)-13)\\ & \left.y^2+2 (x-7) (x-1) y+3 (x-1)\right) F(s,x,y)^2+2 s (y-1) \left(m_c^2 (x y-1) (y (((x-3) x+3) y+x-3)+1) (y (x (y\right.\\ & (x (y (22 (x-3) (2 x-1) y-34 x+153)-12)-75 y-4)+9)+19 y-15)+3)+3 s (x-1) (y-1) y \Big(y \Big(4 ((x\\ & (2 (x-5) x+19)-18) x+5) x^2 y^5+2 \left(5-2 x^2\right) y+(x (((29-8 x) x-28) x+54)-23) x y^4+(5-4 x (3 x (x\\ & \left.\left.+3)-5)) y^3+2 (x (2 x (x+5)-5)-5) y^2+x-5\Big)+1\Big)\right)\right)\Bigg\}-\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s^2 x^2 y }{9216 \pi ^3 (x-1)^3 (y-1)^2}m_c^3\\ & (x y-1) (y (((x-3) x+3) y+x-3)+1) (y (x y (x (y (4 (x-3) (2 x-1) y-4 x+25)-4)-13 y+2)+x\\ & +3 (y-1))+1), \end{aligned} $

$\begin{aligned}[b] \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x}{18432 \pi ^3 (x-1)^3 (y-1)^3}m_c^2 \left((x-1) \left(c_p (x y-1) (y (((x-3) x+3) y+x-3)+1) (x\right.\right.\\ & (y (8 ((x-4) x+2) y+21 x-10)-3)-2 y+2)+8 ((x ((35 x-118) x+104)-24) x+45) x^2 y^5\\ & +40 \left(x^2 ((3 x-11) x+13)-6\right) x^3 y^6+(x (x (x (73 x+101)-669)-204)-72) x y^4+(x (((935-169 x) x\\ & \left.-310) x+252)-24) y^3+(((179-220 x) x-193) x+48) y^2+(-61 (x-1) x-36) y+x+12\right) F(s,x,y)\\ & +4 m_c^2 (x y-1) (y (((x-3) x+3) y+x-3)+1) (y (x (((5 x-6) x+2) y-4 x+3)-1)+1)+s (x-1) (y-1)\\ & \left(y \left(2 c_p (x y-1) (y (((x-3) x+3) y+x-3)+1) (x (y (11 ((x-4) x+2) y+30 x-16)-3)-2 y+2)+2 (((11\right.\right.\\ & (35 x-113) x+839) x+6) x+570) x^2 y^5+140 \left(x^2 ((3 x-11) x+13)-6\right) x^3 y^6+(x (x (x (155 x+691)\\ & -2229)-936)-204) x y^4+(x (((2353-425 x) x-92) x+492)-24) y^3+(((209-656 x) x-409) x+48) y^2\\ & \left.\left.\left.+((173-65 x) x-48) y-25 x+24\right)-6\right)\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{{\rm i} c_1 s x}{18432 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 (y (y (x ((x-3) \end{aligned} $

$ \begin{aligned}[b]& x+3) y-3)+3)-1) \left(2 m_c^2 \left(y \left(-4 x ((5 x-6) x+2) y^2+2 ((2 x-1) x+1) y+x-2\right)+1\right)-s (x-1) x (y-1) y^2\right.\\ & \left.\left(y \left(4 c_p (((x-4) x+2) y+3 x-2)+x (2 y (25 (x (3 x-2)-2) y+130 x-21)+11)+30 y-26\right)+9\right)\right)\Bigg\}, \end{aligned} $

$\begin{aligned}[b] \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{3,9;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x}{36864 \pi ^3 (x-1)^3 (y-1)^3} m_c \left(3 (x-1) \left(2 (x-1) (y-1) c_p (x y (y (x (y (8 (2 x-3) (x-1) y\right.\right.\\& -2 x+21)-8)-25 y+18)-5)+3 (y-1) y+1)+8 \left(\left(x \left(6 x^2-32 x+63\right)-62\right) x+15\right) x^2 y^5+(x (((374\\ & -105 x) x-379) x+490)-137) x y^4+(((2 x (3 x-68)-165) x+20) x+23) y^3+(x ((45 x+34) x+57)-38)\\ & \left.y^2+((5 x-36) x+19) y+7 x-4\right) F(s,x,y)+m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \left(2 (x-1) (y-1) c_p (x y\right.\\ & \left.(8 x y-7)+1)+x y (x (y (8 ((6 x-25) x+9) y-65 x+223)+11)-75 y-26)+12 x+9 y-9\right)+3 s (x-1)\\ & (y-1) \left(y \left(4 (x-1) (y-1) c_p (x y (y (x (y (11 (2 x-3) (x-1) y-2 x+27)-11)-34 y+27)-8)+3 (y-1) y\right.\right.\\ & +1)+22 \left(\left(x \left(6 x^2-32 x+63\right)-62\right) x+15\right) x^2 y^5+(x ((3 (218-61 x) x-547) x+1118)-361) x y^4\\ & +(((x (2 x-341)-666) x+212) x+67) y^3+(x (19 x (6 x+17)-33)-118) y^2+(100-x (53 x+59)) y+26 x\\ & \left.\left.-41\Big)+6\right)\right)+\frac{c_2 x^2 y}{24576 \pi ^3 (x-1)^2 (y-1)^2} m_c^3 (x y-1) (y (x (y (8 ((x-1) x+1) y+26 x-17)-3)+5 y-1)-2)\Bigg\}\\ & +\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x}{36864 \pi ^3 (x-1)^3 (y-1)^2} m_c \left(m_c^2 (-(y (y (x ((x-3) x+3) y-3)+3)-1)) \left(y \left(4 (x-1) (y-1)\right.\right.\right.\\ & \left.c_p (x y (11 x y-10)+1)+x (x y (y (22 ((6 x-25) x+9) y-73 x+517)-51)-7 (29 y+2) y+30)+41 y-33\right)\\ & +6\Big)-3 s (x-1) (y-1) y \left(y \left(4 x^2 y^5 \left(2 (2 x-3) (x-1)^2 c_p+\left(x \left(6 x^2-32 x+63\right)-62\right) x+15\right)-x y^4 \left(8 (2 x-3)\right.\right.\right.\\& \left. (x-1) ((x-1) x-1) c_p+(x ((27 x-94) x+61)-182) x+63\right)+y^3 \left(9-x \left(24 (x-2) (x-1) c_p+(62 x\right.\right.\\ & \left.\left.+141) x-60\right)\right)+y^2 \left(x \left(8 (x-4) (x-1) c_p+(21 x+80) x-33\right)-18\right)+y \left(x \left(8 (x-1) c_p-17 x+2\right)+19\right)\\ & \left.\left.+3 x-10\Big)+2\right)\right)+\frac{c_2 s x^2 y^3}{24576 \pi ^3 (x-1)^2 (y-1)} m_c^3 (x (y (x (y (22 ((x-1) x+1) y+32 x-17)-47)-13 y+20)\\ & +3)+y-1)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{4;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1}{110592 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \left(-8 x^2 y^5 \left((x (x ((3 x-29) x+101)-66)-54) c_p\right.\right.\\& \left.+(((126 x-407) x+245) x+48) x+105\right)+40 ((x-3) x+3) x^3 y^6 \left(2 \left(x^2-2\right) c_p+5 x (2-3 x)+6\right)\\ & +x y^4 \left(((x ((9 x+115) x+395)-1368) x+198) c_p+((2853-x (309 x+845)) x+828) x-24\right)+y^3 \left((x (x ((31\right.\\ & \left.x-443) x+1384)-372)-6) c_p+(x ((763 x-3247) x+414)-204) x\right)+y^2 \left((((60 x-601) x+253) x+12)\right.\\ & \left.\left. c_p+((702 x-295) x+157) x\right)+y \left((x (135 x-73)-8) c_p+61 (3 x-1) x\right)-3 x c_p+2 c_p-19 x\right)\\ & +\frac{c_2 x y}{49152 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \left(c_p \left(8 ((x ((x-4) x+6)-6) x+2) x y^4+(x (x ((5 x-14) x+60)-24)-2) y^3\right.\right.\\& \left.-(x (x (x+45)-15)-4) y^2+(2 x-1) (8 x+3) y-2 x+1\right)+x y \left(40 \left(x^2 ((x-4) x+6)-2\right) x y^4+4 ((x ((34 x\right.\\& \left.-111) x+81)-16) x+10) y^3+(3 x ((36 x-109) x+61)-68) y^2+((99 x-86) x+43) y+39 x-13\right)-10 x\\ & +6 y-6\Big)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{c_1}{110592 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(6 x m_c^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \Big(y \right.\\& \left(2 c_p (((x-4) x+2) y+3 x-2)-4 (1-2 x)^2 y+9 x-4\right)-1\Big)+s (x-1) (y-1) y \left(-2 x^2 y^5 \left((x (x (7 (9 x-67) x\right.\right.\\& \left.+1471)-906)-774) c_p+(((1401 x-4367) x+1595) x+1458) x+1410\right)+140 ((x-3) x+3) x^3 y^6 \left(2 \Big(x^2\right.\\ & \left.-2\Big) c_p+5 x (2-3 x)+6\right)+x y^4 \Big((2 (x (328 x+467)-2070) x+432) c_p+((9669-x (659 x+4243)) x+3216)\\ \end{aligned} $

$ \begin{aligned}[b] &\left.\left.x+12\Big)-y^3 \left(2 (((x (29 x+560)-1891) x+408) x+6) c_p+((5 x (1741-427 x)+708) x+252) x\right)+y^2 \left(2\right.\right.\right.\\ & \left.((11 (9 x-68) x+277) x+12) c_p+((2244 x-145) x+289) x\right)+y \left(2 (x (144 x-79)-8) c_p+(137 x-173) x\right)\\ & \left.\left.+(4-6 x) c_p+37 x\right)\right)+\frac{c_2 x y }{49152 \pi ^3 (x-1)^3 (y-1)^2}m_c^2 \left(2 m_c^2 \left(2 ((x ((x-4) x+10)-8) x+2) x y^4+(x (5 x (1-3 x).\right.\right.\\& \left.+4)-2) y^3+((x (7 x+11)-10) x+4) y^2+((3-8 x) x-3) y+x+1\right)+s (x-1) (y-1) y \left(2 c_p \left(11 ((x ((x-4) x\right.\right.\\& +6)-6) x+2) x y^4+(x (x ((8 x-23) x+87)-36)-2) y^3-(x (x (x+63)-24)-4) y^2+(2 x-1) (11 x+3) y\\ & \left.-2 x+1\right)+x \left(y \left(140 \left(x^2 ((x-4) x+6)-2\right) x y^4+2 ((((207 x-668) x+358) x+2) x+50) y^3+(x ((340 x\right.\right.\\ & \left.\left.\left.\left.-829) x+465)-180) y^2+((305 x-262) x+109) y+41 x-19\right)-8\right)-6 y+6\right)\right)\Bigg\}, \end{aligned} $

$ \begin{aligned}[b] \rho^{pert}_{4;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^3}{12902400 \pi ^5 (y-1)^5} \left(c_p+1\right) F(s,x,y)^3 \left(-15 (y-1) F(s,x,y) \left(7 s x y m_c m_s (11 x y (2 x y+3)\right.\right.\\ & \left.-10) (x y-1)+14 m_c^2 m_s^2 (x y (2 x y-5)+5)-6 s^2 (x-1) x^2 (y-1) y^3 (5 x y (5 x y+7)-7)\right)+21 x F(s,x,y)^2 \Big(20 s\\ & (x-1) x (y-1) y^2 (x y+2) (3 x y-1)-m_c m_s (x y-1) (x y+3) (8 x y-5)\Big)+2 (x-1) x^2 y (10 x y (3 x y+7)-49)\\ & F(s,x,y)^3-60 s x (y-1)^2 y^2 \Big(7 s x y m_c m_s (x y-1) (4 x y+5)+14 m_c^2 m_s^2 (4 x y-5)-2 s^2 (x-1) x^2 (y-1) y^3 (6 x y\\ & +7)\Big)\Big),\\ \rho^{\langle\bar{s}s\rangle}_{4;A(S)}(s) =& 0,\\ \rho^{\langle m_s\bar{s}s\rangle}_{4;A(S)}(s) =& 0,\\ \rho^{\langle g_sG^2\rangle}_{4;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^3}{15482880 \pi ^5 (x-1)^3 (y-1)^5} m_c \left(c_p+1\right) \left(6 (y-1) F(s,x,y) \left(6 s (x-1) x (y-1) y^2 m_c \Big(s x y\right.\right.\\ & (x y-1) (5 x y (5 x y+7)-7) (y (((x-3) x+3) y+x-3)+1)-7 m_s^2 (4 x y-5) (y (((x-2) x+2) y-2)+1)\Big)\\ &-7 s x y m_c^2 m_s (x y-1)^2 (11 x y (2 x y+3)-10) (y (((x-3) x+3) y+x-3)+1)-14 m_c^3 m_s^2 (x y-1) (x y (2 x y-5)\\ & +5) (y (((x-3) x+3) y+x-3)+1)-21 s^2 (x-1) x^2 (y-1) y^3 m_s (x y-1) (4 x y+5) (y (((x-3) x+3) y+x-3)\\ & +1)\Big)-21 F(s,x,y)^2 \left(2 (x-1) (y-1) m_c \left(3 m_s^2 (x y (2 x y-5)+5) (y (((x-2) x+2) y-2)+1)-10 s x^2 y^2 (x y-1)\right.\right.\\ & \left.(x y+2) (3 x y-1) (y (((x-3) x+3) y+x-3)+1)\right)+x m_c^2 m_s (8 x y-5) (x y-1)^2 (y (((x-3) x+3) y+x-3)\\ & \left.+1) (x y+3)+3 s (x-1) x (y-1) y m_s (11 x y (2 x y+3)-10) (x y-1) (y (((x-3) x+3) y+x-3)+1)\right)+(x-1)\\ & x (y (y (x ((x-3) x+3) y-3)+3)-1) F(s,x,y)^3 \left(4 x y m_c (10 x y (3 x y+7)-49)-21 m_s (x y+3) (8 x y-5)\right)\\& -6 s x (y-1)^2 y^2 m_c (y (y (x ((x-3) x+3) y-3)+3)-1) \left(7 s x y m_c m_s (x y-1) (4 x y+5)+14 m_c^2 m_s^2 (4 x y-5)\right.\\ & \left.\left.-2 s^2 (x-1) x^2 (y-1) y^3 (6 x y+7)\right)\right)+\frac{c_3}{11796480 \pi ^5 (y-1)^3} (x-1) x^2 \left(c_p+1\right) F(s,x,y)^2 \left(4 s (y-1) y (293 x y\right.\\ & \left.-27) F(s,x,y)+(181 x y-36) F(s,x,y)^2+588 s^2 x (y-1)^2 y^3\right)\Bigg\},\\ \rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{4;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^2}{512 \pi ^3 (y-1)^3} m_c \left(c_p+1\right) (x y-1) F(s,x,y) \left(s (y-1) y (5 x y-2) F(s,x,y)+(x y-1)\right. \\ & \left. F(s,x,y)^2+2 s^2 x (y-1)^2 y^3\right)\Bigg\},\\ \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{4;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x}{2304 \pi ^3 (y-1)^2} \left(c_p+1\right) \left(18 s x (y-1) y^2 F(s,x,y) \left(s (x-1) (y-1) y (5 x y-1)-m_c^2\right)\right. \end{aligned} $

$ \begin{aligned}[b]& \left.+3 F(s,x,y)^2 \left(m_c^2 (3-3 x y)+10 s (x-1) x (y-1) y^2 (5 x y-2)\right)+2 (x-1) x y (10 x y-7) F(s,x,y)^3+6 s^3 (x-1)\right.\\ & \left. x^2 (y-1)^3 y^5\right)\Bigg\},\\ \rho^{\langle\bar{s}s\bar{s}s\rangle}_{4;A(S)}(s) = &0,\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{4;A(S)}(s) = &0,\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{4;A(S)}(s) =& 0,\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{4;A(S)}(s) = &0,\\ \rho^{\langle g_sG^2\rangle^2\;A(S)}_4(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^5 y^4 m_c^4 \left(c_p+1\right) (10 x y (3 x y+7)-49)}{46448640 \pi ^5 (x-1)^2 (y-1)^2}\\ & +\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s x^5 y^5 m_c^4 \left(c_p+1\right) (x y+2) (3 x y-1)}{1327104 \pi ^5 (x-1)^2 (y-1)},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{4;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^2}{6144 \pi ^3 (x-1)^3 (y-1)^3} m_c \left(c_p+1\right) (y (y (x ((x-3) x+3) y-3)+3)-1) \Big(3 (x-1)\\ & (x y-1) F(s,x,y)+m_c^2 (x y-1)^2+s (x-1) (y-1) y (5 x y-2)\Big)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{c_1 s x^2 y}{18432 \pi ^3 (x-1)^3 (y-1)^2}\\ & m_c \left(c_p+1\right) (y (y (x ((x-3) x+3) y-3)+3)-1) \left(m_c^2 (5 x y-2) (x y-1)+3 s (x-1) x (y-1) y^2\right)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{10;A(S)}(s) = &\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x }{27648 \pi ^3 (x-1)^2 (y-1)^2}m_c^2 \left(c_p+1\right) (x y-1)^2 \left(x y \left(20 ((x-3) x+3) y^2+26 (x-3) y\right.\right.\\ & \left.+23\Big)+18 (y-1) y+9\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{-\frac{c_1 x}{27648 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(c_p+1\right) \left(s (x-1) x (y-1) y^2 (x y (x\right.\\ & y(10 y (5 ((x-3) x+3) y-2 x+6)-9)+42 (4-5 y) y-50)+42 (y-1) y+11)-3 m_c^2 (x y-1)^2 (y (((x-3) x\\ & \left.+3) y+x-3)+1)\right)\Bigg\},\\ \end{aligned} $

$ \begin{aligned}[b]\\ \rho^{pert}_{10;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^3}{614400 \pi ^5 (y-1)^5} \left(c_p-1\right) F(s,x,y)^3 \left(5 (y-1) F(s,x,y) \left(2 s^2 (x-1) x^2 (y-1) y^3 (11 x y\right.\right.\\ & \left.-3)-5 m_c m_s (x y-1) \left(s x y (5 x y-2)-2 m_c m_s\right)\right)+x F(s,x,y)^2 \left(8 s (x-1) x (y-1) y^2 (7 x y-4)-15 m_c m_s\right.\\ & \left.(x y-1)^2\right)+4 (x-1) x^2 y (x y-1) F(s,x,y)^3+20 s x (y-1)^2 y^2 \left(5 m_c m_s \left(2 m_c m_s+s x y (1-x y)\right)+2 s^2 (x-1)\right.\\ & \left.\left.x^2 (y-1) y^3\right)\right),\\ \rho^{\langle\bar{s}s\rangle}_{10;A(S)}(s) = &0,\\ \rho^{\langle m_s\bar{s}s\rangle}_{10;A(S)}(s) = &0,\\ \rho^{\langle g_sG^2\rangle}_{10;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^3}{737280 \pi ^5 (x-1)^3 (y-1)^5} m_c \left(c_p-1\right) \left(2 (y-1) F(s,x,y) \left(2 s (x-1) x (y-1) y^2 m_c\right.\right. \\ & \left(15 m_s^2 (y (((x-2) x+2) y-2)+1)+s x y (11 x y-3) (x y-1) (y (((x-3) x+3) y+x-3)+1)\right)-5 s x y m_c^2 m_s\\ & (x y-1)^2 (5 x y-2) (y (((x-3) x+3) y+x-3)+1)+10 m_c^3 m_s^2 (x y-1)^2 (y (((x-3) x+3) y+x-3)+1)\\ & \left.-15 s^2 (x-1) x^2 (y-1) y^3 m_s (y (y (x ((x-3) x+3) y-3)+3)-1)\right)+(x y-1) F(s,x,y)^2 \left(2 (x-1) (y-1) m_c\right.\\ & \left(15 m_s^2 (y (((x-2) x+2) y-2)+1)+4 s x^2 y^2 (7 x y-4) (y (((x-3) x+3) y+x-3)+1)\right)-15 x m_c^2 m_s (x y-1)^2\\ \end{aligned} $

$ \begin{aligned}[b] & \left.(y (((x-3) x+3) y+x-3)+1)-15 s (x-1) x (y-1) y m_s (5 x y-2) (y (((x-3) x+3) y+x-3)+1)\right)\\ & +(x-1) x (x y-1)^2 (y (((x-3) x+3) y+x-3)+1) F(s,x,y)^3 \left(8 x y m_c-15 m_s\right)+2 s x (y-1)^2 y^2 m_c (y (y (x ((x\\ & \left.-3) x+3) y-3)+3)-1) \left(-5 s x y m_c m_s (x y-1)+10 m_c^2 m_s^2+2 s^2 (x-1) x^2 (y-1) y^3\right)\right)+\frac{c_3}{2359296 \pi ^5 (y-1)^3}\\ & (x-1) x^2 \left(c_p-1\right) F(s,x,y)^2 \left(4 s (y-1) y (15 x y-2) F(s,x,y)+(9 x y-3) F(s,x,y)^2+36 s^2 x (y-1)^2 y^3\right)\Bigg\},\\ \rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{10;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^2}{512 \pi ^3 (y-1)^3} m_c \left(c_p-1\right) (x y-1) F(s,x,y) \left(s (y-1) y (5 x y-2) F(s,x,y)+(x y-1)\right.\\ & \left. F(s,x,y)^2+2 s^2 x (y-1)^2 y^3\right)\Bigg\},\\ \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{10;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x}{768 \pi ^3 (y-1)^2} \left(c_p-1\right) \left(2 s x (y-1) y^2 F(s,x,y) \left(s (x-1) (y-1) y (11 x y-3)-3 m_c^2\right)\right.\\ & +F(s,x,y)^2 \left(m_c^2 (3-3 x y)+4 s (x-1) x (y-1) y^2 (7 x y-4)\right)+4 (x-1) x y (x y-1) F(s,x,y)^3+2 s^3 (x-1) x^2\\ & \left. (y-1)^3 y^5\right)\Bigg\},\\ \rho^{\langle\bar{s}s\bar{s}s\rangle}_{10;A(S)}(s) =& 0,\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{10;A(S)}(s) =& 0,\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{10;A(S)}(s) =& 0,\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{10;A(S)}(s) =& 0,\\ \rho^{\langle g_sG^2\rangle^2}_{10;A(S)}(s) = &-\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^5 y^4 m_c^4 \left(c_p-1\right) (x y-1)}{1105920 \pi ^5 (x-1)^2 (y-1)^2}-\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{i c_1 s x^5 y^5 m_c^4 \left(c_p-1\right) (7 x y-4)}{3317760 \pi ^5 (x-1)^2 (y-1)},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{10;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^2}{6144 \pi ^3 (x-1)^3 (y-1)^3} m_c \left(c_p-1\right) (y (y (x ((x-3) x+3) y-3)+3)-1) \left(3 (x-1) (x y\right.\\ & \left.-1) F(s,x,y)+m_c^2 (x y-1)^2+s (x-1) (y-1) y (5 x y-2)\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x^2 y}{18432 \pi ^3 (x-1)^3 (y-1)^2} m_c\\ & \left(c_p-1\right) (y (y (x ((x-3) x+3) y-3)+3)-1) \left(m_c^2 (5 x y-2) (x y-1)+3 s (x-1) x (y-1) y^2\right)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x}{9216 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 \left(c_p-1\right) (x y-1) \left(y \left(x \left(y \Big(x \left(4 ((x-3) x+3) y^2-3\right)-12 y\right.\right.\right.\\ & \left.\left.\left.+18\Big)-4\right)-6 y+6\right)-3\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 x}{27648 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(c_p-1\right) \left(s (x-1) x (y-1) y^2\right.\\ & \left(x y \left(y \left(28 ((x-3) x+3) x y^2-4 (4 (x-3) x+33) y-9 x+102\right)-28\right)+30 (y-1) y+7\right)-3 m_c^2 (x y-1)^2\\ & \left.(y (((x-3) x+3) y+x-3)+1)\right)\Bigg\},\\ \end{aligned} $

$ \begin{aligned}[b] \\[-4pt]\rho^{pert}_{5,11;A(S)}(s) = &-\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^3}{6451200 \pi ^5 (y-1)^5} F(s,x,y)^3 \left(15 (y-1) F(s,x,y) \left(7 s x y m_c m_s (x y-1) \left(x y \left(11 x y \left(c_p+6\right)\right.\right.\right.\right.\\ & \left.\left.+4 c_p+99\right)-25\right)+14 m_c^2 m_s^2 \left(x y \left(x y \left(c_p+6\right)-15\right)+10\right)-s^2 (x-1) x^2 (y-1) y^3 \left(x y \left(25 x y \left(3 c_p+10\right)+28\right.\right.\\ & \left.\left.\left.\left(c_p+13\right)\right)-63\right)\right)+21 x F(s,x,y)^2 \left(m_c m_s (x y-1) \left(x y \left(4 x y \left(c_p+6\right)+2 c_p+57\right)-35\right)-2 s (x-1) x (y-1) y^2\right.\\ & \left.\left(5 x^2 y^2 \left(3 c_p+10\right)+x y \left(11 c_p+78\right)-2 \left(c_p+12\right)\right)\right)-(x-1) x^2 y \left(10 x^2 y^2 \left(3 c_p+10\right)+28 x y \left(c_p+8\right)\right.\\ \end{aligned} $

$ \begin{aligned}[b]& \left.-7 \left(c_p+18\right)\right) F(s,x,y)^3+60 s x (y-1)^2 y^2 \left(7 s x y m_c m_s (x y-1) \left(2 x y \left(c_p+6\right)+15\right)+14 m_c^2 m_s^2 \left(2 x y \left(c_p+6\right)\right.\right.\\ & \left.\left.\left.-15\right)-2 s^2 (x-1) x^2 (y-1) y^3 \left(x y \left(3 c_p+10\right)+14\right)\right)\right),\\ \rho^{\langle\bar{s}s\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^3}{384 \pi ^3 (y-1)^4} m_c (x y-1) F(s,x,y)^2 \Big(s (y-1) y (x y (11 x y+14)-3) F(s,x,y)+(x y (x y+2)\\ & -1) F(s,x,y)^2+6 s^2 x (y-1)^2 y^3 (x y+1)\Big),\\ \rho^{\langle m_s\bar{s}s\rangle}_{5,11;A(S)}(s) =& -\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\frac{c_1 x^2}{384 \pi ^3 (y-1)^3} F(s,x,y) \left(-3 s x (y-1) y^2 F(s,x,y) \left(4 m_c^2 (x y-1)+s (x-1) (y-1) y (x y (25\right.\right.\\ & \left.x y+26)-3)\right)-2 F(s,x,y)^2 \left(m_c^2 (x y-1)^2+s (x-1) x (y-1) y^2 (x y (35 x y+39)-8)\right)-(x-1) x y (x y (5 x y+8)\\ & \left.-3) F(s,x,y)^3-12 s^3 (x-1) x^2 (y-1)^3 y^5 (x y+1)\right),\\ \rho^{\langle g_sG^2\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x^3}{7741440 \pi ^5 (x-1)^3 (y-1)^5} m_c \left(-6 (y-1) F(s,x,y) \left(-21 s^2 (x-1) x^2 (y-1) y^3 m_s (y (y (x\right.\right.\\ & ((x-3) x+3) y-3)+3)-1) \left(2 x y \left(c_p+6\right)+15\right)+s (x-1) x (y-1) y^2 m_c \left(s x y (y (y (x ((x-3) x+3) y-3)\right.\\ & \left.+3)-1) \left(x y \left(25 x y \left(3 c_p+10\right)+28 \left(c_p+13\right)\right)-63\right)-42 m_s^2 (y (((x-2) x+2) y-2)+1) \left(2 x y \left(c_p+6\right)-15\right)\right)\\ & -7 s x y m_c^2 m_s (x y-1)^2 (y (((x-3) x+3) y+x-3)+1) \left(x y \left(11 x y \left(c_p+6\right)+4 c_p+99\right)-25\right)-14 m_c^3 m_s^2 (y (y (x\\ & \left.((x-3) x+3) y-3)+3)-1) \left(x y \left(x y \left(c_p+6\right)-15\right)+10\right)\right)+(x-1) x (y (y (x ((x-3) x+3) y-3)+3)-1)\\& F(s,x,y)^3 \left(21 m_s \left(x y \left(4 x y \left(c_p+6\right)+2 c_p+57\right)-35\right)+2 x y m_c \left(-10 x^2 y^2 \left(3 c_p+10\right)-28 x y \left(c_p+8\right)\right.\right.\\ & \left.\left.+7 \left(c_p+18\right)\right)\right)+21 F(s,x,y)^2 \left(2 (x-1) (y-1) m_c \left(3 m_s^2 (y (((x-2) x+2) y-2)+1) \Big(x y \left(x y \left(c_p+6\right)-15\right)\right.\right.\\ & \left.+10\Big)-s x^2 y^2 (y (y (x ((x-3) x+3) y-3)+3)-1) \left(5 x^2 y^2 \left(3 c_p+10\right)+x y \left(11 c_p+78\right)-2 \left(c_p+12\right)\right)\right)\\& +x m_c^2 m_s (x y-1)^2 (y (((x-3) x+3) y+x-3)+1) \left(x y \left(4 x y \left(c_p+6\right)+2 c_p+57\right)-35\right)+3 s (x-1) x (y-1) y\\ & \left. m_s (y (y (x ((x-3) x+3) y-3)+3)-1) \left(x y \left(11 x y \left(c_p+6\right)+4 c_p+99\right)-25\right)\right)+6 s x (y-1)^2 y^2 m_c (y (y (x ((x\\ & -3) x+3) y-3)+3)-1) \left(7 s x y m_c m_s (x y-1) \left(2 x y \left(c_p+6\right)+15\right)+14 m_c^2 m_s^2 \left(2 x y \left(c_p+6\right)-15\right)-2 s^2\right.\\ & \left.\left.(x-1) x^2 (y-1) y^3 \left(x y \left(3 c_p+10\right)+14\right)\right)\right)\Bigg\},\\ \rho^{\langle\bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^2}{1536 \pi ^3 (y-1)^3} m_c (x y-1) F(s,x,y) \Big(3 s (y-1) y (x y(55 x y+56)-9) F(s,x,y)+4 (x y\\ & (5 x y+8)-3) F(s,x,y)^2+12 s^2 x (y-1)^2 y^3 (5 x y+4)\Big)+\frac{c_2 x^3}{1024 \pi ^3 (x-1) (y-1)^4} m_c (y (((x-2) x+2) y-2)\\ & +1) F(s,x,y) \Big(3 s (y-1) y (x y (11 x y+14)-3) F(s,x,y)+4 (x y (x y+2)-1) F(s,x,y)^2+12 s^2 x (y-1)^2 y^3\\ & (x y+1)\Big)\Bigg\},\\ \rho^{m_s\langle\bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{-\frac{c_1 x}{1152 \pi ^3 (y-1)^2} \left(-3 s x (y-1) y^2 F(s,x,y) \left(6 m_c^2 (4 x y-3)+s (x-1) (y-1) y \left(x y \left(-4 c_p\right.\right.\right.\right.\\& +125 x y+104\Big)-9\Big)\Big)-3 F(s,x,y)^2 \left(3 m_c^2 (x y-1) (2 x y-1)+s (x-1) x (y-1) y^2 \left(c_p (2-11 x y)+x y (175 x y\right.\right.\\ & \left.\left.+156)-24\right)\right)-(x-1) x y \left(-4 x y c_p+c_p+2 x y (25 x y+32)-18\right) F(s,x,y)^3-6 s^3 (x-1) x^2 (y-1)^3 y^5 (5 x y\\ & +4)\Big)+\frac{c_2 x^2 (x y-1)}{1024 \pi ^3 (x-1) (y-1)^3} \left(3 s x (y-1) y^2 F(s,x,y) \left(4 m_c^2 (x y-1)+s (x-1) (y-1) y (x y (25 x y+26)-3)\right)\right.\\ & +3 F(s,x,y)^2 \left(m_c^2 (x y-1)^2+s (x-1) x (y-1) y^2 (x y (35 x y+39)-8)\right)+2 (x-1) x y (x y (5 x y+8)-3)\\ & \left.F(s,x,y)^3+6 s^3 (x-1) x^2 (y-1)^3 y^5 (x y+1)\right)\Bigg\},\\ \end{aligned} $

$ \begin{aligned}[b]\rho^{\langle\bar{s}s\bar{s}s\rangle}_{5,11;A(S)}(s) =& 0,\\ \rho^{\langle\bar{s}s\rangle\langle\bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) =& 0,\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^3}{4608 \pi ^3 (x-1)^3 (y-1)^4} m_c (y (y (x ((x-3) x+3) y-3)+3)-1) \left(F(s,x,y) \left(4 m_c^2 (x y (x y\right.\right.\\ & \left.+2)-1) (x y-1)+3 s (x-1) (y-1) y (x y (11 x y+14)-3)\right)+6 (x-1) (x y (x y+2)-1) F(s,x,y)^2+s (y-1) y\\& \left.\left(m_c^2 (x y (11 x y+14)-3) (x y-1)+6 s (x-1) x (y-1) y^2 (x y+1)\right)\right)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\frac{c_1 s^2 x^4 y^3}{2304 \pi ^3 (x-1)^3 (y-1)^2}\\ & m_c^3 \left(x^2 y^2-1\right) (y (y (x ((x-3) x+3) y-3)+3)-1),\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}s\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^2}{2304 \pi ^3 (x-1)^3 (y-1)^3} m_c^2 (x y-1) \left((x-1) \Big(y \Big(x \Big(y \Big(x \Big(y \Big(x \Big(10 ((x-3) x+3) y^2+26 (x\right.\\ & -3) y+23\Big)+48 y-36\Big)+7\Big)-12 y+18\Big)-3\Big)-6 y+6\Big)-3\Big) F(s,x,y)+m_c^2 (x y-1)^2 (y (((x-3) x+3) y+x\\ & -3)+1)+s (x-1) x (y-1) y^2 \left(x y \left(y \left(35 ((x-3) x+3) x y^2+(74 (x-3) x+117) y+72 x-105\right)+31\right)-12 (y\right.\\ & \left.-1) y-2\right)\Big)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x^3 y^2}{4608 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 (x y-1) (y (((x-3) x+3) y+x-3)+1) \Big(4 m_c^2 (x y\\& -1)+s (x-1) (y-1) y (x y (25 x y+26)-3)\Big)\Bigg\},\\ \rho^{\langle g_sG^2\rangle^2}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^5 y^4}{46448640 \pi ^5 (x-1)^2 (y-1)^2}m_c^4 \left(c_p (2 x y (15 x y+14)-7)+4 x y (25 x y+56)-126\right)\Bigg\}\\ & +\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x^5 y^5}{6635520 \pi ^5 (x-1)^2 (y-1)} m_c^4 \left(c_p (x y (15 x y+11)-2)+2 x y (25 x y+39)-24\right)\Bigg\},\\ \rho^{\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) = &-\int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x^2}{18432 \pi ^3 (x-1)^3 (y-1)^3} m_c (y (y (x ((x-3) x+3) y-3)+3)-1) \Big(12 (x-1) (x y (5 x y\\ & +8)-3) F(s,x,y)+4 m_c^2 (x y (5 x y+8)-3) (x y-1)+3 s (x-1) (y-1) y (x y (55 x y+56)-9)\Big)\\ & +\frac{c_2 x^3 y^2}{3072 \pi ^3 (x-1)^2 (y-1)^2} m_c^3 (x y-1) (x y (x y+2)-1)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 s x^2 y}{18432 \pi ^3 (x-1)^3 (y-1)^2} m_c (y (y (x\\ & ((x-3) x+3) y-3)+3)-1) \Big(m_c^2 (x y (55 x y+56)-9)(x y-1)+6 s (x-1) x (y-1) y^2 (5 x y+4)\Big)\\ & +\frac{c_2 s x^3 y^3}{12288 \pi ^3 (x-1)^2 (y-1)} m_c^3 (x y-1) (x y (11 x y+14)-3)\Bigg\},\\ \rho^{m_s\langle g_sG^2\rangle\langle \bar{s}\sigma\cdot Gs\rangle}_{5,11;A(S)}(s) =& \int^{x_{\max}}_{0}{\rm d}x\int^{y_{\max}}_{y_{\min}}{\rm d}y\Bigg\{\frac{c_1 x}{13824 \pi ^3 (x-1)^2 (y-1)^2} m_c^2 (x y-1) \left(y \left(-x c_p (4 x y-1) (y (((x-3) x+3) y+x-3)+1)\right.\right.\\ & \left.\left.+y \left(x \left(x \left(50 ((x-3) x+3) x y^3+6 (19 (x-3) x+32) y^2+6 (19 x-29) y+37\right)-18 (y-2)\right)-18\right)+18\right)-9\right)\\ & +\frac{c_2 x^2 y }{12288 \pi ^3 (x-1)^2 (y-1)^2}m_c^2 (x y (x y (x y (2 y (5 ((x-2) x+2) y+8 x-26)+7)+4 (8 y-5) y+7)-12 (y-1) y\\ & +3)-3)\Bigg\}+\int^{1}_{0}{\rm d}x\int^{1}_{0}{\rm d}y\Bigg\{\frac{c_1 x}{13824 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \left(3 m_c^2 (x y-1)^2 (2 x y-1) (y (((x-3) x+3) y+x-3)\right.\\ & +1)+s (x-1) x (y-1) y^2 \Big(-c_p (x y-1) (11 x y-2) (y (((x-3) x+3) y+x-3)+1)+x y \Big(y \Big(x \Big(y \Big(x \Big(175 ((x\\ & \left.-3) x+3) y^2+156 (x-3) y+12\Big)-57 y+525\Big)-202\Big)-468 y+450\Big)-120\Big)+18 (y-1) y-3\Big)\right)\\ & +\frac{c_2 x^2 y}{12288 \pi ^3 (x-1)^3 (y-1)^2} m_c^2 \Big(m_c^2 (x y-1)^2 (y (((x-2) x+2) y-2)+1)+s (x-1) x (y-1) y^2 (x y (y (x (y (35 ((x\\ & -2) x+2) y+39 x-148)+33)+78 y-62)+27)-16 (y-1) y-2)\Big)\Bigg\},\\ \end{aligned} $