Chinese Physics C

2024-6 Contents

2024, 48(6): 1-3.

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Abstract:

Determination of the resonant parameters of ${ \boldsymbol\chi_{\boldsymbol c \bf 0}\bf (3915)} $ with global fit

Chunhua Li, Xijun Wang, Chen Wu

2024, 48(6): 063001. doi: 10.1088/1674-1137/ad3943

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Particle

\begin{document}$ \chi_{c0}(3915) $\end{document}

was first observed by the Belle experiment in the

\begin{document}$ \omega J/\psi $\end{document}

invariant mass spectrum in the process

\begin{document}$ B\to K\omega J/\psi $\end{document}

and subsequently confirmed by the BaBar experiment. Both experiments reported the resonant parameters of this particle in the processes

\begin{document}$ \gamma\gamma\to\omega J/\psi $\end{document}

and

\begin{document}$ B\to K\omega J/\psi $\end{document}

assuming

\begin{document}$ \chi_{c0}(3915) $\end{document}

as an S-wave Breit-Wigner resonance. We performed a global fit to the distributions of invariant mass of

\begin{document}$ \omega J/\psi $\end{document}

measured by the Belle and BaBar experiments and additionally incorporated the measurements reported by the LHCb experiment to extract the mass and width of

\begin{document}$ \chi_{c0}(3915) $\end{document}

. We obtained

\begin{document}$ M=3920.9\pm0.9 $\end{document}

MeV/

\begin{document}$ c^2 $\end{document}

and

\begin{document}$ \Gamma=18.2\pm2.4 $\end{document}

MeV, which are consistent with the values from PDG within one standard deviation but with higher precision.

Mass suppression effect in QCD radiation and hadron angular distribution in jet

Chuan-Hui Jiang, Hai Tao Li, Shi-Yuan Li, Zong-Guo Si

2024, 48(6): 063101. doi: 10.1088/1674-1137/ad2f22

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The finite mass of the heavy quark suppresses the collimated radiations; this is generally referred to as the dead cone effect. In this paper, we study the distribution of hadron multiplicity over the hadron opening angle with respect to the jet axis for various jet flavors. The corresponding measurement can be the most straightforward and simplest approach to explore the dynamical evolution of the radiations in the corresponding jet, which can expose the mass effect. We also propose a transverse energy-weighted angular distribution, which sheds light on the interplay between perturbative and non-perturbative effects in the radiation. Through Monte-Carlo simulations, our calculations show that the dead cone effect can be clearly observed by finding the ratio between the b and light-quark (inclusive) jets; this is expected to be measured at the LHC in the future.

B − L model with D₄ × Z₄ × Z₂ symmetry for fermion mass hierarchies and mixings

V. V. Vien

2024, 48(6): 063102. doi: 10.1088/1674-1137/ad2f23

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We constructed a gauge

\begin{document}$ B-L $\end{document}

model with

\begin{document}$ D_4\times Z_4\times Z_2 $\end{document}

symmetry to explain the quark and lepton mass hierarchies and their mixings with realistic CP phases via the type-I seesaw mechanism. Six quark mases, three quark mixing angles, and the CP phase in the quark sector take the central values whereas Yukawa couplings in the quark sector are diluted in a range of difference of three orders of magnitude by the perturbation theory at the first order. Concerning the neutrino sector, a small neutrino mass is achieved by the type-I seesaw mechanism. Both inverted and normal neutrino mass hierarchies are consistent with the experimental data. The predicted sum of neutrino masses for normal and inverted hierarchies, the effective neutrino masses, and the Dirac CP phase are also consistent with recently reported limits.

QCD sum rule study of J^P = 1^± exotic states with two heavy quarks in the molecular picture

T.M. Aliev, S. Bilmis, M. Savcı

2024, 48(6): 063103. doi: 10.1088/1674-1137/ad305f

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In this study, the spectroscopic parameters of exotic molecular states composed of mesons containing two heavy quarks (scalar - axial and pseudoscalar - axial meson combinations) are investigated within the QCD sum rules. Our findings reveal that molecular states containing charm quarks do not form bound states, whereas states with b-quarks can form exotic molecular states. This observation has significant implications for understanding the structure of these exotic states.

Analysis of the gluon distribution with next-to-leading order splitting function at small-x

Jingxuan Chen, Xiaopeng Wang, Yanbing Cai, Xurong Chen, Qian Wang

2024, 48(6): 063104. doi: 10.1088/1674-1137/ad305d

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An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is presented. We first obtain simplified forms of the LO and NLO splitting functions in the small-x limit. With these approximated splitting functions, we obtain the analytical gluon distribution using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data; however, the NLO results considering the "ladder" structure of gluon emission are slightly better than the LO results. These results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x region. In addition, we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon distribution. The differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.

Electrodynamics with violations of Lorentz and U(1) gauge symmetries and their Hamiltonian structures

Xiu-Peng Yang, Bao-Fei Li, Tao Zhu

2024, 48(6): 063105. doi: 10.1088/1674-1137/ad33be

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This study aims to investigate Lorentz/U(1) gauge symmetry-breaking electrodynamics in the framework of the standard-model extension and analyze the Hamiltonian structure for the theory with a specific dimension

\begin{document}$ d\leq 4 $\end{document}

of Lorentz breaking operators. For this purpose, we consider a general quadratic action of the modified electrodynamics with Lorentz/gauge-breaking operators and calculate the number of independent components of the operators at different dimensions in gauge invariance and breaking. With this general action, we then analyze how Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension

\begin{document}$ d\leq 4 $\end{document}

as examples. We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the theory constrains and the number of physical degrees of freedom of the standard Maxwell electrodynamics. When U(1) gauge symmetry-breaking operators are present, the theories generally lack a first-class constraint and have one additional physical degree of freedom compared to the standard Maxwell electrodynamics.

Exploring dark matter-gauge boson effective interactions at current and future colliders

Yu Zhang, Yi-Wei Huang, Wei-Tao Zhang, Mao Song, Ran Ding

2024, 48(6): 063106. doi: 10.1088/1674-1137/ad2362

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In this study, we systematically investigate collider constraints on effective interactions between Dark Matter (DM) particles and electroweak gauge bosons. We consider the simplified models in which scalar or Dirac fermion DM candidates couple only to electroweak gauge bosons through high dimensional effective operators. Considering the induced DM-quarks and DM-gluons operators from the Renormalization Group Evolution (RGE) running effect, we present comprehensive constraints on the effective energy scale Λ and Wilson coefficients

\begin{document}$ C_B(\Lambda),\,C_W(\Lambda) $\end{document}

from direct detection, indirect detection, and collider searches. In particular, we present the corresponding sensitivity from the Large Hadron Electron Collider (LHeC) and Future Circular Collider in the electron-proton mode (FCC-ep) for the first time, update the mono-j and mono-γ search limits at the Large Hadron Collider (LHC), and derive the new limits at the Circular Electron Positron Collider (CEPC).

$ { \boldsymbol D^{\bf +} \boldsymbol\to \boldsymbol\pi^{\bf +} \boldsymbol\nu\bar{\boldsymbol\nu}} $ decay process within the QCDSR approach

Yu Chen, Hai-Bing Fu, Tao Zhong, Sheng-Bo Wu, Dong Huang

2024, 48(6): 063107. doi: 10.1088/1674-1137/ad30f0

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In this paper, we investigate the charmed meson rare decay process

\begin{document}$ D^+ \to \pi^+\nu\bar\nu $\end{document}

using an approach based on QCD sum rules. First, the pion twist-2, 3 distribution amplitude (DA) moments

\begin{document}$ \langle\xi_{2;\pi}^n\rangle|_\mu $\end{document}

and

\begin{document}$ \langle \xi_{3;\pi}^{(p,\sigma),n}\rangle|_\mu $\end{document}

are calculated up to the tenth and fourth orders, respectively, in the QCD sum rules according to the background field theory. After constructing the light-cone harmonic oscillator model for the pion twist-2, 3 DAs, we obtain their behaviors by matching the calculated ξ-moments. Then, the

\begin{document}$ D\to \pi $\end{document}

transition form factors (TFFs) are calculated using an approach based on QCD light-cone sum rules. The vector form factor at the large recoil region is

\begin{document}$ f_+^{D\to\pi}(0) = 0.627^{+0.120}_{-0.080} $\end{document}

. Using the rapidly converging simplified series expansion of

\begin{document}$ z(q^2,t) $\end{document}

, we present the TFFs and corresponding angular coefficients in the whole squared momentum transfer physical region. Based on non-standard neutrino interactions, the

\begin{document}$ D^+ \to \pi^+ \nu\bar\nu $\end{document}

decay can be related to the

\begin{document}$ \bar D^0 \to \pi^+ e\bar \nu_e $\end{document}

decay indirectly. Thus, we first describe the semileptonic decay process

\begin{document}$ \bar D^0 \to \pi^+ e\bar \nu_e $\end{document}

, differential decay widths, and branching fraction with

\begin{document}$ {\cal B}(\bar D^0\to\pi^+e\bar\nu_e) = 0.308^{+0.155}_{-0.066} \times 10^{2} $\end{document}

. The

\begin{document}$ \bar D^0\to\pi^+e\bar\nu_e $\end{document}

differential/total predictions for forward-backward asymmetry,

\begin{document}$ q^2 $\end{document}

-differential flat terms, and lepton polarization asymmetry are also reported. The prediction for the

\begin{document}$ D^+ \to \pi^+ \nu\bar\nu $\end{document}

branching fraction is

\begin{document}${\cal B}(D^+ \to \pi^+ {\nu }{\bar\nu}) = $\end{document}

\begin{document}$ 1.85^{+0.93}_{-0.46}\times10^{-8}$\end{document}

.

ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay

Tao Zhong, Ya-Hong Dai, Hai-Bing Fu

2024, 48(6): 063108. doi: 10.1088/1674-1137/ad34be

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Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the ρ-meson leading-twist longitudinal DA

\begin{document}$ \phi_{2;\rho}^\|(x,\mu) $\end{document}

in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of

\begin{document}$ \phi_{2;\rho}^\|(x,\mu) $\end{document}

. However, the ξ-moments of

\begin{document}$ \phi_{2;\rho}^\|(x,\mu) $\end{document}

are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero ξ-moments at the typical scale

\begin{document}$ \mu = (1.0, 1.4, 2.0, 3.0)\; {\rm GeV} $\end{document}

are given, e.g., at

\begin{document}$ \mu = 1\; {\rm GeV} $\end{document}

,

\begin{document}$ \langle\xi^2\rangle_{2;\rho}^\| = 0.220(6) $\end{document}

,

\begin{document}$ \langle\xi^4\rangle_{2;\rho}^\| = 0.103(4) $\end{document}

,

\begin{document}$ \langle\xi^6\rangle_{2;\rho}^\| = 0.066(5) $\end{document}

,

\begin{document}$ \langle\xi^8\rangle_{2;\rho}^\| = 0.046(4) $\end{document}

, and

\begin{document}$ \langle\xi^{10}\rangle_{2;\rho}^\| = 0.035(3) $\end{document}

. By fitting these values with the least squares method, the DSE model for

\begin{document}$ \phi_{2;\rho}^\|(x,\mu) $\end{document}

is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, i.e.,

\begin{document}$ A_1(0) = 0.498^{+0.014}_{-0.012} $\end{document}

,

\begin{document}$ A_2(0)=0.460^{+0.055}_{-0.047} $\end{document}

, and

\begin{document}$ V(0) = 0.800^{+0.015}_{-0.014} $\end{document}

, and the ratio

\begin{document}$ r_2 = 0.923^{+0.133}_{-0.119} $\end{document}

,

\begin{document}$ r_V = 1.607^{+0.071}_{-0.071} $\end{document}

. After extrapolating with a rapidly converging series based on

\begin{document}$ z(t) $\end{document}

-expansion, we present the

\begin{document}$ |V_{cd}| $\end{document}

-independent decay width for the semileptonic decays

\begin{document}$ D\to\rho\ell^+\nu_\ell $\end{document}

. Finally, the branching fractions are

\begin{document}$ \mathcal{B}(D^0\to \rho^- e^+ \nu_e) = 1.825^{+0.170}_{-0.162}\pm 0.004 $\end{document}

,

\begin{document}$\mathcal{B}(D^+ \to \rho^0 e^+ \nu_e) = $\end{document}

\begin{document}$ 2.299^{+0.214}_{-0.204}\pm 0.011$\end{document}

,

\begin{document}$ \mathcal{B}(D^0\to \rho^- \mu^+ \nu_\mu) = 1.816^{+0.168}_{-0.160}\pm 0.004 $\end{document}

, and

\begin{document}$\mathcal{B}(D^+ \to \rho^0 \mu^+ \nu_\mu) =2.288^{+0.212}_{-0.201} \pm 0.011$\end{document}

.

X(3960), X₀(4140), and other compact ${\boldsymbol c \boldsymbol s\bar{\boldsymbol c}\bar{\boldsymbol s}} $ states

Shi-Yuan Li, Yan-Rui Liu, Zi-Long Man, Zong-Guo Si, Jing Wu

2024, 48(6): 063109. doi: 10.1088/1674-1137/ad34c4

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We studied the spectrum and rearrangement decays of S-wave

\begin{document}$ cs\bar{c}\bar{s} $\end{document}

tetraquark states in a simplified quark model. The masses and widths were estimated by assuming that

\begin{document}$ X(4140) $\end{document}

is the lower

\begin{document}$ 1^{++} \;\; cs\bar{c}\bar{s} $\end{document}

tetraquark. Comparing our results with experimental measurements, we found that

\begin{document}$ X(3960) $\end{document}

, recently observed by LHCb, can be considered the lowest

\begin{document}$ 0^{++} \;\; cs\bar{c}\bar{s} $\end{document}

tetraquark state and

\begin{document}$ X_0(4140) $\end{document}

could be the second lowest

\begin{document}$ 0^{++} \;\; cs\bar{c}\bar{s} $\end{document}

tetraquark. Predictions of ratios between partial widths for the involved tetraquarks are provided in this paper. We aim to identify more

\begin{document}$ cs\bar{c}\bar{s} $\end{document}

tetraquarks with

\begin{document}$ J^{PC}=1^{+-} $\end{document}

,

\begin{document}$ 0^{++} $\end{document}

, and

\begin{document}$ 2^{++} $\end{document}

.

TALYS calculation and a short review of the experimental status of proton capture studies on p-nuclei: A guide to future investigation

Indrani Ray, Argha Deb

2024, 48(6): 064001. doi: 10.1088/1674-1137/ad2dc3

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TALYS calculations were performed to obtain the theoretical proton capture cross-sections on the p-nuclei. A short review on the status of related experimental studies was also conducted. Some basic properties such as Q-values, Coulomb barrier, Gamow peak, Gamow Window, and decay properties of the parent and daughter nuclei were studied. Various experimental parameters, e.g., beam energy, beam current, targets, and detectors, used in experimental investigations reported in the literature, were tabulated. The results of the TALYS calculations in the Gamow region were compared with the corresponding experimental values wherever available. This study is expected to facilitate the planning of future experiments.

Prompt neutron emission in ²⁵⁰No spontaneous fission associated with ground and isomeric state decays

R.S. Mukhin, A.V. Isaev, A.V. Andreev, M.L. Chelnokov, V.I. Chepigin, H.M. Devaraja, I.N. Izosimov, A.A. Kuznetsova, O.N. Malyshev, A.G. Popeko, Yu.A. Popov, A. Rahmatinejad, B. Sailaubekov, T.M. Shneidman, E.A. Sokol, A.I. Svirikhin, M.S. Tezekbayeva, M.A. Bychkov, A.V. Yeremin, O. Dorvaux, B. Gall, K. Kessaci, K. Hauschild, A. Lopez-Martens

2024, 48(6): 064002. doi: 10.1088/1674-1137/ad361a

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The complete-fusion reaction ²⁰⁴Pb(⁴⁸Ca,2n)²⁵⁰No was used to study two activities of ²⁵⁰No with distinct half-lives. A total of 1357 events were observed in the SFiNx neutron detection system. The average number of neutrons emitted per spontaneous fission of ²⁵⁰No was determined to be

\begin{document}$ (4.1 \pm 0.1) $\end{document}

. The unusually symmetrical shape of the prompt neutron multiplicity distribution was restored and presented for the first time. Statistical tests were performed to compare the prompt neutron multiplicity distributions associated with the ground state and K-isomer state decays.

Systematic study of cluster radioactivity within the generalized liquid drop model

Jun-Gang Deng, Jun-Hao Cheng, Xiao-Jun Bao, Hong-Fei Zhang

2024, 48(6): 064101. doi: 10.1088/1674-1137/ad30ef

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Cluster radioactivity is studied within the generalized liquid drop model (GLDM), in which the shell correction energy, pairing energy, and cluster preformation factor are considered. The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after considering these physical effects. In addition, the systematic trend of the cluster preformation factors

\begin{document}$ P_c $\end{document}

is discussed in terms of the