## 2021 Vol. 45, No. 1

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2021, 45(1): 013101. doi: 10.1088/1674-1137/abc067
Abstract:
We revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators, which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is presented. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain the significant SU(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among various hyperon decays.
2021, 45(1): 013102. doi: 10.1088/1674-1137/abc0ce
Abstract:
We consider a class of models with extra complex scalars that are charged under both the Standard Model and a hidden strongly coupled \begin{document}$SU(N)_H$\end{document} gauge sector and discuss the scenarios in which the new scalars are identified as the messenger fields that mediate the spontaneously broken supersymmetries from the hidden sector to the visible sector. The new scalars are embedded into 5-plets and 10-plets of an \begin{document}$SU(5)_V$\end{document} gauge group that potentially unifies the Standard Model gauge groups. The Higgs bosons remain as elementary particles. In the supersymmetrized version of this class of models, vector-like fermions whose left-handed components are superpartners of the new scalars are introduced. Owing to the hidden strong force, the new low-energy scalars hadronize before decaying and thus evade the common direct searches of the supersymmetric squarks. This can be seen as a gauge mediation scenario with the scalar messenger fields forming low-energy bound states. We also discuss the possibility that in the tower of bound states formed under hidden strong dynamics (of at least the TeV scale), there exist a dark matter candidate and the collider signatures (e.g. diphoton, diboson, or dijet) of models that may show up in the near future.
2021, 45(1): 013103. doi: 10.1088/1674-1137/abc16a
Abstract:
The minimal \begin{document}${U}(1)_{\rm{{B-L}}}$\end{document} extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism; it also offers two new physics states, namely an extra Higgs boson and a new \begin{document}$Z'$\end{document} gauge boson. The emergence of a second Higgs particle as well as a new \begin{document}$Z^\prime$\end{document} gauge boson, both linked to the breaking of a local \begin{document}${U}(1)_{\rm{{B-L}}}$\end{document} symmetry, makes the B-L-SM rather constrained by direct searches in Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon \begin{document}$\left(g-2\right)_\mu$\end{document} anomaly in the B-L-SM yields at most a contribution of approximately \begin{document}$8.9 \times 10^{-12}$\end{document} , which represents a tension of \begin{document}$3.28$\end{document} standard deviations, with the current \begin{document}$1\sigma$\end{document} uncertainty, by means of a \begin{document}$Z^\prime$\end{document} boson if its mass is in the range of \begin{document}$6.3$\end{document} to \begin{document}$6.5\; {\rm{TeV}}$\end{document}, within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed \begin{document}$Z^\prime$\end{document} boson mass range, in practice, does not resolve the tension between the observed anomaly in the muon \begin{document}$\left(g-2\right)_\mu$\end{document} and the theoretical prediction in the Standard Model. Such a heavy \begin{document}$Z^\prime$\end{document} boson also implies that the minimal value for the new Higgs mass is of the order of 400 GeV.
2021, 45(1): 013104. doi: 10.1088/1674-1137/abc16b
Abstract:
The heavy quark effective theory vastly reduces the weak-decay form factors of hadrons containing one heavy quark. Many works attempt to directly apply this theory to hadrons with multiple heavy quarks. In this paper, we examine this confusing application by the instantaneous Bethe-Salpeter method from a phenomenological perspective, and give the numerical results for \begin{document}$B_c$\end{document} decays to charmonium where the final states include \begin{document}$1S$\end{document}, \begin{document}$1P$\end{document}, \begin{document}$2S$\end{document}, and \begin{document}$2P$\end{document}. Our results indicate that the form factors parameterized by a single Isgur-Wise function deviate substantially from the full ones, especially when excited states are involved. The relativistic corrections (\begin{document}$1/m_Q$\end{document} corrections) require the introduction of more non-perturbative universal functions, similar to the Isgur-Wise function, which are the overlapping integrals of the wave functions with the relative momentum between the quark and antiquark.
2021, 45(1): 013105. doi: 10.1088/1674-1137/abc16d
Abstract:
The spectroscopic parameters and decay channels of the axial-vector tetraquark \begin{document}$T_{bb;\overline{u}\overline{s}}^{-}$\end{document} (in what follows, \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}}$\end{document}) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state \begin{document}$m = (10215\pm 250)\; \mathrm{MeV}$\end{document} confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}l\overline{\nu}_l$\end{document} and nonleptonic \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}M$\end{document} decays of \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}}$\end{document}. In these processes, \begin{document}${\cal{Z}}_{b:\overline{s}}^{0}$\end{document} is a scalar tetraquark \begin{document}$[bc][\overline{u}\overline{s}]$\end{document} built of a color-triplet diquark and an antidiquark, whereas M is one of the vector mesons \begin{document}$\rho ^{-}$\end{document}, \begin{document}$K^{\ast}(892)$\end{document}, \begin{document}$D^{\ast }(2010)^{-}$\end{document}, and \begin{document}$D_{s}^{\ast -}$\end{document}. To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors \begin{document}$G_{i}$\end{document}(\begin{document}$i = 0,1,2,3$\end{document}), which govern these processes. The full width \begin{document}$\Gamma _{\mathrm{full}} = (12.9\pm 2.1)\times 10^{-8}\; \mathrm{MeV}$\end{document} and the mean lifetime \begin{document}$\tau = 5.1_{-0.71}^{+0.99}\; \mathrm{fs}$\end{document} of the tetraquark \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}}$\end{document} are computed using the aforementioned weak decays. The obtained information about the parameters of \begin{document}$T_{b:\overline{s}}^{\mathrm{AV}}$\end{document} and \begin{document}${\cal{Z}}_{b:\overline{s}}^{0}$\end{document} is useful for experimental investigations of these double-heavy exotic mesons.
2021, 45(1): 013106. doi: 10.1088/1674-1137/abc1d5
Abstract:
The decay \begin{document}$t \to c V$\end{document} (\begin{document}$V=\gamma,~Z,~g$\end{document}) processes in mirror twin Higgs models with colorless top partners are studied in this paper. We report that the branching ratios of these decays can strongly affect the standard model expectations in some parameter spaces and may be detectable according to the current precision electroweak measurements. Thus, constraints on the model parameters may be obtained from the branching fraction of the decay processes, which may serve as a robust detection tool for this new physics model.
2021, 45(1): 013107. doi: 10.1088/1674-1137/abc1d4
Abstract:
We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time.
2021, 45(1): 013108. doi: 10.1088/1674-1137/abc1d2
Abstract:
The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently, in which the frequencies are separated in the rest frames as in special relativity. It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally for any momentum, whereas in the adiabatic vacuum, this limit remains undefined in rest frames in which the momentum vanishes. An important role is played by the phases of the fundamental solutions in the rest frame vacuum, which must be regularized to obtain the desired Minkowskian flat limits. This procedure fixes the phases of the scalar mode functions and Dirac spinors, resulting in their definitive expressions derived here. The physical consequence is that, in the rest frame vacuum, the flat limits of the one-particle operators are simply the corresponding operators of special relativity.
2021, 45(1): 013109. doi: 10.1088/1674-1137/abc1d3
Abstract:
In this article, we study the ground states and the first radial excited states of the flavor antitriplet heavy baryon states \begin{document}$\Lambda_Q$\end{document} and \begin{document}$\Xi_Q$\end{document} with the spin-parity \begin{document}$J^P={1\over 2}^{+}$\end{document} by carrying out operator product expansion up to vacuum condensates of dimension \begin{document}$10$\end{document} in a consistent way. We observe for the first time that the higher dimensional vacuum condensates play an important role, and obtain very stable QCD sum rules with variations of the Borel parameters for the heavy baryon states. The predicted masses \begin{document}$6.08\pm0.09\,{\rm{GeV}}$\end{document}, \begin{document}$2.78\pm0.08\,{\rm{GeV}}$\end{document}, and \begin{document}$2.96\pm0.09\,{\rm{GeV}}$\end{document} for the first radial excited states \begin{document}$\Lambda_b(2{{S}})$\end{document}, \begin{document}$\Lambda_c(2{{S}})$\end{document}, and \begin{document}$\Xi_c(2{{S}})$\end{document}, respectively, are in excellent agreement with the experimental data and support assigning \begin{document}$\Lambda_b(6072)$\end{document}, \begin{document}$\Lambda_c(2765)$\end{document}, and \begin{document}$\Xi_c(2980/2970)$\end{document} to be the first radial excited states of \begin{document}$\Lambda_b$\end{document}, \begin{document}$\Lambda_c$\end{document}, and \begin{document}$\Xi_c$\end{document}, respectively. The predicted mass \begin{document}$6.24\pm0.07\,{\rm{GeV}}$\end{document} for \begin{document}$\Xi_b(2{{S}})$\end{document} can be confirmed using experimental data in the future.
2021, 45(1): 013110. doi: 10.1088/1674-1137/abc23f
Abstract:
Recently, an action principle for the \begin{document}$D\rightarrow4$\end{document} limit of Einstein-Gauss-Bonnet gravity has been proposed. It is a special scalar-tensor theory that belongs to the family of Horndeski gravity. It also has well defined \begin{document}$D\rightarrow3$\end{document} and \begin{document}$D\rightarrow2$\end{document} limits. In this work, we examine this theory in three and four dimensions in the Bondi-Sachs framework. In both three and four dimensions, we find that there is no news function associated with the scalar field, which means that there is no scalar propagating degree of freedom in the theory. In four dimensions, the mass-loss formula is not affected by the Gauss-Bonnet term. This is consistent with the fact that there is no scalar radiation. However, the effects of the Gauss-Bonnet term are quite significant in the sense that they arise just one order after the integration constants and also arise in the quadrupole of the gravitational source.
2021, 45(1): 013111. doi: 10.1088/1674-1137/abc240
Abstract:
We perform a potential analysis for the holographic Schwinger effect in a deformed \begin{document}$AdS_5$\end{document} model with conformal invariance broken by a background dilaton. We evaluated the static potential by analyzing the classical action of a string attached to a rectangular Wilson loop on a probe D3 brane located at an intermediate position in the bulk AdS space. We observed that the inclusion of the chemical potential tends to enhance the production rate, which is opposite to the effect of the confining scale. In addition, we calculated the critical electric field based on the Dirac-Born-Infeld (DBI) action.
2021, 45(1): 013112. doi: 10.1088/1674-1137/abc241
Abstract:
The strangeonium-like \begin{document}$s\bar{s}g$\end{document} hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for \begin{document}$1^{--}$\end{document} and \begin{document}$(0,1,2)^{-+}$\end{document} states with the color octet \begin{document}$s\bar{s}$\end{document} component being separated from the chromomagnetic field strength by the spatial distance \begin{document}$r$\end{document}, whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the \begin{document}$(1,2)^{-+}$\end{document} channels, the masses and the BS wave functions are reliably derived. The \begin{document}$1^{-+}$\end{document} ground state mass is approximately 2.1-2.2 GeV, and that of \begin{document}$2^{-+}$\end{document} is approximately 2.3-2.4 GeV, whereas the mass of the first excited state is approximately 1.4 GeV higher. This mass splitting is much larger compared to that expected based on the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to \begin{document}$r$\end{document}exhibit clear radial nodal structures of a non-relativistic two-body system, which imply that \begin{document}$r$\end{document} is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids, in which the color octet \begin{document}$s\bar{s}$\end{document} is surrounded by gluonic degrees of freedom. In the \begin{document}$1^{--}$\end{document} channel, the properties of the lowest two states are consistent with those of \begin{document}$\phi(1020)$\end{document} and \begin{document}$\phi(1680)$\end{document}. We did not obtain convincing information with respect to \begin{document}$\phi(2170)$\end{document}. However, we argue that regardless of whether \begin{document}$\phi(2170)$\end{document} is a conventional \begin{document}$s\bar{s}$\end{document} meson or a \begin{document}$s\bar{s}g$\end{document} hybrid in the color halo scenario, the ratio of partial decay widths \begin{document}$\Gamma(\phi \eta)$\end{document} and \begin{document}$\Gamma (\phi \eta')$\end{document} observed by BESIII can be understood based on the mechanism of hadronic transition of a strangeonium-like meson in addition to \begin{document}$\eta-\eta'$\end{document} mixing.
2021, 45(1): 013113. doi: 10.1088/1674-1137/abc242
Abstract:
Experimental data on \begin{document}$R(D^{(*)})$\end{document}, \begin{document}$R(K^{(*)})$\end{document} , and \begin{document}$R(J/\psi)$\end{document}, provided by different collaborations, show sizable deviations from the standard model predictions. To describe these anomalies, many new physics scenarios have been proposed. One of them is the leptoquark model, which introduces the simultaneous coupling of vector and scalar leptoquarks to quarks and leptons. To look for similar possible anomalies in the baryonic sector, we investigate the effects of a vector leptoquark \begin{document}$U_3 (3,3, \frac{2}{3})$\end{document} on various physical quantities related to the tree-level \begin{document}$\Lambda_b \rightarrow \Lambda_c \ell ~ \overline{\nu}_\ell$\end{document} decays (\begin{document}$\ell=\mu, ~\tau$\end{document}), which proceed via \begin{document}$b \rightarrow c~\ell ~ \overline{\nu}_\ell$\end{document} transitions at the quark level. We calculate the differential branching ratio, forward-backward asymmetry, and longitudinal polarizations of leptons and \begin{document}$\Lambda_{c}$\end{document} baryons at the \begin{document}$\mu$\end{document} and \begin{document}$\tau$\end{document} lepton channels in the leptoquark model and compare their behavior to the predictions of the SM in terms of \begin{document}$q^2$\end{document}. In the calculations, we use the form factors calculated in full QCD as the main input and account for all errors coming from the form factors and model parameters. We observe that at the \begin{document}$\tau$\end{document} channel, the \begin{document}$R_A$\end{document} fit solution to data related to the leptoquark model sweeps some regions out of the SM band; nevertheless, the fit has a considerable intersection with the SM predictions. The \begin{document}$R_B$\end{document} type solution gives roughly the same results as the SM on \begin{document}$DBR(q^2)-q^2$\end{document}. At the \begin{document}$\mu$\end{document} channel, the leptoquark model gives results that are consistent with the SM predictions and existing experimental data on the behavior of \begin{document}$DBR(q^2)$\end{document} with respect to \begin{document}$q^2$\end{document}. Concerning the \begin{document}$q^2$\end{document} behavior of the \begin{document}$A_{FB}(q^2)$\end{document} , the two types of fits for \begin{document}$\tau$\end{document} and the predictions at the \begin{document}$\mu$\end{document} channel in the leptoquark model give exactly the same results as the SM. We also investigate the behavior of the parameter \begin{document}$R(q^2)$\end{document} with respect to \begin{document}$q^2$\end{document} and the value of \begin{document}$R(\Lambda_c)$\end{document} in both the vector leptoquark and SM models. Both fit solutions lead to results that deviate considerably from the SM predictions for \begin{document}$R(q^2)- q^2$\end{document} and \begin{document}$R(\Lambda_c)$\end{document}. Future experimental data on \begin{document}$R(q^2)- q^2$\end{document} and \begin{document}$R(\Lambda_c)$\end{document}, made available by measurements of the \begin{document}$\Lambda_b \rightarrow \Lambda_c \tau ~ \overline{\nu}_\tau$\end{document} channel, will be particularly helpful. Any experimental deviations from the SM predictions in this channel would emphasize the importance of tree-level hadronic weak transitions as good probes of new physics effects beyond the SM.
2021, 45(1): 013114. doi: 10.1088/1674-1137/abc244
Abstract:
We present a dark matter model to explain the excess events in the electron recoil data recently reported by the Xenon1T experiment. In our model, dark matter \begin{document}$\chi$\end{document} annihilates into a pair of on-shell particles \begin{document}$\phi$\end{document}, which subsequently decay into the \begin{document}$\psi \psi$\end{document} final state; \begin{document}$\psi$\end{document} interacts with electrons to generate the observed excess events. Because of the mass hierarchy, the velocity of \begin{document}$\psi$\end{document} can be rather large and can have an extended distribution, providing a good fit to the electron recoil energy spectrum. We estimate the flux of \begin{document}$\psi$\end{document} from dark matter annihilations in the galaxy and further determine the interaction cross section, which is sizable but sufficiently small to allow \begin{document}$\psi$\end{document} to penetrate the rocks to reach the underground labs.
2021, 45(1): 013115. doi: 10.1088/1674-1137/abc538
Abstract:
We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration. The flow of the auxiliary mass from the boundary (\begin{document}$\infty$\end{document}) to the physical point (\begin{document}$0^+$\end{document}) is obtained by numerically solving differential equations with respective to the auxiliary mass. For problems with two or more kinematical invariants, the AMF method can be combined with the traditional differential-equation method, providing systematic boundary conditions and a highly nontrivial self-consistency check. The method is described in detail using a pedagogical example of \begin{document}$e^+e^-\rightarrow \gamma^* \rightarrow t\bar{t}+X$\end{document} at NNLO. We show that the AMF method can systematically and efficiently calculate integrals to high precision.
2021, 45(1): 013116. doi: 10.1088/1674-1137/abc539
Abstract:
We investigated different entanglement properties of a holographic QCD (hQCD) model with a critical end point at the finite baryon density. Firstly, we considered the holographic entanglement entropy (HEE) of this hQCD model in a spherical shaped region and a strip shaped region. It was determined that the HEE of this hQCD model in both regions can reflect QCD phase transition. Moreover, although the area formulas and minimal area equations of the two regions were quite different, the HEE exhibited a similar behavior on the QCD phase diagram. Therefore, we assert that the behavior of the HEE on the QCD phase diagram is independent of the shape of the subregions. However, the HEE is not an ideal parameter for the characterization of the entanglement between different subregions of a thermal system. As such, we investigated the mutual information (MI), conditional mutual information (CMI), and the entanglement of purification (Ep) in different strip shaped regions. We determined that the three entanglement quantities exhibited some universal behavior; their values did not change significantly in the hadronic matter phase but increased rapidly with the increase in T and \begin{document}$\mu$\end{document} in the QGP phase. Near the phase boundary, these three entanglement quantities changed smoothly in the crossover region and continuously but not smoothly at CEP; they exhibited discontinuous behavior in the first phase transition region. These properties can be used to distinguish between the different phases of strongly coupled matter.
2021, 45(1): 013117. doi: 10.1088/1674-1137/abc682
Abstract:
By applying the nonrelativistic quantum chromodynamics factorization formalism to \begin{document}$\Upsilon(1S,2S,3S)$\end{document} hadroproduction, a complete analysis of the polarization parameters \begin{document}$\lambda_{\theta}$\end{document}, \begin{document}$\lambda_{\theta\phi}$\end{document}, and \begin{document}$\lambda_{\phi}$\end{document} for the production is presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter \begin{document}$\lambda_{\theta}$\end{document} of \begin{document}$\Upsilon$\end{document} hadroproduction, our results provide a good description of the measured parameters \begin{document}$\lambda_{\theta\phi}$\end{document} and \begin{document}$\lambda_{\phi}$\end{document} in both the helicity and Collins-Soper frames. In our calculations, the frame invariant parameter \begin{document}$\tilde{\lambda}$\end{document} is consistent in the two frames. Finally, we mention that there are discrepancies between the available experimental data and corresponding theoretical predictions for \begin{document}$\tilde{\lambda}$\end{document} .
2021, 45(1): 013118. doi: 10.1088/1674-1137/abc683
Abstract:
We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that, for any given process, these two factorization theories are either both valid or both violated. We use two methods to arrive at this conclusion. In the first method, we apply the two factorization theories to the physical process \begin{document}$J/\psi \to e^+e^-$\end{document}. Our explicit calculation shows that both SGF and NRQCD can correctly reproduce the low energy physics of full QCD, and the two factorizations are thus equivalent. In the second method, by using equations of motion, we successfully deduce SGF from NRQCD effective field theory. By identifying SGF with NRQCD factorization, we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relation as a byproduct. Compared with the NRQCD factorization, the advantage of SGF is that it resums the series of relativistic corrections originating from kinematic effects to all powers, yielding better convergence of the relativistic expansion.
2021, 45(1): 014001. doi: 10.1088/1674-1137/abc0cb
Abstract:
The level structures of \begin{document}$^{93}$\end{document}Mo are investigated using Large Scale Shell Model calculations, and reasonable agreement is obtained between the experimental and calculated values. The calculated results show that the lower-lying states are mainly dominated by proton excitations from the \begin{document}$1f_{5/2}$\end{document}, \begin{document}$2p_{3/2}$\end{document}, and \begin{document}$2p_{1/2}$\end{document} orbitals into the higher orbitals across the Z = 38 or Z = 40 subshell closure. For the higher-spin states, multi-particle excitations, including the excitation of \begin{document}$2d_{5/2}$\end{document} neutrons across the N = 56 subshell closure into the high-j intruder \begin{document}$1h_{11/2}$\end{document} orbital, are essential. Moreover, the previously unknown spin-parity assignments of the six higher excited states in \begin{document}$^{93}$\end{document}Mo are inferred from the shell model calculations.
2021, 45(1): 014101. doi: 10.1088/1674-1137/abc069
Abstract:
We study the emission of fragments in central collisions of light and heavily charged systems of 40Ar+45Sc and 84Kr+197Au, respectively, using the Quantum Molecular Dynamics (QMD) model as the primary model. The fragments are identified using an energy based clusterization algorithm, i.e., the Simulated Annealing Clusterization Algorithm (SACA). The charge distributions of intermediate mass fragments [3≤\begin{document}$Z_{f}$\end{document}≤12] are fitted with power-law (\begin{document}$\propto Z_{f} ^{-\tau}$\end{document}) and exponential (\begin{document}$\propto {\rm{e}} ^{-\lambda {Z_{f}}}$\end{document}) fits in order to extract the parameters τ and \begin{document}$\lambda ,$\end{document} whose minimum values are also sometimes linked with the onset of fragmentation or the critical point for a liquid-gas phase transition. Other parameters such as the normalized second moment \begin{document}$<S_2>$\end{document}, \begin{document}$<\gamma_2>$\end{document}, average size of the second largest cluster \begin{document}$<Z_{\rm max2}>$\end{document}, phase separation parameter (\begin{document}$S_p$\end{document}), bimodal parameter (P), information entropy (H), and Zipf's law are also analyzed to find the exact energy of the onset of fragmentation. Our detailed analysis predicts that an energy point exists between 20-23.1 MeV/nucleon, which is very close to the experimentally observed value of 23.9 MeV/nucleon for the 40Ar+45Sc reaction. We also find that the critical energy deduced using Zipf's law is higher than those predicted from other critical exponents. Moreover, no minimum is found for τ values of the highly charged system of 84Kr+197Au, in agreement with experimental findings and various theoretical calculations. We observe that the QMD + SACA model calculations are in agreement with the experimental observations. This agreement supports our results regarding the energy point of the liquid-gas phase transition and the onset of fragmentation.
2021, 45(1): 014102. doi: 10.1088/1674-1137/abc065
Abstract:
We use a geometric model for hadron polarization in heavy ion collisions with an emphasis on the rapidity dependence. The model is based on the model of Brodsky, Gunion, and Kuhn, as well as the Bjorken scaling model. We make predictions regarding the rapidity dependence of global \begin{document}$\Lambda$\end{document} polarization in the collision energy range of 7.7-200 GeV by assuming the rapidity dependence of two parameters, \begin{document}$\kappa$\end{document} and \begin{document}$\left\langle p_{T}\right\rangle$\end{document}. The predictions can be tested by future beam-energy-scan experiments at the Relativistic Heavy Ion Collider of Brookhaven National Lab.
2021, 45(1): 014103. doi: 10.1088/1674-1137/abc0cc
Abstract:
We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with fixed and running coupling constants in the saturation region. The analytic solution of the S-matrix shows that the \begin{document}$\exp(-{\cal{O}}(\eta^2))$\end{document} rapidity dependence of the solution with the fixed coupling constant is replaced by the \begin{document}$\exp(-{\cal{O}}(\eta^{3/2}))$\end{document} dependence in the smallest dipole running coupling case, as opposed to obeying the law found in our previous publication, where all the solutions of the next-to-leading order evolution equations comply with \begin{document}$\exp(-{\cal{O}}(\eta))$\end{document} rapidity dependence once the QCD coupling is switched from the fixed coupling to the smallest dipole running coupling prescription. This finding indicates that the corrections of the sub-leading double logarithms in the Sudakov suppressed evolution equation are significant, which compensate for a part of the evolution decrease of the dipole amplitude introduced by the running coupling effect. To test the analytic findings, we calculate the numerical solutions of the Sudakov suppressed evolution equation, and the numerical results confirm the analytic outcomes. Moreover, we use the numerical solutions of the evolution equationto fit the HERA data. This demonstrates that the Sudakov suppressed evolution equation can achieve a good quality fit to the data.
2021, 45(1): 014104. doi: 10.1088/1674-1137/abc169
Abstract:
We present a dispersive representation of the \begin{document}$\gamma N\rightarrow \pi N$\end{document} partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for \begin{document}$\pi N$\end{document} final-state-interaction effects is taken into account via an Omnés formalism with elastic \begin{document}$\pi N$\end{document} phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed to pin down the involved subtraction constants. Good fit quality can be achieved with only one free parameter, and the experimental data regarding the multipole amplitude \begin{document}$E_{0}^+$\end{document} in the energy region below the \begin{document}$\Delta(1232)$\end{document} are well described. Furthermore, we extend the \begin{document}$\gamma N\rightarrow \pi N$\end{document} partial-wave amplitude to the second Riemann sheet to extract the couplings of the \begin{document}$N^\ast(890)$\end{document}. The modulus of the residue of the multipole amplitude \begin{document}$E_{0}^+$\end{document} (S\begin{document}${_{11}pE}$\end{document}) is \begin{document}$2.41\;\rm{mfm\cdot GeV^2}$\end{document}, and the partial width of \begin{document}$N^*(890)\to\gamma N$\end{document} at the pole is approximately \begin{document}$0.369\ {\rm MeV}$\end{document}, which is almost the same as that of the \begin{document}$N^*(1535)$\end{document} resonance, indicating that \begin{document}$N^\ast(890)$\end{document} strongly couples to the \begin{document}$\pi N$\end{document} system.
2021, 45(1): 014105. doi: 10.1088/1674-1137/abc1d1
Abstract:
\begin{document}$\beta$\end{document}-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA). The self-consistency is addressed, in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states. First, the impact of \begin{document}${{J}}^2$\end{document} terms on the \begin{document}$\beta$\end{document}-decay half-lives is investigated by using the SGII interaction, revealing a large influence. Subsequently, numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII, LNS, SKX, and SAMi. Finally, comparisons to available experimental data and predictions of different theoretical models are discussed.
2021, 45(1): 014106. doi: 10.1088/1674-1137/abc23d
Abstract:
In this paper, we study the symmetry energy and the Wigner energy in the binding energy formula for atomic nuclei. We simultaneously extract the \begin{document}$I^2$\end{document} symmetry energy and Wigner energy coefficients using the double difference of "experimental" symmetry-Wigner energies, based on the binding energy data of nuclei with \begin{document}$A \geqslant 16$\end{document}. Our study of the triple difference formula and the "experimental" symmetry-Wigner energy suggests that the macroscopic isospin dependence of binding energies is explained well by the \begin{document}$I^{2}$\end{document} symmetry energy and the Wigner energy, and further consideration of the \begin{document}$I^{4}$\end{document} term in the binding energy formula does not substantially improve the calculation result.
2021, 45(1): 014107. doi: 10.1088/1674-1137/abc245
Abstract:
Ultraperipheral collisions (UPCs) of protons and nuclei are important for the study of the photoproduction of vector mesons and exotic states. The photoproduction of vector mesons in the pentaquark resonance channel in p-\begin{document}${\rm Au}$\end{document} UPCs at the Relative Heavy Ion Collider (RHIC) and p-\begin{document}${\rm Pb}$\end{document} UPCs at the Large Hadron Collider (LHC) is investigated by employing the STARlight package. The cross sections of vector mesons via the pentaquark state resonance channel are obtained using the effective Lagrangian method. The pseudo-rapidity and rapidity distributions of \begin{document}$J/\psi$\end{document} and \begin{document}$\Upsilon(1S)$\end{document} are given for p-\begin{document}${\rm Au}$\end{document} UPCs at the RHIC and p-\begin{document}${\rm Pb}$\end{document}UPCs at the LHC. It is found that the RHIC is a better platform for discovering pentaquark states than the LHC. Moreover, \begin{document}$P_{b}(11080)$\end{document} is easier to identify than \begin{document}$P_c(4312)$\end{document} because the background of \begin{document}$\Upsilon (1S)$\end{document} is weaker than that of \begin{document}$J/\psi$\end{document} in the t-channel at the RHIC.
2021, 45(1): 014108. doi: 10.1088/1674-1137/abc248
Abstract:
The problem of the deuteron interaction with lithium nuclei, treated as a system of two coupled pointlike clusters, is formulated to calculate the cross sections of the d+Li reaction. The d+Li reaction mechanism is described using the Faddeev theory for the three-body problem of deuteron-nucleus interaction. This theory is slightly extended for calculation of the stripping processes 6Li(d,p)7Li, 7Li(d,p)8Li, 6Li(d,n)7Be, and 7Li(d,n)8Be, as well as fragmentation reactions yielding tritium, \begin{document}$\alpha$\end{document}-particles, and continuous neutrons and protons in the initial deuteron kinetic-energy region \begin{document}$E_d=0.5-20$\end{document} MeV. The phase shifts found for \begin{document}$d+^6$\end{document}Li and \begin{document}$d+^7$\end{document}Li elastic scattering, as part of the simple optic model with a complex central potential, were used to find the cross sections for the 6Li\begin{document}$(d,\gamma_{M1})^8{\rm{Be}}$\end{document} and 7Li\begin{document}$(d,\gamma_{E1})^9{\rm{Be}}$\end{document} radiation captures. The three-body dynamics role is also summarized to demonstrate its significant influence within the \begin{document}$d+^7$\end{document}Li system.
2021, 45(1): 014109. doi: 10.1088/1674-1137/abc536
Abstract:
Qualities of nucleons, such as the fundamental parameter mass, might be modified in extreme conditions relative to those of isolated nucleons. We show the ratio of the EMC-effect tagged nucleon mass to that of the free one (\begin{document}$m^{\ast}/m$\end{document}); these values are derived from the nuclear structure function ratio between heavy nuclei and deuterium measured in the electron Deep Inelastic Scattering (DIS) reaction in 0.3 \begin{document}$\leqslant x\leqslant$\end{document}0.7. The increase in \begin{document}$m^{\ast}/m$\end{document} with \begin{document}$A^{-1/3}$\end{document} is phenomenologically interpreted via the release of a color-singlet cluster formed by sea quarks and gluons in bound nucleons holding high momentum in the nucleus, from which the mass and fraction of non-nucleonic components in nuclei can be deduced. The mass of color-singlet clusters released per short range correlated (SRC) proton in the high momentum region (\begin{document}$k>$\end{document} 2 fm\begin{document}$^{-1}$\end{document}) is extracted to be 16.890\begin{document}$\pm$\end{document}0.016 MeV/c\begin{document}$^{2}$\end{document}, which evidences the possibility of a light neutral boson and quantized mass of matter.
2021, 45(1): 014110. doi: 10.1088/1674-1137/abc684
Abstract:
In this contribution, the \begin{document}$\alpha$\end{document} preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model (GLDM). Through the systematic analysis of the \begin{document}$\alpha$\end{document} preformation factors of even-even Po-U isotopes, we found that there is a significant weakening of influence of \begin{document}$N=126$\end{document} shell closure in uranium, which is consistent with the results of a recent experiment [J. Khuyagbaatar et al., Phys. Rev. Lett. 115, 242502 (2015)], implying that \begin{document}$N=126$\end{document} may not be the magic number for U isotopes. Furthermore, we propose an improved formula with only 7 parameters to calculate \begin{document}$\alpha$\end{document} preformation factors suitable for all types of \begin{document}$\alpha$\end{document}-decay; it has fewer parameters than the original formula proposed by Zhang et al. [H. F. Zhang et al., Phys. Rev. C 80, 057301 (2009)] with higher precision. The standard deviation of the \begin{document}$\alpha$\end{document} preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3, indicating that our improved formula can accurately reproduce the \begin{document}$\alpha$\end{document} preformation factors. Encouraged by this, the \begin{document}$\alpha$\end{document}-decay half-lives of actinide elements are predicted, which could be useful in future experiments. Notably, the predicted \begin{document}$\alpha$\end{document}-decay half-lives of two new isotopes \begin{document}$^{220}$\end{document}Np [Z. Y. Zhang, et al., Phys. Rev. Lett. 122, 192503 (2019)] and \begin{document}$^{219}$\end{document}Np [H. B. Yang et al., Phys. Lett. B 777, 212 (2018)] are in good agreement with the experimental \begin{document}$\alpha$\end{document}-decay half-lives.
2021, 45(1): 015101. doi: 10.1088/1674-1137/abc068
Abstract:
We investigate the evolution of abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. Next, we discuss the effect of kinetic decoupling on the relic abundance of asymmetric Dark Matter when the interaction rate depends on velocity. Usually, the relic density of asymmetric Dark Matter is analyzed in the frame of chemical decoupling. Indeed, after decoupling from chemical equilibrium, asymmetric Dark Matter particles and anti-particles are still in kinetic equilibrium for a while. This has no effect for the case of s-wave annihilation since there is no temperature dependence in this case. However, kinetic decoupling has impacts for the case of p-wave annihilation and Sommerfeld enhanced s- and p-wave annihilations. We investigate in detail the extent to which kinetic decoupling affects the relic abundance of asymmetric Dark Matter particles and anti-particles. We find the constraints on the cross section and asymmetry factor using observational data of the relic density of Dark Matter.
2021, 45(1): 015102. doi: 10.1088/1674-1137/abc066
Abstract:
The transonic phenomenon of black hole accretion and the existence of the photon sphere characterize strong gravitational fields near a black hole horizon. Here, we study the spherical accretion flow onto general parametrized spherically symmetric black hole spacetimes. We analyze the accretion process for various perfect fluids, such as the isothermal fluids of ultra-stiff, ultra-relativistic, and sub-relativistic types, and the polytropic fluid. The influences of additional parameters, beyond the Schwarzschild black hole in the framework of general parameterized spherically symmetric black holes, on the flow behavior of the above-mentioned test fluids are studied in detail. In addition, by studying the accretion of the ideal photon gas, we further discuss the correspondence between the sonic radius of the accreting photon gas and the photon sphere for general parameterized spherically symmetric black holes. Possible extensions of our analysis are also discussed.
2021, 45(1): 015103. doi: 10.1088/1674-1137/abc0cd
Abstract:
We investigate the bulk viscosity of strange quark matter in the framework of the equivparticle model, where analytical formulae are obtained for certain temperature ranges, which can be readily applied to those with various quark mass scalings. In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions, the obtained bulk viscosity increases by \begin{document}$1 \sim 2$\end{document} orders of magnitude compared with those in bag model scenarios. Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model, which are essentially attributed to the strong interquark interactions and are related to the dynamical chiral symmetry breaking. Due to the high bulk viscosity, the predicted damping time of oscillations for a canonical 1.4 \begin{document}${\rm M}_\odot$\end{document} strange star is less than one millisecond, which is shorter than previous findings. Consequently, the obtained \begin{document}$r$\end{document}-mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in low-mass X-ray binaries (LMXBs).
2021, 45(1): 015104. doi: 10.1088/1674-1137/abc0cf
Abstract:
Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and charged black holes surrounded by quintessence are studied in the extended phase space. The quintessence field, with the state parameter \begin{document}$-1 < w < -1/3$\end{document}, modifies the temperature and the Gibbs free energy of a black hole. The phase transition temperature \begin{document}$T_{\rm{HP}}$\end{document} and the Gibbs free energy \begin{document}$G$\end{document} are first analytically investigated for the special case of \begin{document}$w=-2/3$\end{document}, and then, the results of numerical simulations are shown for general \begin{document}$w$\end{document}. The phase transition temperature \begin{document}$T_{\rm{HP}}$\end{document} increases with pressure and decreases with electric potential. In addition, \begin{document}$T_{\rm{HP}}$\end{document} significantly decreases owing to the quintessence field, which generates negative pressure around the black hole.
2021, 45(1): 015105. doi: 10.1088/1674-1137/abc16c
Abstract:
Recently, a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) theory of gravity was proposed by Glavan and Lin [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)], which includes a regularized Gauss-Bonnet term using the re-scalaring of the Gauss-Bonnet coupling constant \begin{document}$\alpha \to \alpha/(D-4)$\end{document} in the limit \begin{document}$D\to 4$\end{document}. This theory has also been reformulated to a specific class of the Horndeski theory with an additional scalar degree of freedom and to a spatial covariant version with a Lagrangian multiplier, which can eliminate the scalar mode. Here, we study the physical properties of the electromagnetic radiation emitted from a thin accretion disk around a static spherically symmetric black hole in 4EGB gravity. For this purpose, we assume the disk is in a steady-state and in hydrodynamic and thermodynamic equilibrium, so that the emitted electromagnetic radiation is a black body spectrum. We study in detail the effects of the Gauss-Bonnet coupling constant \begin{document}$\alpha$\end{document} in 4EGB gravity on the energy flux, temperature distribution, and electromagnetic spectrum of the disk. With an increase in the parameter \begin{document}$\alpha$\end{document}, the energy flux, temperature distribution, and electromagnetic spectrum of the accretion disk all increase. We also show that the accretion efficiency increases with the growth of the parameter \begin{document}$\alpha$\end{document}. Our results indicate that the thin accretion disk around a static spherically symmetric black hole in 4EGB gravity is hotter, more luminous, and more efficient than that around a Schwarzschild black hole with the same mass for positive \begin{document}$\alpha$\end{document}, while it is cooler, less luminous, and less efficient for negative \begin{document}$\alpha$\end{document}.
2021, 45(1): 015106. doi: 10.1088/1674-1137/abc23e
Abstract:
Inspired by the hypothesis of the black hole molecule, with the help of the Hawking temperature, entropy, and the thermodynamic curvature of black holes, we propose a new measure of the relation between the interaction and the thermal motion of molecules of the AdS black hole as a preliminary and coarse-grained description. The proposed measure introduces a dimensionless ratio to characterize this relation and shows that there is indeed competition between the interactions of black hole molecules and their thermal motion. For a charged AdS black hole, below the critical dimensionless pressure, there are three transitions between the interaction and thermal motion states. In contrast, above the critical dimensionless pressure, only one transition takes place. For the Schwarzschild-AdS and five-dimensional Gauss-Bonnet AdS black holes, a transition always occurs between the interaction and thermal motion states.
2021, 45(1): 015107. doi: 10.1088/1674-1137/abc247
Abstract:
It was previously claimed by the author that black holes can be considered as topological insulators. Both black holes and topological insulators have boundary modes, and the boundary modes can be described by an effective BF theory. In this paper, the boundary modes on the horizons of black holes are analyzed using methods developed for topological insulators. BTZ black holes are analyzed first, and the results are found to be compatible with previous works. The results are then generalized to Kerr black holes, for which new results are obtained: dimensionless right- and left-temperatures can be defined and have well behavior in both the Schwarzschild limit \begin{document}$a\rightarrow 0$\end{document} and the extremal limit \begin{document}$a\rightarrow M$\end{document}. Upon the Kerr/CFT correspondence, a central charge \begin{document}$c=12 M r_+$\end{document} can be associated with an arbitrary Kerr black hole. Moreover, the microstates of the Kerr black hole can be identified with the quantum states of this scalar field. From this identification, the number of microstates of the Kerr black hole can be counted, yielding the Bekenstein-Hawking area law for the entropy.
2021, 45(1): 015108. doi: 10.1088/1674-1137/abc537
Abstract:
Recent low-redshift observations have yielded the present-time Hubble parameter value \begin{document}$H_{0}\simeq 74\;\rm{km s}^{-1} \rm{Mpc}^{-1}$\end{document}. This value is approximately 10% higher than the predicted value of \begin{document}$H_{0}=67.4\;\rm{km s}^{-1}\rm{Mpc}^{-1}$\end{document}, based on Planck's observations of the Cosmic Microwave Background radiation (CMB) and the \begin{document}$\Lambda$\end{document}CDM model. Phenomenologically, we show that, by adding an extra component, X, with negative density to the Friedmann equation, it can address the Hubble tension without changing the Planck's constraint on the matter and dark energy densities. To achieve a sufficiently small extra negative density, its equation-of-state parameter must satisfy \begin{document}$1/3\leqslant w_{X}\leqslant 1$\end{document}. We propose a quintom model of two scalar fields that realizes this condition and potentially alleviate the Hubble tension. One scalar field acts as a quintessence, while another “phantom” scalar conformally couples to matter such that a viable cosmological scenario is achieved. The model only depends on two parameters, \begin{document}$\lambda_{\phi}$\end{document} and \begin{document}$\delta$\end{document} , which represent the rolling tendency of the self-interacting potential of the quintessence and the strength of the conformal phantom-matter coupling, respectively. The toy quintom model with \begin{document}$H_{0}=73.4\;\rm{km s}^{-1}\rm{Mpc}^{-1}$\end{document} (Quintom I) yields a good Supernovae-Ia luminosity fit and acceptable \begin{document}$r_{\rm BAO}$\end{document} fit but slightly small acoustic multipole \begin{document}$\ell_{A}=285.54$\end{document}. A full parameter scan revealed that the quintom model was superior to the \begin{document}$\Lambda$\end{document}CDM model in certain regions of the parameter space, \begin{document}$0.02<\delta<0.10, \Omega_{m}^{(0)}<0.31$\end{document}, while significantly alleviating the Hubble tension, although it is not completely resolved. A benchmark quintom model, Quintom II, is presented as an example.
2021, 45(1): 015109. doi: 10.1088/1674-1137/abc53a
Abstract:
The cosmic distance relation (DDR) associates the angular diameters distance (\begin{document}$D_A$\end{document}) and luminosity distance (\begin{document}$D_L$\end{document}) by a simple formula, i.e., \begin{document}$D_L = (1+z)^2D_A$\end{document}. The strongly lensed gravitational waves (GWs) provide a unique way to measure \begin{document}$D_A$\end{document} and \begin{document}$D_L$\end{document} simultaneously to the GW source, hence they can be used as probes to test DDR. In this study, we investigated the use of strongly lensed GW events from the future Einstein Telescope to test DDR. We assumed the possible deviation of DDR as \begin{document}$(1+z)^2D_A/D_L = \eta(z)$\end{document}, and considered two different parametrizations of \begin{document}$\eta(z)$\end{document}, namely, \begin{document}$\eta_1(z) = 1+\eta_0 z$\end{document} and \begin{document}$\eta_2(z) = 1+\eta_0 z/(1+z)$\end{document}. Numerical simulations showed that, with about 100 strongly lensed GW events observed by ET, the parameter \begin{document}$\eta_0$\end{document} was constrained at 1.3% and 3% levels for the first and second parametrizations, respectively.
2021, 45(1): 015110. doi: 10.1088/1674-1137/abc680
Abstract:
It was found that dark matter (DM) in an intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of a stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors, including LISA, Taiji, and Tianqin in future observations. In this paper, we study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: (1) in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; (2) in the presence of a DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BH's mass; and (3) considering the change in the eccentricity in the presence and absence of a DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at a scale of approximately \begin{document}$10^{5} {\rm GM}/c^{2}$\end{document}.
2021, 45(1): 015111. doi: 10.1088/1674-1137/abc681
Abstract:
In this paper, by introducing the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power \begin{document}$(E/E_{\rm QG})^2$\end{document}, we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordström (RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle. However, at the same energy level, it was insensitive to changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation. We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.