Chinese Physics C

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

Abstract:
We constructed a gauge $ B-L $ model with $ D_4\times Z_4\times Z_2 $ 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.

Critical behavior and Joule-Thomson expansion of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

Meng-Yao Zhang, Hao Chen, Hassan Hassanabad, Zheng-Wen Long, Hui Yang

2024, 48(6): 065101. doi: 10.1088/1674-1137/ad32c0

Abstract:
By considering the concept of a unified single fluid model, referred to as modified Chaplygin gas (MCG), which amalgamates dark energy and dark matter, we explore the thermodynamic characteristics of charged anti-de Sitter (AdS) black holes existing in an unconventional fluid accompanied by MCG. To accomplish this objective, we derive the equations of state by regarding the charge $ Q^{2} $ as a thermodynamic variable. The effects of MCG parameters on the critical thermodynamic quantities ($ \psi_{c} $, $ T_{c} $, $ Q_{c}^{2} $) are examined, followed by a detailed analysis of the $ Q^{2}-\psi $ diagram. To provide a clearer explanation of the phase transition, we present an analysis of the Gibbs free energy. It is important to note that if the Hawking temperature exceeds the critical temperature, a distinct pattern is observed known as swallowtail behavior. This indicates that the system undergoes a first-order phase transition from a smaller black hole to a larger one. The critical exponent of the system is found to be in complete agreement with that of the van der Waals fluid system. Furthermore, we investigate the impact of MCG parameters and black hole charge on Joule-Thomson (J-T) expansion in the extended phase space. The J-T coefficient is examined to pinpoint the exact region experiencing cooling or heating, and the observation reveals that the presence of negative heat capacity results in the occurrence of a cooling process. The impact of MCG on the inversion curve of charged black holes exhibits a striking resemblance to that observed in most multi-dimensional black hole systems. In addition, it is worth noting that certain parameters exert a significant influence on the ratio $\dfrac{T_{\min}}{T_{c}}$. For specific values of the MCG parameters, the ratio is consistent with the charged AdS black hole. The parameters γ and β have a non-negligible effect on the isenthalpic curve.

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

Abstract:
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.

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

Abstract:
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.

Revisiting the spin effects induced by thermal vorticity

Jian-Hua Gao, Shi-Zheng Yang

2024, 48(5): 053114. doi: 10.1088/1674-1137/ad2363

Abstract:
We revisit the spin effects induced by thermal vorticity by calculating them directly from the spin-dependent distribution functions. For spin-1/2 particles, we provide the polarization up to the first order of thermal vorticity and compare it with the usual results calculated from the spin vector. For spin-1 particles, we show that all the non-diagonal elements vanish and there is no spin alignment up to the first order of thermal vortcity. We present the spin alignment at second-order contribution from thermal vorticity. We also show that the spin effects for both Dirac and vector particles receive an extra contribution when the spin direction is associated with the momentum of the particle.

Cross sections for 14 MeV neutron interaction with lutetium isotopes and their theoretical excitation functions

Yueli Song, Fengqun Zhou, Yong Li, Xiaopeng Zhang, Pengfei Ji, Xiaojun Sun

2024, 48(5): 054104. doi: 10.1088/1674-1137/ad2b55

Abstract:
The cross-sections for the ¹⁷⁵Lu(n,p)¹⁷⁵Yb, ¹⁷⁵Lu(n,α)¹⁷²Tm, ¹⁷⁶Lu(n,α)¹⁷³Tm, ¹⁷⁵Lu(n,2n)^174mLu, and ¹⁷⁵Lu(n,2n)^174gLu reactions at 13.57, 14.03 14.62, and 14.86 MeV neutron energies were measured using an activation technique. The theoretical excitation functions of these reactions were calculated using the Talys-1.95 code. The reaction cross-section data experimentally obtained were analyzed and compared with experimental data reported in the literature, data from five major evaluated nuclear data libraries of IAEA, and theoretical values based on Talys-1.95. The data obtained at some neutron energies agree with some of the data reported in the literature and theoretical values based on Talys-1.95. The consistency of the theoretical curves of excitation functions based on Talys-1.95 with the data obtained in this study and those reported in the literature is higher than that of the evaluation curves of excitation functions for the ¹⁷⁵Lu(n,p)¹⁷⁵Yb, ¹⁷⁵Lu(n,α)¹⁷² Tm, and ¹⁷⁶Lu(n,α)¹⁷³Tm reactions. This study is helpful because it provides new evaluated reaction cross-section data on lutetium (which is a fusion reactor material), improves the quality of neutron-induced reaction cross section data libraries, and advances the research on related applications.

Different coalescence sources of light nucleus production in Au-Au collisions at ${ \sqrt{\boldsymbol s_{\boldsymbol N\boldsymbol N}}=\bf 3 }$ GeV

Rui-Qin Wang, Ji-Peng Lv, Yan-Hao Li, Jun Song, Feng-Lan Shao

2024, 48(5): 053112. doi: 10.1088/1674-1137/ad2b56

Abstract:
We study the production of light nuclei in the coalescence mechanism of Au-Au collisions at midrapidity at $ \sqrt{s_{NN}}=3 $GeV. We derive analytic formulas of the momentum distributions of two bodies, three bodies, and four nucleons coalescing into light nuclei and naturally explain the transverse momentum spectra of the deuteron (d), triton (t), helium-3 (³He), and helium-4 (⁴He). We reproduce data on the yield rapidity densities, yield ratios, and averaged transverse momenta of d, t, ³He, and ⁴He and provide the proportions of contributions from different coalescence sources for t, ³He, and ⁴He in their production. We find that besides nucleon coalescence, nucleon+nucleus coalescence and nucleus+nucleus coalescence may play requisite roles in light nucleus production in Au-Au collisions at $ \sqrt{s_{NN}}=3 $ GeV.

Precise determination of the top-quark on-shell mass ${\boldsymbol M_t}$ via its scale- invariant perturbative relation to the top-quark ${\overline{\bf MS}}$ mass ${{\overline {\boldsymbol m}}_{\boldsymbol t}({\overline {\boldsymbol m}}_{\boldsymbol t})}$

Xu-Dong Huang, Xing-Gang Wu, Xu-Chang Zheng, Jiang Yan, Zhi-Fei Wu, Hong-Hao Ma

2024, 48(5): 053113. doi: 10.1088/1674-1137/ad2dbf

Abstract:
The principle of maximum conformality (PMC) provides a systematic approach to solve the conventional renormalization scheme and scale ambiguities. Scale-fixed predictions of physical observables using the PMC are independent of the choice of renormalization scheme – a key requirement for renormalization group invariance. In this paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual β-function and the quark mass anomalous dimension $ \gamma_m $-function. These new degeneracy relations enable improved PMC scale-setting procedures for correct magnitudes of the strong coupling constant and $ \overline{{\rm{MS}}} $-running quark mass to be determined simultaneously. By using these improved PMC scale-setting procedures, the renormalization scale dependence of the $ \overline{{\rm{MS}}} $-on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or $ \overline{{\rm{MS}}} $) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark $ \overline{{\rm{MS}}} $ mass $ {\overline m}_t({\overline m}_t)=162.5^{+2.1}_{-1.5} $ GeV as the input, we obtain $ M_t\simeq 172.41^{+2.21}_{-1.57} $ GeV. Here, the uncertainties arise from errors combined with those from $ \Delta \alpha_s(M_Z) $ and the approximate uncertainty resulting from the uncalculated five-loop terms predicted through the Padé approximation approach.

Study of the topological quantities of lattice QCD using a modified DCGAN frame

Lin Gao, Heping Ying, Jianbo Zhang

2024, 48(5): 053111. doi: 10.1088/1674-1137/ad2b51

Abstract:
A modified deep convolutional generative adversarial network (M-DCGAN) frame is proposed to study the N-dimensional (ND) topological quantities in lattice QCD based on Monte Carlo (MC) simulations. We construct a new scaling structure including fully connected layers to support the generation of high-quality high-dimensional images for the M-DCGAN. Our results suggest that the M-DCGAN scheme of machine learning will help to more efficiently calculate the 1D distribution of topological charge and the 4D topological charge density compared with MC simulation alone.

Probing valence quark width of the proton in deeply virtual Compton scattering at high energies

Wenchang Xiang, Dewen Cao, Daicui Zhou

2024, 48(5): 054103. doi: 10.1088/1674-1137/ad2b50

Abstract:
We use the refined hot spot model to study the valence quark shape of the proton with the deeply virtual Compton scattering at high energies in the color glass condensate framework. To investigate the individual valence quark shape, a novel treatment of the valence quark width is employed. We calculate the cross-sections for coherent and incoherent deeply virtual Compton scattering using, for the first time, different widths (${B_u}$ and ${B_d}$) for the profile density distributions of the up and down quarks instead of using the same width as in the literature. We find that the cross-sections calculated with ${B_u \geq B_d}$ at each collision energy are consistent with each other, which is in agreement with theoretical expectations, whereas those computed with ${B_u < B_d}$ show some discrepancies. This outcome implies that the up quark might emit more gluons than the down quark, leading to ${B_u \geq B_d}$ at high energy. The impact of energy on the outcome is estimated. Our results show that as the collision energy increases, the aforementioned discrepancies are not only significantly broadened, but also shift to a relatively smaller momentum transfer range at the future Electron-Ion Collider (EIC) and Large Hadron Electron Collider (LHeC) energies, which indicates that the EIC and LHeC can provide an unprecedented chance to access the shape of the valence quark of the proton.

Study of bending angle and shadow in a new Schwarzschild-like black hole affected by plasma and non-plasma mediums

Riasat Ali, Tiecheng Xia, Muhammad Awais, Rimsha Babar

2024, 48(5): 055105. doi: 10.1088/1674-1137/ad2a60

Abstract:
In this study, we analyze the models of the deflection angle of a new Schwarzschild-like black hole (BH) and employ the optical metric of the BH. To achieve this, we use the Gaussian curvature of the optical metric and the Gauss-Bonnet theorem, known as the Gibbons-Werner technique, to determine the deflection angle. Furthermore, we examine the deflection angle in the presence of a plasma medium and the effect of the plasma medium on the deflection angle. The deflection angle of the BH solution in the gauged super-gravity is computed using the Keeton-Petters approach. Utilizing the ray-tracing technique, we investigate the shadow of the corresponding BH and analyze the plots of the deflection angle and shadow to verify the influence of the plasma and algebraic thermodynamic parameters on the deflection angle and shadow.

Correlation function and the inverse problem in the BD interaction

Hai-Peng Li, Jing-Yu Yi, Chu-Wen Xiao, De-Liang Yao, Wei-Hong Liang, Eulogio Oset

2024, 48(5): 053107. doi: 10.1088/1674-1137/ad2dc2

Abstract:
We study the correlation functions of the $ B^0 D^+, B^+ D^0 $ system, which develops a bound state of approximately $ 40 \;{\rm{MeV}} $, using inputs consistent with the $ T_{cc}(3875) $ state. Then, we address the inverse problem starting from these correlation functions to determine the scattering observables related to the system, including the existence of the bound state and its molecular nature. The important output of the approach is the uncertainty with which these observables can be obtained, considering errors in the $ B^0 D^+, B^+ D^0 $ correlation functions typical of current values in correlation functions. We find that it is possible to obtain scattering lengths and effective ranges with relatively high precision and the existence of a bound state. Although the pole position is obtained with errors of the order of 50% of the binding energy, the molecular probability of the state is obtained with a very small error of the order of 6%. All these findings serve as motivation to perform such measurements in future runs of high energy hadron collisions.

Multiplicity dependence of the freezeout parameters in high energy hadron-hadron collisions

Muhammad Ajaz, Majid Shehzad, Muhammad Waqas, Haifa I. Alrebdi, Mohammad Ayaz Ahmad, Antalov Jagnandan, Shawn Jagnandan, Murad Badshah, Jalal Hasan Baker, Abdul Mosawir Quraishi

2024, 48(5): 053108. doi: 10.1088/1674-1137/ad2a4c

Abstract:
We examined the transverse momentum ($ p_T $) spectra of various identified particles, encompassing both light-flavored and strange hadrons ($ \pi^+ + \pi^- $, $ K^+ + K^- $, $ p + \bar{p} $, ϕ, $ K_s^0 $, $ \Lambda + \bar{\Lambda} $, $ \Xi^- + {\bar{\Xi}}^+ $, and $ \Omega^- + {\bar{\Omega}}^+ $), across different multiplicity classes in proton-proton collisions (p-p) at a center-of-mass energy of $ \sqrt{s}= 7 $ TeV. Utilizing the Tsallis and Hagedorn models, parameters relevant to the bulk properties of nuclear matter were extracted. Both models exhibit good agreement with experimental data. In our analyses, we observed a consistent decrease in the effective temperature (T) for the Tsallis model and the kinetic or thermal freeze-out temperature ($ T_0 $) for the Hagedorn model, as we transitioned from higher multiplicity (class-I) to lower multiplicity (class-X). This trend is attributed to the diminished energy transfer in higher multiplicity classes. Additionally, we observed that the transverse flow velocity ($ \beta_T $) experiences a decline from class-I to class-X. The normalization constant, which represents the multiplicity of produced particles, was observed to decrease as we moved toward higher multiplicity classes. While the effective and kinetic freeze-out temperatures, as well as the transverse flow velocity, show a mild dependency on multiplicity for lighter particles, this dependency becomes more pronounced for heavier particles. The multiplicity parameter for heavier particles was observed to be smaller than that of lighter particles, indicating a greater abundance of lighter hadrons compared to heavier ones. Various particle species were observed to undergo decoupling from the fireball at distinct temperatures: lighter particles exhibit lower temperatures, while heavier ones show higher temperatures, thereby supporting the concept of multiple freeze-out scenarios. Moreover, we identified a positive correlation between the kinetic freeze-out temperature and transverse flow velocity, a scenario where particles experience stronger collective motion at a higher freeze-out temperature. The reason for this positive correlation is that, as the multiplicity increases, more energy is transferred into the system. This increased energy causes greater excitation and pressure within the system, leading to a quick expansion.

Gravitational form factors of the proton from near-threshold vector meson photoproduction

Xiao-Yun Wang, Fancong Zeng, Jiyuan Zhang

2024, 48(5): 054102. doi: 10.1088/1674-1137/ad2a66

Abstract:
We systematically analyze the quark and gluon gravitational form factors (GFFs) of the proton by connecting the energy-momentum tensor and near-threshold vector meson photoproduction (NTVMP). Specifically, the quark contributions of GFFs are determined by applying global fitting to the cross section of the lightest vector meson $ \rho^0 $ photoproduction. Combined with the gluon GFFs obtained from heavy quarkonium $ J/\psi $ photoproduction data, the complete GFFs are obtained and compared with the experimental results and lattice quantum chromodynamics determinations. In addition, we use the resonance via Padé (RVP) method based on the Schlessinger point method to obtain a model-independent quark D-term distribution through direct analytical continuation of deeply virtual Compton scattering experimental data. If errors are considered, the results obtained with RVP are essentially consistent with those obtained by NTVMP. Moreover, the comprehensive information on GFFs helps to uncover the mass distribution and mechanical properties inside the proton. This study is not only an important basis for delving into the enigmatic properties of the proton, but also has significance for theoretically guiding future JLab and EIC experimental measurements.

Molecular components in J/ψ and ρ-π puzzle

Xing-Dao Guo, Dian-Yong Chen, Xue-Qian Li, Zhong-Yuan Yuan, Shijing Sang

2024, 48(5): 053110. doi: 10.1088/1674-1137/ad2a65

Abstract:
Motivated by the large branching fractions of $ J/\psi \to f_0 (1710) \omega/f_0(1710) \phi $ and the light exotic candidates, we found that there may exist molecular states composed of $ f_0(1710) \omega $ and $ f_0 (1710) \phi $, which correspond to $ X(2440) $ and $ X(2680) $ observed a few decades ago. The branching fractions of $ X(2440) $ and $ X(2680) $to various $ PV $ and $ KK\omega(\phi) $ channels were estimated in the molecular scenario. In addition, the large branching fractions of $ J/\psi \to f_0 (1710) \omega/f_0(1710) \phi $ indicate sizable molecular components in the $ J/\psi $ state. Thus, we consider $ J/\psi $as the superposition of the$ c\bar{c}(1S) $, $ f_0(1710) \omega $, and $ f_0 (1710) \phi $ molecular states. These molecular components have a significant impact on the light hadron decays of $ J/\psi $, which may elucidate the long standing $ \rho-\pi $ puzzle.

Refined symmetry-resolved Page curve and charged black holes

Pan Li, Yi Ling

2024, 48(5): 053109. doi: 10.1088/1674-1137/ad2e83

Abstract:
The Page curve plotted using the typical random state approximation is not applicable to a system with conserved quantities, such as the evaporation process of a charged black hole, during which the electric charge does not macroscopically radiate out with a uniform rate. In this context, the symmetry-resolved entanglement entropy may play a significant role in describing the entanglement structure of such a system. We attempt to impose constraints on microscopic quantum states to match the macroscopic phenomenon of charge radiation during black hole evaporation. Specifically, we consider a simple qubit system with conserved spin/charge serving as a toy model for the evaporation of charged black holes. We propose refined rules for selecting a random state with conserved quantities to simulate the distribution of charges during the different stages of evaporation and obtain refined Page curves that exhibit distinct features in contrast to the original Page curve. We find that the refined Page curve may have a different Page time and exhibit asymmetric behavior on both sides of the Page time. Such refined Page curves may provide a more realistic description for the entanglement between the charged black hole and radiation during the evaporation process.

Dark energy and matter interacting scenario to relieve H₀ and S₈ tensions

Li-Yang Gao, She-Sheng Xue, Xin Zhang

2024, 48(5): 051001. doi: 10.1088/1674-1137/ad2b52

Abstract:
We consider a new cosmological model (called $ \tilde\Lambda $CDM), in which the vacuum energy interacts with matter and radiation, and test this model using the current cosmological observations. Using the CMB+BAO+SN (CBS) dataset to constrain the model, we find that $ H_0 $ and $ S_8 $ tensions are relieved to $ 2.87\sigma $ and $ 2.77\sigma $, respectively. However, in this case, the $ \tilde\Lambda $CDM model is not favored by the data, compared with ΛCDM. We find that when the $ H_0 $ and $ S_8 $ data are added to the data combination, the situation is significantly improved. In the CBS+$ H_0 $ case, the model relieves the $ H_0 $ tension to $ 0.47\sigma $, and the model is favored over ΛCDM. In the CBS+$ H_0 $+$ S_8 $ case, we obtain a synthetically best situation, in which the $ H_0 $ and $ S_8 $ tensions are relieved to $ 0.72\sigma $ and $ 2.11\sigma $, respectively. In this case, the model is most favored by the data. Therefore, this cosmological model can greatly relieve the $ H_0 $ tension and simultaneously effectively alleviate the $ S_8 $ tension.

Merger estimates for a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories

Hongxin Jiang, Xinyi Du, Qiyuan Pan, Songbai Chen, Jiliang Jing

2024, 48(5): 055103. doi: 10.1088/1674-1137/ad2ce5

Abstract:
We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories. In the ringdown stage of the black hole merger, for the prograde orbit, the real part of the quasinormal modes decreases with an increase in the disformal parameter, and the imaginary part also decreases, except in the Kerr case for a large spin parameter. However, for the retrograde orbit, the real part increases with an increase in the disformal parameter, and the imaginary part always decreases with it. For the approximate final spin, regardless of an equal spin, unequal spin, or generic spin configuration merger, the final black hole spin always increases with an increase in the disformal parameter. Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger, which suggests the differences between these two spacetime structures.

Test particles and quasiperiodic oscillations around Kiselev black hole with cloud of strings

Javlon Rayimbaev, Uktambek Eshimbetov, Bushra Majeed, Ahmadjon Abdujabbarov, Alisher Abduvokhidov, Bakhrom Abdulazizov, Akram Xalmirzayev

2024, 48(5): 055104. doi: 10.1088/1674-1137/ad2060

Abstract:
In the present study, we investigate the dynamics of test particles around a Schwarzschild black hole surrounded by quintessence and immersed in a scalar string cloud field. We start our study by defining the possible values of the quintessence and cloud of string parameters corresponding to the existence of the black hole horizon for fixed values of the parameters of the equation of state for dark energy. We also study the effects of the effective potential on the circular motion, energy, and angular momentum of the test particles together with the innermost stable circular orbits (ISCOs). We investigate the fundamental frequencies in the particle oscillations along stable circular orbits. We relate the stability of the orbits to the Lyapunov exponent, and the chaotic behavior is studied graphically. Finally, we apply the fundamental frequencies to describe quasiperiodic oscillations (QPOs) and find that, in the presence of both fields, low-frequency twin-peak QPOs are not observed. In addition, we obtain the constraint values for the string cloud parameter and mass of the black hole candidates located in the center of the microquasars GRO J1655-40 and GRS 1915+105 as well as the Milky Way galaxy.

Production of charmonium pentaquarks from b-baryon and B-meson decays: SU(3) analysis

Wei-Hao Han, Ye Xing, Ji Xu

2024, 48(5): 053106. doi: 10.1088/1674-1137/ad24d1

Abstract:
Here, we study the production of charmonium pentaquarks $ c \bar c q q q $ from bottom baryon and B-meson decays under the flavor $S U(3) $ symmetry. Decay amplitudes for various processes are parameterized in terms of $S U(3) $ irreducible nonperturbative amplitudes. Numerous relations between decay widths are deduced. Moreover, the strong decays of pentaquarks are considered. Our results can be tested in future measurements at LHCb, Belle II, and CEPC. Once decay branching fractions are measured, this study will be useful for the exploration of new decay channels and pentaquark states.

A scheme to fix multiple solutions in amplitude analyses

Yuanning Gao, Tianze Rong, Zhenwei Yang, Chenjia Zhang, Yanxi Zhang

2024, 48(5): 053001. doi: 10.1088/1674-1137/ad2674

Abstract:
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better understanding of the underlying dynamics. In special cases where two spin-1/2 particles and two (pseudo-) scalar particles are present in the process, multiple equivalent solutions are found owing to intrinsic symmetries in the summed probability density function. In this study, the problem of multiple solutions is discussed, and a scheme to overcome this problem is proposed by fixing some free parameters. Toys are generated to validate the strategy. A new approach to align the helicities of initial- and final-state particles in different decay chains is also introduced.

Bubble nucleation in the two-flavor quark-meson model

Junrong Wang, Ziwan Yu, Hong Mao

2024, 48(5): 053105. doi: 10.1088/1674-1137/ad2a4b

Abstract:
We investigate the dynamics of a first-order quark-hadron transition via homogeneous thermal nucleation in the two-flavor quark-meson model. The contribution of the fermionic vacuum loop in the effective thermodynamics potential and phase diagram, together with the location of the critical endpoint (CEP), is obtained in the temperature and chemical potential plane. For weak and strong first-order phase transitions, by taking the temperature as a variable, the critical bubble profiles, evolutions of the surface tension, and saddle-point action in the presence of a nucleation bubble are numerically calculated in detail when fixing the chemical potentials at $\mu=306~ \mathrm{MeV}$ and $\mu=309 ~\mathrm{MeV}$. Our results show that the system could be trapped in the metastable state for a long time as long as the temperature is between the metastable region characterized by the up and low spinodal lines. Moreover, the surface tension at criticality will rise to approximately $4~ \mathrm{MeV/fm^2}$ when the chemical potential is very high. Such a small surface tension value would favor a mixed phase in the cores of compact stars and may have an important implication in astrophysics.

B meson rare decays in the TNMSSM

Hai-Xiang Chen, Sheng-Kai Cui, Ning-Yu Zhu, Zhao-Yang Zhang, Huai-Cong Hu

2024, 48(5): 053104. doi: 10.1088/1674-1137/ad2a62

Abstract:
We investigate the two loop electroweak corrections to B meson rare decays $ \bar B\rightarrow X_s\gamma $ and $ B_s^0\rightarrow \mu^+\mu^- $ in the minimal supersymmetry standard model (MSSM) extension with two triplets and one singlet (TNMSSM). The new particle contents and interactions in the TNMSSM can affect the theoretical predictions of the branching ratios $ {\rm{Br}}(\bar B\rightarrow X_s\gamma) $ and $ {\rm{Br}}(B_s^0\rightarrow \mu^+\mu^-) $, and the corrections from two loop diagrams to the process $ \bar B\rightarrow X_s\gamma $ can reach around $ 4\% $. Considering the latest experimental measurements, the numerical results of $ {\rm{Br}}(\bar B\rightarrow X_s\gamma) $ and $ {\rm{Br}}(B_s^0\rightarrow \mu^+\mu^-) $ in the TNMSSM are presented and analyzed. The findings indicate that the results in the TNMSSM can fit the updated experimental data well, and the new parameters $ T_{\lambda},\;\kappa,\;\lambda $, clearly affect the theoretical predictions of $ {\rm{Br}}(\bar B\rightarrow X_s\gamma) $ and $ {\rm{Br}}(B_s^0\rightarrow \mu^+\mu^-) $.

Systematic study of cluster radioactivity in trans-lead nuclei with various versions of proximity potential formalisms

Xiao Liu, Jie-Dong Jiang, Xi-Jun Wu, Xiao-Hua Li

2024, 48(5): 054101. doi: 10.1088/1674-1137/ad260b

Abstract:
In this study, based on the framework of the Coulomb and proximity potential model (CPPM), we systematically investigate the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability, which possesses a simple mass dependence on the emitted cluster according to R. Blendowske and H. Walliser [Phys. Rev. Lett. 61, 1930 (1988)]. Moreover, we investigate 28 different versions of the proximity potential formalisms, which are the most complete known proximity potential formalisms proposed to describe proton radioactivity, two-proton radioactivity, α decay, heavy-ion radioactivity, quasi-elastic scattering, fusion reactions, and other applications. The calculated results show that the modified forms of proximity potential 1977, denoted as Prox.77-12, and proximity potential 1981, denoted as Prox.81, are the most appropriate proximity potential formalisms for the study of cluster radioactivity, as the root-mean-square deviation between experimental data and relevant theoretical results obtained is the least; both values are 0.681. For comparison, the universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], unified formula of half-lives for α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)], and scaling law (SL) in cluster radioactivity proposed by Horoi et al. [J. Phys. G 30, 945 (2004)] are also used. In addition, utilizing CPPM with Prox.77-12, Prox.77-1, Prox.77-2, and Prox.81, we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are in the same order of magnitude as those obtained using the compared semi-empirical and/or empirical formulae. At the same time, the competition between α decay and cluster radioactivity of these predicted nuclei is discussed. By comparing the half-lives, this study reveals that α decay predominates.

Black hole shadows in Einstein-Bel-Robinson gravity

B. Hamil, B. C. Lütfüoğlu

2024, 48(5): 055102. doi: 10.1088/1674-1137/ad2a4d

Abstract:
Gravity models given by higher-order scalar curvature corrections are believed to bear important consequences. Einstein-Bel-Robinson (EBR) gravity with quartic curvature modification motivated Sajadi et al. to explore static spherically symmetric black hole solutions using perturbative methods. In this study, inspired by their work, we investigate AdS black hole shadows in EBR gravity and demonstrate how the gravity parameter alters the energy emission rate. Finally, we address the same problem in the presence of plasma, because the black holes are thought to be surrounded by a medium that changes the geodesic of photons.

One-loop contributions for ${\boldsymbol h \bf\rightarrow \boldsymbol\ell \bar{\boldsymbol\ell}\boldsymbol\gamma}$ and ${{\boldsymbol e}^{\bf -}{\boldsymbol e}^{\bf +}{\bf\rightarrow} {\boldsymbol h \boldsymbol \gamma}}$ in the ${{\boldsymbol U}{\bf (1)}_{{\boldsymbol B}{\bf -}{\boldsymbol L}}}$ extension of the standard model

Tran Dzung Tri, Thanh Huy Nguyen, Khiem Hong Phan

2024, 48(5): 053101. doi: 10.1088/1674-1137/ad2441

Abstract:
We present one-loop contributions for $ h\rightarrow \ell \bar{\ell}\gamma $ with $ \ell =\nu_{e, \mu, \tau}, e, \mu $ and $ e^-e^+\rightarrow h\gamma $ in the $ U(1)_{B-L} $ extension of the standard model. In the phenomenological results, the signal strengths for $ h\rightarrow \ell \bar{\ell}\gamma $ at the Large Hadron Collider and for $ e^-e^+\rightarrow h\gamma $ at future lepton colliders are analyzed in the physical parameter space for both the vector and chiral $ B-L $ models. We found that the contributions from the neutral gauge boson $ Z' $ to the signal strengths are rather small. Consequently, the effects will be difficult to probe at future colliders. However, the impacts of charged Higgs and CP-odd Higgs in the chiral $ B-L $ model on the signal strengths are significant and can be measured with the help of the initial polarization beams at future lepton colliders.

Strong decays of the P_c(4312) and its isospin cousin via the QCD sum rules

Xiu-Wu Wang, Zhi-Gang Wang

2024, 48(5): 053102. doi: 10.1088/1674-1137/ad2442

Abstract:
In this study, considering the conservation of isospin in the strong decays, we investigate the strong decays of the pentaquark molecule candidate $ P_c(4312) $ and its possible higher isospin cousin $ P_c(4330) $ in the framework of the QCD sum rules. Further, the pole residue of the Δ baryon with isospin eigenstate $ |II_3\rangle=|\frac{3}{2}\frac{1}{2}\rangle $ is obtained. If the possible pentaquark molecule candidate $ P_c(4330) $ could be determined, it would shed light on the interpretations of the $ P_c $ states in future experiments.

Pair of dyon production near magnetized dyonic Reissner-Nordstrom black holes

Haryanto M. Siahaan

2024, 48(5): 055101. doi: 10.1088/1674-1137/ad25f6

Abstract:
We investigate the phenomenon of pair production of massive scalar particles with magnetic charge near the horizon of a magnetized dyonic Reissner-Nordstrom black hole. The intrinsic symmetry between the electric and magnetic quantities in the Einstein-Maxwell equations suggests that the pair can be generated through Hawking radiation and the Schwinger effect, provided that the Dirac quantization condition is satisfied.

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU (3) quark mean field model

Dhananjay Singh, Arvind Kumar

2024, 48(5): 053103. doi: 10.1088/1674-1137/ad2a64

Abstract:
In the present study, we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3) quark mean field model. Within this model, the properties of the quark matter were modified through the scalar fields $ \sigma, \zeta, \delta, \chi $, vector fields $ \omega, \rho $, ϕ, and Polyakov fields Φ and $ \bar{\Phi} $at finite temperature and chemical potential. Non-extensive effects were introduced through a dimensionless parameter q, and the results were compared to those of the extensive case ($ q\rightarrow 1 $). In the non-extensive case, the exponential in the Fermi-Dirac (FD) function was modified to a q-exponential form. The influence of the q parameter on the thermodynamic properties, pressure, energy, and entropy density, as well as trace anomaly, was investigated. The speed of sound and specific heat with non-extensive effects were also studied. Furthermore, the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of $ u, d, $ and s quarks was explored. We found that the critical end point (CEP), which defines the point in the $ (T - \mu) $ phase diagram where the order of the phase transition changes, shifts to a lower value of temperature, $T_{\rm CEP}$, and a higher value of chemical potential, $\mu_{\rm CEP}$, as the non-extensivity is increased, that is, $ q> $1.

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