Chinese Physics C

Semi-inclusive lepto-production of hidden-charm exotic hadrons

Zhi Yang, Feng-Kun Guo

2021, 45(12): 123101. doi: 10.1088/1674-1137/ac2359

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Abstract:
We investigate the semi-inclusive production of hidden-charm exotic states, including the

\begin{document}$X(3872)$\end{document}

,

\begin{document}$Z_c$\end{document}

,

\begin{document}$Z_{cs}$\end{document}

and pentaquark

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

states, in lepton-proton scattering processes. These hadrons are close to the thresholds of a pair of charm and anticharm hadrons and are assumed to possess a hadronic molecular structure as their main feature. To provide order-of-magnitude estimates of the cross sections, we use Pythia to simulate the short-distance productions of the constituent hadrons, which then rescatter to form exotic hadrons. The estimates for the

\begin{document}$X(3872)$\end{document}

and

\begin{document}$Z_c(3900)^\pm$\end{document}

states are not in conflict with the upper limits measured in the COMPASS experiment for the exclusive photoproduction process. The results indicate that the considered hidden-charm states can be copiously produced at the proposed electron-ion colliders EicC and US-EIC.

Scalar-pseudoscalar pair production at the Large Hadron Collider at NLO+NLL accuracy in QCD

He-Yi Li, Ren-You Zhang, Yu Zhang, Wen-Gan Ma, Ming-Ming Long, Shu-Xiang Li

2021, 45(12): 123102. doi: 10.1088/1674-1137/ac23d2

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Abstract:
We thoroughly investigate both transverse momentum and threshold resummation effects on scalar-pseudoscalar pair production via quark-antiquark annihilation at the

\begin{document}$ 13 \; \text{TeV}$\end{document}

Large Hadron Collider at QCD NLO+NLL accuracy. A factorization method is introduced to properly supplement the soft-gluon (threshold) resummation contribution from parton distribution functions to the resummed results obtained by the Collins-Soper-Sterman resummation approach. We find that the impact of the threshold-resummation improved PDFs is comparable to the resummation effect of the partonic matrix element and can even predominate in high invariant mass regions. Moreover, the loop-induced gluon-gluon fusion channel in the type-I two-Higgs-doublet model is considered in our calculations. The numerical results show that the electroweak production via quark-antiquark annihilation dominates over the gluon-initiated QCD production by

\begin{document}$ 1 \sim 2$\end{document}

orders of magnitude.

A non-renormalizable B-L model with Q₄ × Z₄ × Z₂ flavor symmetry for cobimaximal neutrino mixing

V. V. Vien

2021, 45(12): 123103. doi: 10.1088/1674-1137/ac28f2

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Abstract:
We construct a non-renormalizable gauge

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

model based on

\begin{document}$ Q_4\times Z_4\times Z_2 $\end{document}

symmetry that successfully explains the cobimaximal lepton mixing scheme. Small active neutrino masses and both neutrino mass hierarchies are produced via the type-I seesaw mechanism at the tree-level. The model is predictive; hence, it reproduces the cobimaximal lepton mixing scheme, and the reactor neutrino mixing angle

\begin{document}$ \theta_{13} $\end{document}

and the solar neutrino mixing angle

\begin{document}$ \theta_{12} $\end{document}

can obtain best-fit values from recent experimental data. Our model also predicts the effective neutrino mass parameters of

\begin{document}$ m_{\beta }\in (8.80, 9.05)\, \mathrm{meV} $\end{document}

and

\begin{document}$ \langle m_{ee}\rangle \in (3.65, 3.95)\, \mathrm{meV} $\end{document}

for normal ordering (NO) and

\begin{document}$ m_{\beta }\in (49.16, 49.21)\, \mathrm{meV} $\end{document}

and

\begin{document}$ \langle m_{ee}\rangle \in (48.59, 48.67)\, \mathrm{meV} $\end{document}

for inverted ordering (IO), which are highly consistent with recent experimental constraints.

Radial excited heavy mesons

Muyang Chen

2021, 45(12): 123104. doi: 10.1088/1674-1137/ac2a1a

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In this study, the first radial excited heavy pseudoscalar and vector mesons (

\begin{document}$\eta_c(2S)$\end{document}

,

\begin{document}$\psi(2S)$\end{document}

,

\begin{document}$B_c(2S)$\end{document}

,

\begin{document}$B^*_c(2S)$\end{document}

,

\begin{document}$\eta_b(2S)$\end{document}

, and

\begin{document}$\varUpsilon(2S)$\end{document}

) are investigated using the Dyson-Schwinger equation and Bethe-Salpeter equation approach. It is shown that the effective interactions of the radial excited states are harder than those of the ground states. With the interaction well determined by fitting the masses and leptonic decay constants of

\begin{document}$\psi(2S)$\end{document}

and

\begin{document}$\varUpsilon(2S)$\end{document}

, the first radial excited heavy mesons could be quantitatively described in the rainbow ladder approximation. The masses and leptonic decay constants of

\begin{document}$\eta_c(2S)$\end{document}

,

\begin{document}$B_c(2S)$\end{document}

,

\begin{document}$B^*_c(2S)$\end{document}

, and

\begin{document}$\eta_b(2S)$\end{document}

are predicted.

Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules

Zhi-Gang Wang, Qi Xin

2021, 45(12): 123105. doi: 10.1088/1674-1137/ac2a1d

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Abstract:
In this study, we investigate the

\begin{document}$\bar{D}\Sigma_c$\end{document}

,

\begin{document}$\bar{D}\Xi^\prime_c$\end{document}

,

\begin{document}$\bar{D}\Sigma_c^*$\end{document}

,

\begin{document}$\bar{D}\Xi_c^*$\end{document}

,

\begin{document}$\bar{D}^{*}\Sigma_c$\end{document}

,

\begin{document}$\bar{D}^{*}\Xi^\prime_c$\end{document}

,

\begin{document}$\bar{D}^{*}\Sigma_c^*$\end{document}

, and

\begin{document}$\bar{D}^{*}\Xi_c^*$\end{document}

pentaquark molecular states with and without strangeness via the QCD sum rules in detail, focusing on the light flavor,

\begin{document}$SU(3)$\end{document}

, breaking effects, and make predictions for new pentaquark molecular states besides assigning

\begin{document}$P_c(4312)$\end{document}

,

\begin{document}$P_c(4380)$\end{document}

,

\begin{document}$P_c(4440)$\end{document}

,

\begin{document}$P_c(4457)$\end{document}

, and

\begin{document}$P_{cs}(4459)$\end{document}

self-consistently. In the future, we can search for these pentaquark molecular states in the decay of

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

,

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

, and

\begin{document}$\Xi_b^-$\end{document}

. Furthermore, we discuss high-dimensional vacuum condensates in detail.

Analytic two-loop master integrals for tW production at hadron colliders: I

Long-Bin Chen, Jian Wang

2021, 45(12): 123106. doi: 10.1088/1674-1137/ac2a1e

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Abstract:
We present the analytic calculation of two-loop master integrals that are relevant for tW production at hadron colliders. We focus on the integral families with only one massive propagator. After selecting a canonical basis, the differential equations for the master integrals can be transformed into the d ln form. The boundaries are determined by simple direct integrations or regularity conditions at kinematic points without physical singularities. The analytical results in this work are expressed in terms of multiple polylogarithms, and have been checked via numerical computations.

Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions

Fan Si, Yifei Zhang, Xiaofeng Luo

2021, 45(12): 124001. doi: 10.1088/1674-1137/ac24f6

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We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space. The theoretical conclusions are supported by a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method. The valid averaged efficiency is found to suppress the statistical uncertainties of the reproduced cumulants dramatically. Thus, usage of the averaged efficiency requires a careful study of phase space dependence. This study is important for carrying out precision measurements of higher-order cumulants in heavy-ion collision experiments at present and in future.

Measurements of ^natCd(γ, x) reaction cross sections and isomer ratio of ^115m,gCd with the bremsstrahlung end-point energies of 50 and 60 MeV

Muhammad Nadeem, Md. Shakilur Rahman, Muhammad Shahid, Guinyun Kim, Haladhara Naik, Nguyen Thi Hien

2021, 45(12): 124002. doi: 10.1088/1674-1137/ac256b

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Abstract:
The flux-weighted average cross sections of ^natCd(γ, xn)^{115g,m,111m,109,107,105,104}Cd and ^natCd(γ, x)^{113g,112,111g,110m}Ag reactions were measured at the bremsstrahlung end-point energies of 50 and 60 MeV. The activation and off-line γ-ray spectrometric technique was carried out using the 100 MeV electron linear accelerator at the Pohang Accelerator Laboratory, Korea. The ^natCd(γ, xn) reaction cross sections as a function of photon energy were theoretically calculated using the TALYS-1.95 and the EMPIRE-3.2 Malta codes. Then, the flux-weighted average cross sections were obtained from the theoretical values of mono-energetic photons. These values were compared with the flux-weighted values from the present study and were found to be in general agreement. The measured experimental reaction cross-sections and integral yields were described for cadmium and silver isotopes in the ^natCd(γ, xn)^{115g,m,111m,109,107,105,104}Cd and ^natCd(γ, x)^{113g,112,111g,110m}Ag reactions. The isomeric yield ratio (IR) of ^115g,mCd in the ^natCd(γ, xn) reaction was determined for the two bremsstrahlung end-point energies. The measured isomeric yield ratios of ^115g,mCd in the ^natCd(γ, xn) reaction were also compared with the theoretical values of the nuclear model codes and previously published literature data of the ¹¹⁶Cd(γ, n) and ¹¹⁶Cd(n, 2n) reactions. It was found that the IR value increases with increasing projectile energy, which demonstrates the characteristic of excitation energy. However, the higher IR value of ^115g,mCd in the ¹¹⁶Cd(n, 2n) reaction compared to that in the ¹¹⁶Cd(γ, n) reaction indicates the role of compound nuclear spin alongside excitation energy.

Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon forpositive and negative Q-value systems using the proximity-type potential

R. Gharaei, A. Fuji, B. Azadegan

2021, 45(12): 124101. doi: 10.1088/1674-1137/ac23d3

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A systematic survey of the accurate measurements of heavy-ion fusion cross sections at extreme sub-barrier energies is performed using the coupled-channels (CC) theory that is based on the proximity formalism. This work theoretically explores the role of the surface energy coefficient and energy-dependent nucleus-nucleus proximity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative

\begin{document}$Q$\end{document}

-values, including ¹¹B+¹⁹⁷Au, ¹²C+¹⁹⁸Pt, ¹⁶O+²⁰⁸Pb, ²⁸Si+⁹⁴Mo, ⁴⁸Ca+⁹⁶Zr, ²⁸Si+⁶⁴Ni, ⁵⁸Ni+⁵⁸Ni, ⁶⁰Ni+⁸⁹Y, ¹²C+²⁰⁴Pb, ³⁶S+⁶⁴Ni, ³⁶S+⁹⁰Zr, ⁴⁰Ca+⁹⁰Zr, ⁴⁰Ca+⁴⁰Ca, and ⁴⁸Ca+⁴⁸Ca, as well as five typical colliding systems with positive

\begin{document}$Q$\end{document}

-values, including ¹²C+³⁰Si, ²⁴Mg+³⁰Si, ²⁸Si+³⁰Si, ³⁶S+⁴⁸Ca, and ⁴⁰Ca+⁴⁸Ca. It is shown that the outcomes based on the proximity potential along with the above-mentioned physical effects achieve reasonable agreement with the experimentally observed data of the fusion cross sections

\begin{document}$\sigma_{\rm{fus}}(E)$\end{document}

, astrophysical

\begin{document}$S(E)$\end{document}

factors, and logarithmic derivatives

\begin{document}$L(E)$\end{document}

in the energy region far below the Coulomb barrier. A discussion is also presented on the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.

Influence of different fields of mesons on the pseudospin symmetry in single-neutron resonant states

Hua-Ming Dai, Min Shi, Shou-Wan Chen, Quan Liu

2021, 45(12): 124102. doi: 10.1088/1674-1137/ac23d4

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In the framework of the relativistic mean field theory combined with the complex momentum representation method, we elucidate the pseudospin symmetry in the single-neutron resonant states and its dependence on the

\begin{document}$\sigma$\end{document}

,

\begin{document}$\omega$\end{document}

, and

\begin{document}$\rho$\end{document}

meson fields. Compared with the effect of the

\begin{document}$\rho$\end{document}

field, the

\begin{document}$\sigma$\end{document}

and

\begin{document}$\omega$\end{document}

fields provide the main contributions to the pseudospin energy and width splitting of the resonant pseudospin doublets. Especially, we compare quantitatively the pseudospin wave functions' splittings in resonant doublets, and investigate their dependencies on different fields of mesons, which is consistent with that of energy and width splittings. Current research is helpful to understand the mechanism and properties of pseudospin symmetry for resonant states.

Modeling complex networks of nuclear reaction data for probing their discovery processes

Xiaohang Wang, Long Zhu, Jun Su

2021, 45(12): 124103. doi: 10.1088/1674-1137/ac23d5

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Abstract:
Hundreds of thousands of experimental data sets of nuclear reactions have been systematically collected, and their number is still growing rapidly. The data and their correlations compose a complex system, which underpins nuclear science and technology. We model the nuclear reaction data as weighted evolving networks for the purpose of data verification and validation. The networks are employed to study the growing cross-section data of a neutron induced threshold reaction (n,2n) and photoneutron reaction. In the networks, the nodes are the historical data, and the weights of the links are the relative deviation between the data points. It is found that the networks exhibit small-world behavior, and their discovery processes are well described by the Heaps law. What makes the networks novel is the mapping relation between the network properties and the salient features of the database: the Heaps exponent corresponds to the exploration efficiency of the specific data set, the distribution of the edge-weights corresponds to the global uncertainty of the data set, and the mean node weight corresponds to the uncertainty of the individual data point. This new perspective to understand the database will be helpful for nuclear data analysis and compilation.

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches

Xiao Pan, You-Tian Zou, Hong-Ming Liu, Biao He, Xiao-Hua Li, Xi-Jun Wu, Zhen Zhang

2021, 45(12): 124104. doi: 10.1088/1674-1137/ac2421

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In this work, we systematically study the two-proton (

\begin{document}$2p$\end{document}

) radioactivity half-lives using the two-potential approach, and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8. For true

\begin{document}$2p$\end{document}

radioactivity (

\begin{document}$Q_{2p}$\end{document}

\begin{document}$>$\end{document}

0 and

\begin{document}$Q_p$\end{document}

\begin{document}$< $\end{document}

0, where

\begin{document}$Q_p$\end{document}

and

\begin{document}$Q_{2p}$\end{document}

are the released energies of the one-proton and two-proton radioactivity, respectively), the standard deviation between the experimental half-lives and our theoretical calculations is 0.701. In addition, we extend this model to predict the half-lives of 15 possible

\begin{document}$2p$\end{document}

radioactivity candidates with

\begin{document}$Q_{2p}$\end{document}

\begin{document}$>$\end{document}

0 obtained from the evaluated atomic mass table AME2016. The calculated results indicate a clear linear relationship between the logarithmic

\begin{document}$2p$\end{document}

radioactivity half-lives (

\begin{document}${\log}_{10}T_{1/2}$\end{document}

) and coulomb parameters [(

\begin{document}$Z_{d}^{0.8}$\end{document}

+

\begin{document}${l}^{\,0.25}$\end{document}

)

\begin{document}$Q_{2p}^{-1/2}$\end{document}

] considering the effect of orbital angular momentum proposed by Liu

\begin{document}$et$\end{document}

\begin{document}$al.$\end{document}

[Chin. Phys. C 45, 024108 (2021)]. For comparison, the generalized liquid drop model (GLDM), effective liquid drop model (ELDM), and Gamow-like model are also used. Our predicted results are consistent with those obtained using other relevant models.

Two-proton radioactivity of ground and excited states within a unified fission model

Fengzhu Xing, Jianpo Cui, Yanzhao Wang, Jianzhong Gu

2021, 45(12): 124105. doi: 10.1088/1674-1137/ac2425

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A unified fission model is extended to study two-proton radioactivity of the ground states of nuclei, and a good agreement between the experimental and calculated half-lives is found. The two-proton radioactivity half-lives of the ground states of some probable candidates are predicted within this model by inputting the released energies taken from the AME2020 table. It is shown that the predictive accuracy of the half-lives is comparable to those of other models. Then, two-proton radioactivity of the excited states of ¹⁴O, ^17,18Ne, ²²Mg, ²⁹S, and ⁹⁴Ag is discussed within the unified fission model and two analytical formulas. It is found that the experimental half-lives of the excited states are reproduced better within the unified fission model. Furthermore, the two formulas are not suitable for the study of two-proton radioactivity of excited states because their physical appearance deviates from the mechanism of quantum tunneling, and the parameters involved are obtained without including experimental data from the excited states.

Theoretical study on the favored alpha-decay half-lives of deformed nuclei

M. Hassanzad, O.N. Ghodsi

2021, 45(12): 124106. doi: 10.1088/1674-1137/ac28f3

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A systematic study on the α-decay half-lives of nuclei in the range

\begin{document}$93\leqslant Z \leqslant 118$\end{document}

is performed by employing various versions of proximity potentials. To obtain more reliable results, deformation terms are included up to hexadecapole (

\begin{document}$\beta_{4}$\end{document}

) in the spherical-deformed nuclear and Coulomb interaction potentials. First, the favored α-decay processes in this region are categorized as even-even, odd A, and odd-odd nuclei. Second, they are grouped into two transitions: ground state to ground state and ground state to isomeric states. Owing to the comparison of their root-mean-square deviations (RMSD's),

\begin{document}$Bass 77$\end{document}

and

\begin{document}$Ngo 80$\end{document}

have the lowest values and better reproduce experimental data. Moreover, by considering preformation probability within the cluster formation model, the results validate the significant reduction in root-mean-square deviations obtained for different versions of proximity. Hence, the deviation between the calculated and experimental data is detracted.

Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach

Zilong Yuan, Dachuan Tian, Jian Li, Zhongming Niu

2021, 45(12): 124107. doi: 10.1088/1674-1137/ac28f9

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The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei. The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square (rms) deviations from data, i.e., 0.949

\begin{document}$ \mu_\mathrm{N} $\end{document}

and 1.272

\begin{document}$ \mu_\mathrm{N} $\end{document}

for odd-neutron nuclei and odd-proton nuclei, respectively. By including the dependence of the nuclear spin and Schmidt magnetic moment, the machine-learning approach precisely describes the magnetic moments of odd-A nuclei with rms deviations of 0.036

\begin{document}$ \mu_\mathrm{N} $\end{document}

for odd-neutron nuclei and 0.061

\begin{document}$ \mu_\mathrm{N} $\end{document}

for odd-proton nuclei. Furthermore, the evolution of magnetic moments along isotopic chains, including the staggering and sudden jump trend, which are difficult to describe using nuclear models, have been well reproduced by the Bayesian neural network (BNN) approach. The magnetic moments of doubly closed-shell

\begin{document}$ \pm1 $\end{document}

nuclei, for example, isoscalar and isovector magnetic moments, have been well studied and compared with the corresponding non-relativistic and relativistic calculations.

Potential energy surfaces and fission fragment mass yields of even-even superheavy nuclei

Pavel V. Kostryukov, Artur Dobrowolski, Bożena Nerlo-Pomorska, Michał Warda, Zhigang Xiao, Yongjing Chen, Lile Liu, Jun-Long Tian, Krzysztof Pomorski

2021, 45(12): 124108. doi: 10.1088/1674-1137/ac29a3

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Abstract:
Potential energy surfaces and fission barriers of superheavy nuclei are analyzed in a macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD) model is used to obtain the macroscopic part of the energy, whereas the shell and pairing energy corrections are evaluated using the Yukawa-folded potential; a standard flooding technique is utilized to determine barrier heights. A Fourier shape parametrization containing only three deformation parameters is shown to effectively reproduce the nuclear shapes of nuclei approaching fission. In addition, a non-axial degree of freedom is taken into account to better describe the structure of nuclei around the ground state and in the saddle region. In addition to the symmetric fission valley, a new highly asymmetric fission mode is predicted in most superheavy nuclei. The fission fragment mass distributions of the considered nuclei are obtained by solving 3D Langevin equations.

Probing the anisotropic distribution of baryon matter in the Universe using fast radio bursts

Hai-Nan Lin, Yu Sang

2021, 45(12): 125101. doi: 10.1088/1674-1137/ac2660

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Abstract:
We propose that fast radio bursts (FRBs) can be used as probes to constrain the possible anisotropic distribution of baryon matter in the Universe. Monte Carlo simulations show that 400 (800) FRBs are sufficient to detect the anisotropy at a 95% (99%) confidence level if the dipole amplitude has an order of magnitude of 0.01. However, more FRBs are required to tightly constrain the dipole direction. Even 1000 FRBs are insufficient to constrain the dipole direction within the angular uncertainty

\begin{document}$\Delta\theta<40^{\circ}$\end{document}

at a 95% confidence level. The uncertainty on the dispersion measure of a host galaxy does not significantly affect the results. However, if the dipole amplitude is in the region of 0.001, 1000 FRBs are not enough to correctly detect the anisotropic signal.

Observational constraint on dark energy from quantum uncertainty

Long Huang, Xiaofeng Yang, Xiang Liu

2021, 45(12): 125102. doi: 10.1088/1674-1137/ac2946

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Abstract:
We explore the theoretical possibility that dark energy density is derived from massless scalar bosons in vacuum and present a physical model for dark energy. By assuming massless scalar bosons fall into the horizon boundary of the cosmos with the expansion of the universe, we can deduce the uncertainty in the relative position of scalar bosons based on the quantum fluctuation of space-time and the assumption that scalar bosons satisfy P-symmetry under the parity transformation

\begin{document}$ {P}\varphi ({r}) = - \varphi ({r})$\end{document}

, which can be used to estimate scalar bosons and dark energy density. Furthermore, we attempt to explain the origin of negative pressure from the increasing entropy density of the Boltzmann system and derive the equation for the state parameter, which is consistent with the specific equations of state for dark energy. Finally, we employ the SNIa Pantheon sample and Planck 2018 CMB angular power spectra to constrain the models and provide statistical results for the cosmology parameters.

2021 Vol. 45, No. 12