2022 Vol. 46, No. 5

Towards the establishment of the light JP (C )=1–(+) hybrid nonet
Lin Qiu, Qiang Zhao
2022, 46(5): 051001. doi: 10.1088/1674-1137/ac567e
The observation of the light hybrid candidate \begin{document}$ \eta_1(1855) $\end{document} by the BESIII Collaboration offers great opportunities for advancing our knowledge on exotic hadrons in terms of flavor sector. We demonstrate that this observation provides a crucial clue for establishing the \begin{document}$ J^{P(C)}=1^{-(+)} $\end{document} hybrid nonet. Based on the flux tube model picture, the production and decay mechanisms for the \begin{document}$ J^{P(C)}=1^{-(+)} $\end{document} hybrid nonet in the \begin{document}$ J/\psi $\end{document} radiative decays into two pseudoscalar mesons are investigated. In the \begin{document}$ I=0 $\end{document} sector, we deduce that the SU(3) flavor octet and singlet mixing is non-negligible and apparently deviates from the flavor ideal mixing. Because only signals for one isoscalar \begin{document}$ \eta_1(1855) $\end{document} are observed in the \begin{document}$ \eta\eta' $\end{document} channel, we investigate two schemes of the nonet structure in which \begin{document}$ \eta_1(1855) $\end{document} can either be the higher or lower mass state that strongly couples to \begin{document}$ \eta\eta' $\end{document}. Possible channels for detecting the multiplets are suggested. In particular, a combined analysis of the hybrid production in \begin{document}$ J/\psi\to VH $\end{document}, where \begin{document}$ V $\end{document} and \begin{document}$ H $\end{document} denote the light vector mesons and \begin{document}$ 1^{-(+)} $\end{document} hybrid states, respectively, may provide further evidence for this nonet structure and ultimately establish these mysterious exotic species in the experiment.
Linear seesaw model with a modular S4 flavor symmetry
Takaaki Nomura, Hiroshi Okada
2022, 46(5): 053101. doi: 10.1088/1674-1137/ac4975
We discuss a linear seesaw model with a field content as minimum as possible, introducing a modular \begin{document}$ S_4 $\end{document} using gauged \begin{document}$ U(1)_{B-L} $\end{document} symmetries. Owing to the rank two neutrino mass matrix, we obtain a vanishing neutrino mass eigenvalue, and only the normal mass hierarchy of neutrinos is favored via the modular \begin{document}$ S_4 $\end{document} symmetry. In our numerical \begin{document}$ \Delta \chi^2 $\end{document} analysis, we especially determine a relatively sharp prediction on the sum of neutrino masses to be approximately \begin{document}$ 60 $\end{document} meV, in addition to other predictions.
Lattice calculation of χc0 → 2γ decay width
Zuoheng Zou, Yu Meng, Chuan Liu
2022, 46(5): 053102. doi: 10.1088/1674-1137/ac4bcc
We perform a lattice QCD calculation of the \begin{document}$ \chi_{c0} \rightarrow 2\gamma $\end{document} decay width using a model-independent method that does not require the momentum extrapolation of corresponding off-shell form factors. The simulation is performed on ensembles of \begin{document}$ N_f = 2 $\end{document} twisted mass lattice QCD gauge configurations with three different lattice spacings. After the continuum extrapolation, the decay width is obtained to be \begin{document}$ \Gamma_{\gamma\gamma}(\chi_{c0}) = 3.65(83)_{\mathrm{stat}}(21)_{\mathrm{lat.syst}}(66)_{\mathrm{syst}}\, \rm{keV} $\end{document}. Regardless of this large statistical error, our result is compatible with the experimental results within 1.3σ. Potential improvements of the lattice calculation in the future are also discussed.
$ {\boldsymbol B_c \to \boldsymbol J/\boldsymbol\psi }$ helicity form factors and the $ {\boldsymbol B_{\boldsymbol c}^+ \to \boldsymbol J/\boldsymbol\psi+\boldsymbol(P, V, \boldsymbol\ell^+ \boldsymbol\nu_{\boldsymbol\ell}) }$ decays
Wei Cheng, Yi Zhang, Long Zeng, Hai-Bing Fu, Xing-Gang Wu
2022, 46(5): 053103. doi: 10.1088/1674-1137/ac4c9f
In this paper, we calculate the \begin{document}$ B_c\to J/\psi $\end{document} helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable \begin{document}$ q^2 $\end{document} region, we investigate the \begin{document}$ B^+_c $\end{document}-meson two-body decays and semi-leptonic decays \begin{document}$ B_c^+ \to J/\psi+(P, V, \ell^+ \nu_\ell) $\end{document}, where \begin{document}$ P/V $\end{document} stand for light pseudoscalar and vector mesons, respectively. The branching fractions can be derived using the CKM matrix element and the \begin{document}$ B_c $\end{document} lifetime from the Particle Data Group, and we obtain \begin{document}${\cal{B}}(B_c^+ \to J/\psi \pi^+) = (0.136^{+0.002}_{-0.002}){\text{%}}$\end{document}, \begin{document}${\cal{B}}(B_c^+ \to $\end{document}\begin{document}$ J/\psi K^+) = (0.010^{+0.000}_{-0.000}){\text{%}}$\end{document}, \begin{document}$ {\cal{B}}(B_c^+ \to J/\psi \rho^+) = (0.768^{+0.029}_{-0.033}){\text{%}} $\end{document}, \begin{document}$ {\cal{B}}(B_c^+ \to J/\psi K^{\ast +}) = (0.043^{+0.001}_{-0.001}){\text{%}} $\end{document}, \begin{document}${\cal{B}}(B_c^+ \to $\end{document}\begin{document}$ J/\psi \mu^+\nu_\mu) = (2.802^{+0.526}_{-0.675}){\text{%}}$\end{document} and \begin{document}$ {\cal{B}}(B_c^+ \to J/\psi \tau^+\nu_\tau) = (0.559^{+0.131}_{-0.170}){\text{%}} $\end{document}. We then obtain \begin{document}${\cal{R}}_{\pi^+/\mu^+\nu_\mu} = 0.048^{+ 0.009}_{-0.012}$\end{document} and \begin{document}$ {\cal{R}}_{K^+ / \pi^+} = 0.075^{+0.005}_{-0.005} $\end{document}, which agree with the LHCb measured value within \begin{document}$ 1\sigma $\end{document}-error. We also obtain \begin{document}$ {\cal{R}}_{J/\psi} = 0.199^{+ 0.060}_{-0.077} $\end{document}, which like other theoretical predictions, is consistent with the LHCb measured value within \begin{document}$ 2\sigma $\end{document}-error. These imply that the HFFs under the LCSR approach are also applicable to the \begin{document}$ B^+_c $\end{document} meson two-body decays and semi-leptonic decays \begin{document}$ B_c^+ \to J/\psi+(P, V, \ell^+ \nu_\ell) $\end{document}, and the HFFs obtained using LCSR in a new way implies that there may be new physics in the \begin{document}$ B_c\to J/\psi \ell^+ \nu_\ell $\end{document} semi-leptonic decays.
Resonances ρ(1450)+ and ρ(1700)+ in BDKK decays
Ai-Jun Ma, Wen-Fei Wang
2022, 46(5): 053104. doi: 10.1088/1674-1137/ac4cb5
The contributions for the kaon pair from the intermediate states \begin{document}$ \rho(1450)^+ $\end{document} and \begin{document}$ \rho(1700)^+ $\end{document} in the decays \begin{document}$ B^+ \to \bar{D}^0 K^+ \bar{K}^0 $\end{document}, \begin{document}$ B^0 \to D^- K^+ \bar{K}^0 $\end{document}, and \begin{document}$ B_s^0 \to D_s^-K^+ \bar{K}^0 $\end{document} are analyzed within the perturbative QCD factorization approach. The decay amplitudes for all concerned decays in this work are dominated by the factorizable Feynman diagrams with the emission of the kaon pair, and the charged ρ mesons should be of great importance in the \begin{document}$ KK $\end{document} channel of the related three-body B decays. Moreover, these quasi-two-body decays are CKM-favored, and the relevant branching ratios are predicted to be in the order of \begin{document}$ 10^{-5} $\end{document}, which have the potential to be measured by experiments. It is also shown that the contributions of the subprocesses \begin{document}$ \rho(1450, 1700)^+ \to KK $\end{document} for the three-body B meson decays are considerable according to the total three-body branching fractions presented by Belle. Therefore, the decays \begin{document}$ B^+ \to \bar{D}^0 K^+ \bar{K}^0 $\end{document}, \begin{document}$ B^0 \to D^- K^+ \bar{K}^0 $\end{document}, and \begin{document}$ B_s^0 \to D_s^-K^+ \bar{K}^0 $\end{document} can be employed to study the properties of \begin{document}$ \rho(1450) $\end{document} and \begin{document}$ \rho(1700) $\end{document} in the LHCb and Belle-II experiments.
Photoproduction ${ \boldsymbol\gamma \boldsymbol p \boldsymbol \to {\boldsymbol K}^+\boldsymbol\Lambda{\boldsymbol{(1690)}} }$ in an effective Lagrangian approach
Neng-Chang Wei, Ai-Chao Wang, Fei Huang
2022, 46(5): 053105. doi: 10.1088/1674-1137/ac4e7c
A gauge-invariant model is constructed for the \begin{document}$ \gamma p \to K^+\Lambda(1690) $\end{document} reaction within a tree-level effective Lagrangian approach to understand the underlying production mechanisms and study the resonance contributions in this reaction. In addition to the t-channel K and \begin{document}$ K^\ast $\end{document} exchanges, s-channel nucleon exchange, and interaction current, the s-channel nucleon resonance exchanges are included in constructing the reaction amplitudes to describe the data. It is found that the contributions from the s-channel \begin{document}$ N(2570)5/2^- $\end{document} exchange are required to describe the most recently measured total cross-section data for \begin{document}$ \gamma p \to K^+\Lambda(1690) $\end{document} from the CLAS Collaboration. Further analysis indicates that the interaction current dominates the \begin{document}$ \gamma p \to K^+\Lambda(1690) $\end{document} reaction near the threshold as a result of gauge invariance. The t-channel K exchange contributes significantly, while the contributions from the t-channel \begin{document}$ K^\ast $\end{document} exchange and s-channel nucleon exchange are ultimately negligible. The contributions from the s-channel \begin{document}$ N(2570)5/2^- $\end{document} exchange are found to be responsible for the bump structure shown in the CLAS total cross-section data above the center-of-mass energy \begin{document}$ W \approx 2.7 $\end{document} GeV. The predictions of the differential cross sections for \begin{document}$ \gamma p \to K^+\Lambda(1690) $\end{document} are presented and discussed, which can provide theoretical guidance for future experiments.
Investigating the Z' gauge boson at future lepton colliders
Xinyue Yin, Honglei Li, Yi Jin, Zhilong Han, Zongyang Lu
2022, 46(5): 053106. doi: 10.1088/1674-1137/ac500e
\begin{document}$ Z^\prime $\end{document} boson as a new gauge boson has been proposed in many new physics models. The interactions of \begin{document}$ Z^\prime $\end{document} coupling to fermions have been studied in detail at the large hadron collider. A \begin{document}$ Z^\prime $\end{document} with the mass of a few TeV has been excluded in some special models. Future lepton colliders will focus on the studies of Higgs physics, which provide the advantage to investigate the interactions of the Higgs boson with the new gauge bosons. We investigate the \begin{document}$ Z^\prime ZH $\end{document} interaction via the process of \begin{document}$ e^+e^- \to Z^\prime/Z \to ZH \to l^+l^- b \bar{b} $\end{document}. The angular distribution of the final leptons decaying from the Z-boson is related to the mixing of \begin{document}$ Z^\prime $\end{document}-Z and the mass of \begin{document}$ Z^\prime $\end{document}. The forward-backward asymmetry is proposed as an observable to investigate \begin{document}$ Z^\prime $\end{document}-Z mixing. The angular distributions change significantly with some special beam polarization compared with the unpolarized condition.
High-quality grand unified theories with three generations
Ning Chen
2022, 46(5): 053107. doi: 10.1088/1674-1137/ac5010
We extend the unitary groups beyond the \begin{document}$SU(5)$\end{document} and \begin{document}$ SU(6) $\end{document} to determine possible grand unified theories that give rise to three-generational Standard Model fermions without simple repetitions. By demanding asymptotic free theories at short distances, we find gauge groups of \begin{document}$ SU(7) $\end{document}, \begin{document}$ SU(8) $\end{document}, and \begin{document}$ SU(9) $\end{document}, together with their anomaly-free irreducible representations, are such candidates. Two additional gauge groups of \begin{document}$ SU(10) $\end{document} and \begin{document}$ SU(11) $\end{document} can also achieve the generational structure without asymptotic freedom. We also deduce that these models can solve the Peccei-Quinn (PQ) quality problem, which is intrinsic in the axion models, with the leading PQ-breaking operators determined from the symmetry requirement.
Investigation of negative-parity states in 16C via deuteron inelastic scattering
Z. W. Tan, J. L. Lou, Y. L. Ye, Y. Liu, D. Y. Pang, C. X. Yuan, J. G. Li, W. Liu, Y. Jiang, B. Yang, L. C. Tao, K. Ma, Z. H. Li, Q. T. Li, X. F. Yang, J. Y. Xu, H. Z. Yu, J. X. Han, S. W. Bai, S. W. Huang, G. Li, H. Y. Wu, H. L. Zang, J. Feng, J. S. Wang, Y. Y. Yang, P. Ma, Q. Hu, Z. Bai, Z. H. Gao, F. F. Duan, L. Y. Hu, J. H. Tan, S. Q. Sun, Y. S. Song, H. J. Ong, D. T. Tran, H. Y. Zhu, B. L. Xia
2022, 46(5): 054001. doi: 10.1088/1674-1137/ac488b
Two low-lying unbound states in 16C are investigated by deuteron inelastic scattering in inverse kinematics. Besides the 2\begin{document}$ ^- $\end{document} state at 5.45 MeV previously measured in a 1n knockout reaction, a new resonant state at 6.89 MeV is observed for the first time. The inelastic scattering angular distributions of these two states are well reproduced by the distorted-wave Born approximation (DWBA) calculation with an l = 1 excitation. In addition, the spin-parities of the unbound states are discussed and tentatively assigned based on shell model calculations using the modified YSOX interaction.
Systematic study of the (n, 2n) reaction cross section for 121Sb and 123Sb isotopes
R. K. Singh, N. L. Singh, R. D. Chauhan, Mayur Mehta, S. V. Suryanarayana, Rajnikant Makwana, B. K. Nayak, H. Naik, Tarak Nath Nag, K. Katovsky
2022, 46(5): 054002. doi: 10.1088/1674-1137/ac4a5a
The cross sections of the 121Sb\begin{document}$ (n, 2n) $\end{document}120Sbm and 123Sb\begin{document}$ (n, 2n) $\end{document}122Sb reactions were measured at 12.50, 15.79 and 18.87 MeV neutron energies relative to the standard 27Al\begin{document}$ (n,\alpha ) $\end{document}24Na monitor reaction using neutron activation and offline γ-ray spectrometry. Irradiation of the samples was performed at the BARC-TIFR Pelletron Linac Facility, Mumbai, India. The quasi-monoenergetic neutrons were generated via the 7Li\begin{document}$ (p,n) $\end{document} reaction. Statistical model calculations were performed by nuclear reaction codes TALYS (ver. 1.9) and EMPIRE (ver. 3.2.2) using various input parameters and nuclear level density models. The cross sections of the ground and the isomeric state as well as the isomeric cross section ratio were studied theoretically from reaction threshold to 26 MeV energies. The effect of pre-equilibrium emission is also discussed in detail using different theoretical models. The present measured cross sections were discussed and compared with the reported experimental data and evaluation data of the JEFF-3.3, ENDF/B-VIII.0, JENDL/AD-2017 and TENDL-2019 libraries. A detailed analysis of the uncertainties in the measured cross section data was performed using the covariance analysis method. Furthermore, a systematic study of the \begin{document}$ (n, 2n) $\end{document} reaction cross section for 121Sb and 123Sb isotopes was also performed within 14–15 MeV neutron energies using various systematic formulae. This work helps to overcome discrepancies in Sb data and illustrate a better understanding of pre-equilibrium emission in the \begin{document}$ (n, 2n) $\end{document} reaction channel.
New cross section measurements on tungsten isotopes around 14 MeV neutrons and their excitation functions
Yong Li, Fengqun Zhou, Yajuan Hao, Xiaoqiang Ma, Pengfei Ji, Xiaopeng Zhang, Shuqing Yuan
2022, 46(5): 054003. doi: 10.1088/1674-1137/ac4ca0
New cross sections of the 183W(n,α)180mHf, 186W(n,d*)185Ta, 182W(n,p)182Ta, 184W(n,p)184Ta, 182W(n,2n)181W, 184W(n,α)181Hf, and 186W(n,α)183Hf reactions were measured in the neutron energy range of 13.5-14.8 MeV via the activation technique to improve the database and resolve discrepancies. Monoenergetic neutrons in this energy range were produced via the T(d,n)4He reaction on a solid Ti-T target. The activities of the irradiated monitor foils and samples were measured using a well-calibrated high-resolution HPGe detector. Theoretical calculations of the excitation functions of the seven nuclear reactions mentioned above in the neutron energies from the threshold to 20 MeV were performed using the nuclear theoretical model program TALYS-1.9 to aid new evaluations of cross sections on tungsten isotopes. The experimental data obtained were analyzed and compared with that of previous experiments conducted by other researchers, and with the evaluated data available in the five major evaluated nuclear data libraries of IAEA (namely ENDF/B-VIII.0 or ENDF/B-VII.0, JEFF-3.3, JENDL-4.0u+, CENDL-3.2, and BROND-3.1 or ROSFOND-2010), and the theoretical values acquired using TALYS-1.9 nuclear-reaction modeling tools. The new cross section measurements agree with those of some recent experiments and theoretical excitation curves at the corresponding energies. The consistency of the theoretical excitation curves based on TALYS-1.9 with these experimental data is better than that of the evaluated curves available in the five major nuclear data libraries of IAEA.
Charge radii of potassium isotopes in the RMF (BCS)* approach
Rong An, Shi-Sheng Zhang, Li-Sheng Geng, Feng-Shou Zhang
2022, 46(5): 054101. doi: 10.1088/1674-1137/ac4b5c
We apply the recently proposed RMF (BCS)* ansatz to study the charge radii of the potassium isotopic chain up to 52K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd–even staggerings (OES). Nonetheless, both methods fail for 50K and to a lesser extent for 48,52K. It is shown that if these nuclei are deformed with a \begin{document}$ \beta_{20}\approx-0.2 $\end{document}, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond-mean-field studies are needed to properly describe the charge radii of these three nuclei, particularly for 50K.
Research on α-decay for the superheavy nuclei with Z = 118120
Chen He, Zhong-Ming Niu, Xiao-Jun Bao, Jian-You Guo
2022, 46(5): 054102. doi: 10.1088/1674-1137/ac4c3a
The generalized liquid-drop model (GLDM) with the microscopic shell correction from relativistic Hartree-Fock (RHF) calculations is used to explore the α-decay of superheavy nuclei. The known nuclei with \begin{document}$ Z = 106-118 $\end{document} are chosen as examples for testing. The calculated half-lives of α-decay agree with the experimental data better than those from the GLDM with the shell correction in the Weizs\begin{document}$ {\rm {\ddot{a}}} $\end{document}cker-Skyrme model. Moreover, the influence of the decay energy \begin{document}$ Q_{\alpha} $\end{document} on α-decay is investigated. It is determined that the \begin{document}$ Q_{\alpha} $\end{document} values obtained from the WS4 model with radial basis function (RBF) correction match the experimental data optimally. Owing to these advantages, the GLDM with the RHF shell correction and WS4+RBF \begin{document}$ Q_{\alpha} $\end{document} values is adopted to predict the α-decay lifetime for the unknown superheavy nuclei with \begin{document}$ Z = 118-120 $\end{document}. The trend of the available α-decay half-lives according to the neutron number is similar to the trends of the values from the GLDM calculation without shell correction as well as the universal decay law (UDL) formula. Comparably, the RHF shell correction depresses (raises) the α-decay lifetime for most nuclei with \begin{document}$ N<186 $\end{document} (\begin{document}$ N>186 $\end{document}). In comparison with the half-lives of spontaneous fission, it can be concluded that the α-decay is dominant in the superheavy nuclei \begin{document}$ ^{281-304}118 $\end{document}, \begin{document}$ ^{284-306}119 $\end{document}, and \begin{document}$ ^{287-308}120 $\end{document}. These results are beneficial to the exploration of superheavy nuclei in experiments.
Doubly-heavy tetraquark states ${\boldsymbol c \boldsymbol c\bar{\boldsymbol u}\bar{\boldsymbol d}} $ and ${\boldsymbol b \boldsymbol b\bar{\boldsymbol u}\bar{\boldsymbol d}} $
Xiaoyun Chen, Youchang Yang
2022, 46(5): 054103. doi: 10.1088/1674-1137/ac4ee8
Inspired by the recent observation of a very narrow state, called \begin{document}$ T_{cc}^+ $\end{document}, by the LHCb collaboration, the possible bound states and low-lying resonance states of the doubly-heavy tetraquark states \begin{document}$ cc\bar{u}\bar{d} $\end{document} (\begin{document}$ T_{cc} $\end{document}) and \begin{document}$ bb\bar{u}\bar{d} $\end{document} (\begin{document}$ T_{bb} $\end{document}) are searched in the framework of a chiral quark model with an accurate few-body method, the Gaussian expansion method. The real scaling method is also applied to identify the genuine resonance states. In the calculation, the meson–meson structure, diquark–antidiquark structure, and their coupling are all considered. The numerical results show: (i) For \begin{document}$ T_{cc} $\end{document} and \begin{document}$ T_{bb} $\end{document}, only \begin{document}$ I(J^P) = 0(1^+) $\end{document} states are bound in different quark structures. The binding energy varies from a few MeV for the meson–meson structure to over 100 MeV for the diquark–antidiquark structure. For example, for \begin{document}$ T_{cc} $\end{document}, in the meson–meson structure, there exists a weakly bound molecule \begin{document}$ DD^* $\end{document} state around 3841.4 MeV, 1.8 MeV below the \begin{document}$ D^0D^{*+} $\end{document}, which may be a good candidate for the observed state by LHCb; however in the diquark–antidiquark structure, a deeper bound state with mass 3700.9 MeV is obtained. When considering the structure mixing, the energy of system decreases to 3660.7 MeV and the shallow bound state disappears. (ii) Besides bound states, several resonance states for \begin{document}$ T_{QQ}(Q = c, b) $\end{document} with \begin{document}$ I(J^P) = 1(0^+), 1(1^+), 1(2^+), 0(1^+) $\end{document} are proposed.
Running coupling effect in next-to-leading order Balitsky-Kovchegov evolution equations
Wenchang Xiang, Mengliang Wang, Yanbing Cai, Daicui Zhou
2022, 46(5): 054104. doi: 10.1088/1674-1137/ac4ee9
Balitsky-Kovchegov equations in projectile and target rapidity representations are analytically solved for fixed and running coupling cases in the saturation domain. Interestingly, we find that the respective analytic S-matrices in the two rapidity representations have almost the same rapidity dependence in the exponent in the running coupling case, which provides a method to explain why the equally good fits to HERA data were obtained when using three different Balitsky-Kovchegov equations formulated in the two representations. To test the analytic outcomes, we solve the Balitsky-Kovchegov equations and numerically compute the ratios between these dipole amplitudes in the saturation region. The ratios are close to one, which confirms the analytic results. Moreover, the running coupling, collinearly-improved, and extended full collinearly-improved Balitsky-Kovchegov equations are used to fit the HERA data. We find that all of them provide high quality descriptions of the data, and the \begin{document}$ \chi^2/\mathrm{d.o.f} $\end{document} obtained from the fits are similar. Both the analytic and numerical calculations imply that the Balitsky-Kovchegov equation at the running coupling level is robust and has a sufficiently strong predictive power at HERA energies; however, higher order corrections could be significant for future experiments, such as those at the EIC or LHeC.
Exploring the half-lives of extremely long-lived α emitters
Jingya Fan, Chang Xu
2022, 46(5): 054105. doi: 10.1088/1674-1137/ac500d
Naturally occurring α emitters with extremely long half-lives are investigated using the latest experimental data. Within the time-dependent perturbation theory, α decay with a rather narrow width is treated as a quasi-stationary problem by dividing the potential between the α particle and daughter nucleus into a stationary part and a perturbation. The experimental α decay half-lives of seven available long-lived α emitters with \begin{document}$ T^{\rm{total}}_{1/2}>10^{14} $\end{document} y are reproduced with a good accuracy. It is also found that the deformation effect should be treated carefully for long-lived nuclei, especially with low \begin{document}$ Q_\alpha $\end{document} values. Predictions of the α decay half-lives of twenty naturally occurring nuclei are provided, namely, \begin{document}$ ^{142} $\end{document}Ce, \begin{document}$ ^{145,146} $\end{document}Nd, \begin{document}$ ^{149} $\end{document}Sm, \begin{document}$ ^{156} $\end{document}Dy, \begin{document}$ ^{162,164} $\end{document}Er, \begin{document}$ ^{168} $\end{document}Yb, \begin{document}$ ^{182,183,184,186} $\end{document}W, \begin{document}$ ^{187,188,189,190} $\end{document}Os, \begin{document}$ ^{192,195} $\end{document}Pt, and \begin{document}$ ^{204,206} $\end{document}Pb. These nuclei are energetically unstable to α decay with low decay energies and extremely long decay half-lives. In particular, the candidates \begin{document}$ ^{187} $\end{document}Os and \begin{document}$ ^{149} $\end{document}Sm are strongly recommended for future experiments.
Influence of electron density, temperature and decay energy on β decay rates in a stellar environment
Shuo Liu, Chang Xu
2022, 46(5): 054106. doi: 10.1088/1674-1137/ac500f
In this paper, the \begin{document}$ \beta^- $\end{document} decay rates in the magnetic field of a neutron star are investigated under different conditions of electron density, temperature, and decay energy. By considering the influence of magnetic field on the electron spectrum, we improve the Takahashi–Yokoi model and perform the calculations of \begin{document}$ \beta^- $\end{document} decay rates for the nickel (Ni) isotopes, which are the typical neutron-rich nuclei participating in the rapid neutron-capture process (r-process). It is found that the \begin{document}$ \beta^- $\end{document} decay rates are increased significantly in the extremely strong magnetic field (\begin{document}$ B>10^{15} $\end{document} G). Furthermore, we find oscillation of \begin{document}$ \beta^- $\end{document} decay rates with the increase of magnetic field strength, implying that the magnitude of \begin{document}$ \beta^- $\end{document} decay rates is closely related to not only the decay energy but also the environmental electron density. In contrast, the impact of temperature on the \begin{document}$ \beta^- $\end{document} decay rates is found to be negligible in the range of \begin{document}$ 10^{7} $\end{document} K\begin{document}$ <T<10^{10} $\end{document} K.
Implications of gamma-ray photon measurements at the LHAASO on Lorentz symmetry
Yi Ling, Yuxuan Liu, Sai Wang, Meng-He Wu
2022, 46(5): 055101. doi: 10.1088/1674-1137/ac4704
The Large High Altitude Air Shower Observatory (LHAASO) has reported the measurement of photons with high energies of up to 1.42 PeV from twelve gamma-ray sources. We are concerned with the implications of the LHAASO data on the fate of Lorenz symmetry at such high energy levels; thus, we consider the interaction between gamma rays and photons in the cosmic microwave background (CMB) and compute the optical depth, mean free path, and survival probability of photons from these gamma-ray sources. Employing the threshold value predicted by standard special relativity, the lowest survival probability for observed gamma ray photons is found to be approximately 0.60, which is fairly high and implies that abundant photons with energies above the threshold may reach the Earth without Lorentz symmetry violation. We conclude that it is unreasonable to argue that Lorentz symmetry would be violated using current observations at the LHAASO.
Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model
Huai-Min Chen, Cheng-Jun Xia, Guang-Xiong Peng
2022, 46(5): 055102. doi: 10.1088/1674-1137/ac4b5b
The properties of strange quark matter and the structures of (proto-)strange stars are studied within the framework of a baryon density-dependent quark mass model, where a novel quark mass scaling and self-consistent thermodynamic treatment are adopted. Our results indicate that the perturbative interaction has a significant impact on the properties of strange quark matter. It is determined that the energy per baryon increases with temperature, while the free energy decreases and eventually becomes negative. At fixed temperatures, the pressure at the minimum free energy per baryon is zero, suggesting that the thermodynamic self-consistency is preserved. Furthermore, the sound velocity v in quark matter approaches the extreme relativistic limit (\begin{document}$ c/\sqrt{3} $\end{document}) as the density increases. By increasing the strengths of the confinement parameter D and perturbation parameter C, the tendency for v to approach the extreme relativistic limit at high density is slightly weakened. For (proto-)strange stars, the novel quark mass scaling can accommodate massive proto-strange stars with their maximum mass surpassing twice the solar mass by considering the isentropic stages along the star evolution line, where the entropy per baryon of the star matter is set to be 0.5 and 1 with the lepton fraction \begin{document}$ Y_{l} $\end{document} = 0.4.
Stochastic gravitational wave background from PBH-ABH mergers
Wenfeng Cui, Fei Huang, Jing Shu, Yue Zhao
2022, 46(5): 055103. doi: 10.1088/1674-1137/ac4cab
The measurement of gravitational waves produced by binary black-hole mergers at the Advanced LIGO has encouraged extensive studies on the stochastic gravitational wave background. Recent studies have focused on gravitational wave sources made of the same species, such as mergers from binary primordial black holes or those from binary astrophysical black holes. In this paper, we study a new possibility – the stochastic gravitational wave background produced by mergers of one primordial black hole and one astrophysical black hole. Such systems are necessarily present if primordial black holes exist. We study the isotropic gravitational wave background produced through the history of the universe. We find it is very challenging to detect such a signal. We also demonstrate that it is improper to treat the gravitational waves produced by such binaries in the Milky Way as a directional stochastic background due to a very low binary formation rate.
Dynamic property of phase transition for non-linear charged anti-de Sitter black holes
Yun-Zhi Du, Huai-Fan Li, Fang Liu, Li-Chun Zhang
2022, 46(5): 055104. doi: 10.1088/1674-1137/ac4df1
Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity. In this work, we investigate the phase transition and its dynamics for the charged EPYM AdS black hole. Through reconstructing Maxwell's equal-area law, we find there exists a high-/low-potential black hole (HPBH/LPBL) phase transition, not only the pure large/small black hole phase transition. The Gibbs free energy landscape (\begin{document}$ G_{\rm L} $\end{document}) is treated as a function of the black hole horizon, which is the order parameter of the phase transition due to thermal fluctuation. From the viewpoint of \begin{document}$ G_{\rm L} $\end{document}, the stable HPBH/LPBL states correspond to two wells of \begin{document}$ G_{\rm L} $\end{document}, which have the same depth. The unstable intermediate-potential black hole state corresponds to the local maximum of \begin{document}$ G_{\rm L} $\end{document}. Then we focus on the probability evolution governed by the Fokker–Planck equation. Through solving the Fokker–Planck equation with different reflection/absorption boundary conditions and initial conditions, the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time. Furthermore, the effect of temperature on the dynamic properties of the phase transition is also investigated.
Thermodynamics for higher dimensional rotating black holes with variable Newton constant
Liu Zhao
2022, 46(5): 055105. doi: 10.1088/1674-1137/ac4f4c
The extensivity for the thermodynamics of general D-dimensional rotating black holes with or without a cosmological constant can be proved analytically, provided that the effective number of microscopic degrees of freedom and the chemical potential are given respectively as \begin{document}$ N = L^{D-2}/G,\; \mu = GTI_D/L^{D-2} $\end{document}, where G is the variable Newton constant, \begin{document}$ I_D $\end{document} is the Euclidean action, and L is a constant length scale. In the cases without a cosmological constant, i.e., the Myers-Perry black holes, the physical mass and the intensive variables can be expressed as explicit macro state functions in the extensive variables in a simple and compact form, which allows for an analytical calculation of the heat capacity. The results indicate that the Myers-Perry black holes with zero, one, and k equal rotation parameters are all thermodynamically unstable.
Erratum and Addendum
Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)]
Ying Chen, Ming Gong, Ning Li, Chuan Liu, Yu-Bin Liu, Zhaofeng Liu, Jian-Ping Ma, Yu Meng, Chao Xiong, Ke-Long Zhang
2022, 46(5): 059001. doi: 10.1088/1674-1137/ac4bcd