Chinese Physics C

Invariant-mass distribution of top-quark pairs and top-quark mass determination

Wan-Li Ju, Guoxing Wang, Xing Wang, Xiaofeng Xu, Yongqi Xu, Li Lin Yang

2020, 44(9): 091001. doi: 10.1088/1674-1137/44/9/091001

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Abstract:
In this study, we investigate the invariant-mass distribution of top-quark pairs near the 2m_t threshold, which strongly influences the determination of the top-quark mass m_t. Higher-order non-relativistic corrections lead to large contributions, which are not included in the state-of-the-art theoretical predictions. A factorization formula is derived to resum such corrections to all orders in the strong-coupling, and necessary ingredients are calculated to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numerical results. The resummation effect significantly increases the differential cross-section in the threshold region and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of

\begin{document}$m_t $\end{document}

will lead to a value closer to the direct measurement result.

QCD corrections to ${{{e^+e^-}}{{\rightarrow}}{{H^{\pm}}}{{W^{\mp}}}}$ in Type-I THDM at electron positron colliders

Qiang Yang, Ren-You Zhang, Ming-Ming Long, Shao-Ming Wang, Wen-Gan Ma, Jian-Wen Zhu, Yi Jiang

2020, 44(9): 093101. doi: 10.1088/1674-1137/44/9/093101

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Abstract:
We investigate in detail the charged Higgs production associated with a W boson at electron-positron colliders within the framework of the Type-I two-Higgs-doublet model (THDM). We calculate the integrated cross section at the LO and analyze the dependence of the cross section on the THDM parameters and the colliding energy in a benchmark scenario of the input parameters of the Higgs sector. The numerical results show that the integrated cross section is sensitive to the charged Higgs mass, especially in the vicinity of

\begin{document}$m_{H^{\pm}} \simeq 184~ {\rm GeV}$\end{document}

at a

\begin{document}$500~ {\rm GeV}$\end{document}

\begin{document}$e^+e^-$\end{document}

collider, and decreases consistently with the increase of

\begin{document}$\tan\beta$\end{document}

in the low

\begin{document}$\tan\beta$\end{document}

region. The peak in the colliding energy distribution of the cross section arises from the resonance of the loop integrals, and it moves towards the low colliding energy with the increase of

\begin{document}$m_{H^{\pm}}$\end{document}

. We also study the two-loop NLO QCD corrections to both the integrated cross section and the angular distribution of the charged Higgs boson and find that the QCD relative correction is also sensitive to the charged Higgs mass and strongly depends on the final-state phase space. For

\begin{document}$\tan\beta = 2$\end{document}

, the QCD relative correction at a

\begin{document}$500~ {\rm GeV}$\end{document}

\begin{document}$e^+e^-$\end{document}

collider varies in the range of [-10%, 11%] as

\begin{document}$m_{H^{\pm}}$\end{document}

increases from 150 to 400 GeV.

Holographic technicolor model and dark matter

Yidian Chen, Xiao-Jun Bi, Mei Huang

2020, 44(9): 093102. doi: 10.1088/1674-1137/44/9/093102

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We investigate the strongly coupled minimal walking technicolor model (MWT) in the framework of a bottom-up holographic model, where the global

\begin{document}$ SU(4)$\end{document}

symmetry breaks into

\begin{document}$ SO(4)$\end{document}

subgroups. In the holographic model, we found that 125 GeV composite Higgs particles and small Peskin–Takeuchi S parameter can be achieved simultaneously. In addition, the model predicts a large number of particles at the TeV scale, including dark matter candidates Technicolor Interacting Massive Particles (TIMPs). If we consider the dark matter nuclear spin-independent cross-section in the range of

\begin{document}$ 10^{-45}\sim 10 ^ {-48} \;{\rm{cm}}^2$\end{document}

, which can be detected by future experiments, the mass range of TIMPs predicted by the holographic technicolor model is

\begin{document}$ 2 \sim 4$\end{document}

TeV.

Heavy Higgs bosons at the LHC upgrade

Tong Li

2020, 44(9): 093103. doi: 10.1088/1674-1137/44/9/093103

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We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with

\begin{document}$\sqrt{s}=27$\end{document}

TeV. We assume the degenerate mass spectrum and an approximate alignment limit in the Type-II Two Higgs Doublet Model for illustration. We explore the observability of the heavy neutral Higgs bosons by examining the clean signals from

\begin{document}$H^0\to W^+W^-, ZZ$\end{document}

via gluon-gluon fusion production. The associated production of a top quark and a charged Higgs boson via

\begin{document}$gb\to t H^\pm$\end{document}

is adopted to predict the discovery potential of heavy charged Higgses. We also emphasize the potential importance of the electroweak production of Higgs boson pairs, i.e.

\begin{document}$pp\to W^\ast \to H^\pm A^0$\end{document}

and

\begin{document}$pp\to Z^\ast/\gamma^\ast \to H^+ H^-$\end{document}

. These are only governed by pure electroweak gauge couplings and can provide complementary information to the conventional signals in the determination of the nature of the Higgs sector.

Study on the possible molecular state composed of $ {{D}^ * _s} {\bar{{D}}_{{s1}}}$ within the Bethe-Salpeter framework

Hong-Wei Ke, Xiao-Hai Liu, Xue-Qian Li

2020, 44(9): 093104. doi: 10.1088/1674-1137/44/9/093104

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Recently, a vector charmonium-like state

\begin{document}$Y(4626)$\end{document}

was observed in the portal of

\begin{document}$D^+_sD_{s1}(2536)^-$\end{document}

. This intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure that contains suitable inner constituents. Therefore, this observation concerns the general theoretical framework about possible structures of exotic states. Since the mass of

\begin{document}$Y(4626)$\end{document}

is slightly above the production threshold of

\begin{document}$ D^+_s D_{s1}(2536)^- ,$\end{document}

whereas it is below that of

\begin{document}$D^ * _s\bar D_{s1}(2536)$\end{document}

with the same quark contents as that of

\begin{document}$D^+_s D_{s1}(2536)^-$\end{document}

, it is natural to conjecture that

\begin{document}$Y(4626)$\end{document}

is a molecular state of

\begin{document}$D^{ * }_s\bar D_{s1}(2536)$\end{document}

, as suggested in the literature. Confirming or negating this allegation would shed light on the goal we are concerned with. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e.,

\begin{document}$D^ * _s\bar D_{s1}(2536)$\end{document}

within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter

\begin{document}$\lambda$\end{document}

in the form factor, which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing even a very small binding energy

\begin{document}$\Delta E$\end{document}

. It implies that the

\begin{document}$D^ * _s\bar D_{s1}(2536)$\end{document}

system cannot exist in the nature as a hadronic molecule in this model. Therefore, we may not be able to assume the resonance

\begin{document}$Y(4626)$\end{document}

to be a bound state of

\begin{document}$ D^ * _s\bar D_{s1}(2536) ,$\end{document}

and instead, it could be attributed to something else, such as a tetraquark.

Gluon-pair-creation production model of strong interaction vertices

Bing-Dong Wan, Cong-Feng Qiao

2020, 44(9): 093105. doi: 10.1088/1674-1137/44/9/093105

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By studying the

\begin{document}$\eta_c$\end{document}

exclusive decay to double glueballs, we introduce a model to phenomenologically mimic the gluon-pair-vacuum interaction vertices, namely the

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

model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly

\begin{document}$\eta_c \to f_0(1500)\eta(1405)$\end{document}

,

\begin{document}$\eta_b\to f_0(1500)\eta(1405)$\end{document}

, and

\begin{document}$\eta_b\to f_0(1710)\eta(1405)$\end{document}

processes. Among them

\begin{document}$f_0(1500)$\end{document}

and

\begin{document}$f_0(1710)$\end{document}

are well-known scalars possessing large glue components, while

\begin{document}$\eta(1405)$\end{document}

is a potential candidate for a pseudoscalar glueball. The preliminary calculation results indicate that these processes are marginally accessible in the presently running experiments BES III, BELLE II, and LHCb.

Complete reduction of integrals in two-loop five-light-parton scattering amplitudes

Xin Guan, Xiao Liu, Yan-Qing Ma

2020, 44(9): 093106. doi: 10.1088/1674-1137/44/9/093106

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We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals.

Search for the ${{{D^*}}\!{{\bar{D}^*}}}$ molecular state ${{Z_c(4000)}}$ in the reaction ${{B^{-}\! \rightarrow\! J/\psi \rho^0 K^{-}}}$

Yang Zhang, En Wang, De-Min Li, Yu-Xiao Li

2020, 44(9): 093107. doi: 10.1088/1674-1137/44/9/093107

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Based on the prediction of a

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

molecular state

\begin{document}$Z_c(4000)$\end{document}

with isospin

\begin{document}$I=1$\end{document}

in the coupled channel approach, we suggest the search for this state in the reaction

\begin{document}$B^- \to J/\psi \rho^0 K^-$\end{document}

. By considering the final state interactions of

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

and

\begin{document}$D^{*0}\bar{D}^{*0}$\end{document}

and the contribution from the

\begin{document}$K_1(1270)$\end{document}

resonance, we observed that the

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

mass distribution shows a peak around 4000 MeV, which might be associated with the

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

molecular state

\begin{document}$Z_c(4000)$\end{document}

. The search for

\begin{document}$Z_c(4000)$\end{document}

in the reaction

\begin{document}$B^- \to J/\psi \rho^0 K^-$\end{document}

is critical for understanding the internal structures of exotic hadrons. Our predictions can be tested by the Belle II and LHCb in future studies.

Lifetime measurement for the $ {{2_1^+}}$ state in ¹⁰⁶Cd

Jian Zhong, Ying-Jun Ma, Xiao-Guang Wu, Bao-Ji Zhu, Cong-Bo Li, Guang-Sheng Li, Yun Zheng, Qi-Ming Chen, Chuang-Ye He, Li-Tao Deng, Wen-Kui Zhou, Ke-Yan Ma, Dong Yang, Hao Guo, Jia-Qi Wang, Xian Guang, Ji Sun, Hui-Bin Sun, Shi-Peng Hu, Lin Gan, Hai-Ge Zhao, Qi Luo, Zheng-Xin Wu

2020, 44(9): 094001. doi: 10.1088/1674-1137/44/9/094001

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The lifetime of the

\begin{document}$2_{1}^{+}$\end{document}

state in

\begin{document}$^{106}$\end{document}

Cd populated via the

\begin{document}$^{94}$\end{document}

Zr (

\begin{document}$^{16}$\end{document}

O, 4n)

\begin{document}$^{106}$\end{document}

Cd reaction has been measured with the Recoil Distance Doppler Shift technique in combination with the Differential Decay Curve Method. By subtracting the contamination in the data, the mean lifetime of the

\begin{document}$I^{\pi}$\end{document}

=2

\begin{document}$^{+}_{1}$\end{document}

633 keV state was determined as 9.9 (12) ps. The

\begin{document}$B(E2)$\end{document}

value calculated in this study is in good agreement with the experimental systematics and was compared to the shell model calculations.

Covariant spin kinetic theory I: collisionless limit

Yu-Chen Liu, Kazuya Mameda, Xu-Guang Huang

2020, 44(9): 094101. doi: 10.1088/1674-1137/44/9/094101

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We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory. We derive four coupled semi-classical kinetic equations accurate to

\begin{document}$O(\hbar)$\end{document}

, which describe the transports of particle number and spin degrees of freedom. The relationship with chiral kinetic theory is discussed. As an application, we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.

Analysis of survival probability based on superasymmetric reaction systems

Na-Na Li, Xiao-Jun Bao

2020, 44(9): 094102. doi: 10.1088/1674-1137/44/9/094102

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The survival probability of an excited compound nucleus was studied using two different approaches of the washing out of shell effects with excitation energy based on a superasymmetric reaction system. The estimated evaporation residue cross sections based on the two different methods are compared with the available experimental data. Both methods are in agreement with the experimental data to a certain extent for some specific reactions and

\begin{document}$ xn$\end{document}

emission channels.

Chiral magnetic effect in isobar collisions from stochastic hydrodynamics

Gui-Rong Liang, Jinfeng Liao, Shu Lin, Li Yan, Miao Li

2020, 44(9): 094103. doi: 10.1088/1674-1137/44/9/094103

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We studied the chiral magnetic effect in AuAu, RuRu, and ZrZr collisions at

\begin{document}$\sqrt{s_{{NN}}}=200\;{\rm{GeV}}$\end{document}

. The axial charge evolution was modeled with stochastic hydrodynamics, and geometrical quantities were calculated with the Monte Carlo Glauber model. By adjusting the relaxation time of the magnetic field, we found our results are in good agreement with background subtracted data for AuAu collisions at the same energy. We also made predictions for RuRu and ZrZr collisions. We found a weak centrality dependence on initial chiral imbalance, which implies that the centrality dependence of chiral magnetic effect signals results mainly from the effects of the magnetic field and volume factor. Furthermore, our results show an unexpected dependence on system size. While the AuAu system has larger chiral imbalance and magnetic field, it was observed to have a smaller signal for the chiral magnetic effect due to the larger volume suppression factor.

Multiple configurations of neutron stars containing quark matter

Wei Wei, Shu-Hua Yang, Ze-Han Bao, Chong Zhang, Chang Gao, Wei-Ru Fan

2020, 44(9): 094104. doi: 10.1088/1674-1137/44/9/094104

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The main purpose of this study is to interpret the possibilities of hybrid star configurations under different phase transition paths and provide a general description of the conditions and features of the different configurations. We assume that there are two possible phase transition paths, i.e., from a nuclear phase to a 2flavor(2f)/3flavor(3f) quark phase directly, or first from a nuclear phase to a 2f quark phase, and then from that phase to a 3f quark phase sequentially. In addition, we consider Maxwell and Gibbs constructions based on the assumption of a first-order transition, which yields multiple configurations of hybrid stars: N-2f, N-3f, and N-2f-3f for a Maxwell construction, and N-2fmix-2f, N-3fmix-3f, N-2f3fmix, and N-2fmix-3f for a Gibbs construction. From the radii analysis of different hybrid star configurations with the same mass of

\begin{document}$1.95M_\odot$\end{document}

, the appearance of the quark matter (from nuclear to 2f or 3f quark matter) causes a radius difference of 0.5km~2km and provides the possibility of detection by NICER in the future. However, the sequential transition from 2f to 3f quark matter is difficult to detect because the transition does not lead to too high of a change in radius (far smaller than

\begin{document}$0.5\; {\rm{km}}$\end{document}

). The dependence solely on the measurements of the stellar radii to probe the equation of state of dense matter in neutron stars causes difficulties. Multi-messenger observations can help us to infer the interior of a neutron star in the future.

Emission time sequence of neutrons and protons as probes of α-clustering structure

Bo-Song Huang, Yu-Gang Ma

2020, 44(9): 094105. doi: 10.1088/1674-1137/44/9/094105

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Neutron–proton momentum correlation functions are constructed from a three-body photodisintegration channel, i.e., core

\begin{document}$ + n + p$\end{document}

, and used to explore the spatial-time information of the non-clustering Woods–Saxon spherical structure as well as the

\begin{document}$\alpha$\end{document}

-clustering structures of

\begin{document}$^{12}{\rm{C}}$\end{document}

or

\begin{document}$^{16}{\rm{O}}$\end{document}

based on an extended quantum molecular dynamics model. The emission time sequence of neutrons and protons is indicated by the ratio of velocity-gated neutron–proton correlation functions, demonstrating its sensitivity to

\begin{document}$\alpha$\end{document}

-clustering structures. This work sheds light on a new probe for

\begin{document}$\alpha$\end{document}

-clustering structures.

Systematic study of the α decay preformation factors of the nuclei around the Z = 82, N = 126 shell closures within the generalized liquid drop model

Hong-Ming Liu, You-Tian Zou, Xiao Pan, Xiao-Jun Bao, Xiao-Hua Li

2020, 44(9): 094106. doi: 10.1088/1674-1137/44/9/094106

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In this study, we systematically investigate the

\begin{document}$\alpha$\end{document}

decay preformation factors,

\begin{document}$P_{\alpha}$\end{document}

, and the

\begin{document}$\alpha$\end{document}

decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with

\begin{document}$P_{\alpha}$\end{document}

being extracted from the ratio of the calculated

\begin{document}$\alpha$\end{document}

decay half-life to the experimental one. The results show that there is a remarkable linear relationship between

\begin{document}$P_{\alpha}$\end{document}

and the product of valance protons (holes)

\begin{document}$N_p$\end{document}

and valance neutrons (holes)

\begin{document}$N_n$\end{document}

. At the same time, we extract the

\begin{document}$\alpha$\end{document}

decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun

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

[J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the

\begin{document}$\alpha$\end{document}

decay was calculated by two different microscopic formulas. We find that the

\begin{document}$\alpha$\end{document}

decay preformation factors are also related to

\begin{document}$N_pN_n$\end{document}

. Combining with our previous studies [Sun

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

, Phys. Rev. C, 94: 024338 (2016); Deng

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

, ibid. 96: 024318 (2017); Deng

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

, ibid. 97: 044322 (2018)] and that of Seif

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

[Phys. Rev. C, 84: 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the

\begin{document}$\alpha$\end{document}

decay preformation factor data calculated by the GLDM, we calculate the

\begin{document}$\alpha$\end{document}

decay half-lives of these nuclei. The calculated results agree with the experimental data well.

Systematic study of odd-mass ^151-161Pm and ^154,156Pm isotopes using projected shell model

Veerta Rani, Preeti Verma, Suram Singh, Manvi Rajput, Arun Bharti, G. H. Bhat, J. A. Sheikh

2020, 44(9): 094107. doi: 10.1088/1674-1137/44/9/094107

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Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass ^151-161Pm and odd-odd ^154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.

Abnormal odd-even staggering behavior around ¹³²Sn studied by density functional theory

Haoqiang Shi, Xiao-Bao Wang, Guo-Xiang Dong, Hualei Wang

2020, 44(9): 094108. doi: 10.1088/1674-1137/44/9/094108

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In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around ¹³²Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around ¹³²Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around ¹³²Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.

Warm tachyon inflation and swampland criteria

Abolhassan Mohammadi, Tayeb Golanbari, Haidar Sheikhahmadi, Kosar Sayar, Lila Akhtari, M. A. Rasheed, Khaled Saaidi

2020, 44(9): 095101. doi: 10.1088/1674-1137/44/9/095101

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In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.

Dirac quasinormal modes of Born-Infeld black hole spacetimes

Hong Ma, Jin Li

2020, 44(9): 095102. doi: 10.1088/1674-1137/44/9/095102

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Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.

Generalized uncertainty principle and black hole thermodynamics

Jin Pu, Qin-Bin Mao, Qing-Quan Jiang, Jing-Xia Yu, Xiao-Tao Zu

2020, 44(9): 095103. doi: 10.1088/1674-1137/44/9/095103

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Banerjee-Ghosh's work shows that the singularity problem can be naturally avoided by the fact that black hole evaporation stops when the remnant mass is greater than the critical mass when including the generalized uncertainty principle (GUP) effects with first- and second-order corrections. In this paper, we first follow their steps to reexamine Banerjee-Ghosh's work, but we find an interesting result: the remnant mass is always equal to the critical mass at the final stage of black hole evaporation with the inclusion of the GUP effects. Then, we use Hossenfelder's GUP, i.e., another GUP model with higher-order corrections, to restudy the final evolution behavior of the black hole evaporation, and we confirm the intrinsic self-consistency between the black hole remnant and critical masses once more. In both cases, we also find that the thermodynamic quantities are not singular at the final stage of black hole evaporation.

A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green’s function

Yang Zhang, Bo Wang, Xuan Ye

2020, 44(9): 095104. doi: 10.1088/1674-1137/44/9/095104

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We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker (RW) spacetimes. For the conformal coupling, the 2nd-order regularized power spectrum and 4th-order regularized stress tensor are zero, and no trace anomaly exists in general RW spacetimes. This is a new result that exceeds those found in de Sitter space. For the minimal coupling, the regularized spectra are also zero in the radiation-dominant and matter-dominant stages, as well as in de Sitter space. The vanishing of these adiabatically regularized spectra is further confirmed by direct regularization of the Green's function. For a general coupling and general RW spacetimes, the regularized spectra can be negative under the conventional prescription. At a higher order of regularization, the spectra will generally become positive, but will also acquire IR divergence, which is inevitable for a massless field. To avoid the IR divergence, the inside-horizon regularization is applied. Through these procedures, nonnegative UV- and IR-convergent power spectrum and spectral energy density will eventually be achieved.

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

G. Abbas, Asif Mahmood, M. Zubair

2020, 44(9): 095105. doi: 10.1088/1674-1137/44/9/095105

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The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter,

\begin{document}$ \alpha$\end{document}

, for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter,

\begin{document}$ \alpha$\end{document}

; both modify the features of the photon sphere, angle of deflection, and functions

\begin{document}$ (\bar{a}$\end{document}

and

\begin{document}$ \bar{b})$\end{document}

owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.

Fine micro-thermal structures for Reissner-Nordström black hole

Zhen-Ming Xu, Bin Wu, Wen-Li Yang

2020, 44(9): 095106. doi: 10.1088/1674-1137/44/9/095106

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Abstract:
We solve the condundrum on whether the molecules of the Reissner-Nordström black hole interact through the Ruppeiner thermodynamic geometry, basing our study on the concept of the black hole molecule proposed in [Phys. Rev. Lett. 115 (2015) 111302] and choosing the appropriate extensive variables. Our results show that the Reissner-Nordström black hole is indeed an interaction system that may be dominated by repulsive interaction. More importantly, with the help of a novel quantity, namely the thermal-charge density, we describe the fine micro-thermal structures of the Reissner-Nordström black hole in detail. Three different phases are presented, namely the free, interactive, and balanced phases. The thermal-charge density plays a role similar to the order parameter, and the back hole undergoes a new phase transition between the free phase and interactive phase. The competition between the free phase and interactive phase exists, which leads to extreme behavior of the temperature of the Reissner-Nordström black hole. For the extreme Reissner-Nordström black hole, the entire system is completely in the interactive phase. More importantly, we provide the thermodynamic micro-mechanism for the formation of the naked singularity of the Reissner-Nordström black hole.

Constraints on the generalized natural inflation after Planck 2018

Nan Zhang, Ya-Bo Wu, Jun-Wang Lu, Chu-Wen Sun, Li-Jie Shou, Hai-Zhou Xu

2020, 44(9): 095107. doi: 10.1088/1674-1137/44/9/095107

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Abstract:
Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. We introduce constraints on the scalar spectral index

\begin{document}$n_{s}$\end{document}

and the tensor-to scalar ratio r for the

\begin{document}$\Lambda$\end{document}

CDM

\begin{document}$+r$\end{document}

model, according to the latest data from Planck 2018 TT, TE, EE+low E+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., with

\begin{document}$n_{s}=0.9659\pm0.0044$\end{document}

at 68% confidence level (CL), and

\begin{document}$r<0.0623$\end{document}

at 95% CL. We find that the GNI model is favored by P18 and BK15 in the ranges

\begin{document}$\log_{10}(f/M_{p})= 0.62^{+0.17}_{-0.18}$\end{document}

and

\begin{document}$m=0.35^{+0.13}_{-0.23}$\end{document}

at 68% CL. In addition, the corresponding predictions of generalized and two-phase reheating are discussed. It follows that the parameter m has significant effect on the model behavior.

2020 Vol. 44, No. 9