2023 Vol. 47, No. 5

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2023-5 Contents
2023, 47(5): 1-2.
Production of ${\boldsymbol X_{{\boldsymbol{ cs}}\bar{\boldsymbol c}\bar{\boldsymbol s}} }$ in heavy ion collisions
Yuanyuan Hu, Hui Zhang
2023, 47(5): 051001. doi: 10.1088/1674-1137/acc3f4
The yields of \begin{document}$ X_{cs\bar{c}\bar{s}} $\end{document} with its two possible configurations, i.e., the hadronic molecular state and tetraquark state, for Pb-Pb collisions at \begin{document}$ \sqrt{s_{NN}}=5.02\;{\rm{TeV}} $\end{document} is studied. A volume effect is found from the centrality distribution of \begin{document}$ X_{cs\bar{c}\bar{s}} $\end{document}, which could help to distinguish the inner structure of \begin{document}$ X_{cs\bar{c}\bar{s}} $\end{document}. We also show the rapidity and the transverse momentum distributions of \begin{document}$ X_{cs\bar{c}\bar{s}} $\end{document} production as well as its elliptic flow coefficient as a function of the transverse momentum.
Regular black holes with improved energy conditions and their analogues in fluids
Chen Lan, Yan-Gang Miao, Yi-Xiong Zang
2023, 47(5): 052001. doi: 10.1088/1674-1137/acc1cd
On the premise of the importance of energy conditions for regular black holes, we propose a method to remedy those models that break the dominant energy condition, e.g., the Bardeen and Hayward black holes. We modify the metrics but ensure their regularity at the same time, so that the weak, null, and dominant energy conditions are satisfied, with the exception of the strong energy condition. Likewise, we prove a no-go theorem for conformally related regular black holes, which states that the four energy conditions can never be met in this class of black holes. In order to seek evidences for distinguishing regular black holes from singular black holes, we resort to analogue gravity and regard it as a tool to mimic realistic regular black holes in a fluid. The equations of state for the fluid are solved via an asymptotic analysis associated with a numerical method, which provides a modus operandi for experimental observations, in particular, the conditions under which one can simulate realistic regular black holes in the fluid.
Production and decay of polarized hyperon-antihyperon pairs
Karin Schönning, Varvara Batozskaya, Patrik Adlarson, Xiaorong Zhou
2023, 47(5): 052002. doi: 10.1088/1674-1137/acc790
Polarized hyperon-antihyperon pairs shed light on various unresolved puzzles in contemporary physics: How the strong interaction confines quarks into hadrons, how accurately the Standard Model describes microcosmos and even why our universe consists of so much more matter than antimatter. Thanks to their weak, parity violating decays, hyperons reveal their spin properties. This can be exploited e.g. the decomposition of the electromagnetic structure of hyperons, precision tests of flavour symmetry and searches for CP violation. At the BESIII experiment at BEPC-II, Beijing, China, hyperon-antihyperon pairs can be produced in abundance. Recently collected large data samples have triggered the development of new methods that provide unprecedented precision and a plethora of new results have emerged. When applied at future high-intensity facilities like PANDA and STCF, precision physics will be taken to a new level which can contribute to the solution to the aforementioned puzzles.
Study of parity violation in $ {\boldsymbol{\Lambda_c^+} \boldsymbol{\to\phi p}} $ and $ {\boldsymbol{\Lambda_c^+} \boldsymbol{\to \omega p}} $ decays
Peng-Cheng Hong, Fang Yan, Rong-Gang Ping, Tao Luo
2023, 47(5): 053101. doi: 10.1088/1674-1137/acb7ce
CP violation in baryonic decays has not been significantly observed. With large data events accumulated at \begin{document}$ {e^+e^-} $\end{document} colliders or the Large Hadron Collider, charmed baryon decays would provide a promising laboratory to test CP symmetry. In this study, we formulate \begin{document}$ {{\Lambda_c^+}}\to\phi p $\end{document} and \begin{document}$ {{\Lambda_c^+}}\to\omega p $\end{document} decays for the measurement of their asymmetry parameters in weak decays at the BESIII or LHCb experiments. The polarization transfer is analyzed in the two processes of \begin{document}$ {e^+e^-}\to\Lambda_c^+\bar\Lambda_c^- $\end{document} and \begin{document}$ \Lambda_b^0\to \Lambda^+_c\pi^- $\end{document}, and the formulas for the joint angular distribution of these processes are provided. The sensitivity of the measurement of the asymmetry parameters of the above two decay processes is estimated for future experiments.
Investigation of Z-boson decay into $ {\boldsymbol\Xi_{\boldsymbol bc}} $ and ${ \boldsymbol\Xi_{\boldsymbol bb}} $ baryons within the NRQCD factorization approach
Xuan Luo, Hai-Bing Fu, Hai-Jiang Tian
2023, 47(5): 053102. doi: 10.1088/1674-1137/acbc0e
Z-boson decay provides a good opportunity to search for the \begin{document}$ \Xi_{bQ} $\end{document} baryon because a large number of its events can be collected at high energy colliders. In this paper, we perform a complete investigation of the indirect production of the \begin{document}$ \Xi_{bc} $\end{document} and \begin{document}$ \Xi_{bb} $\end{document} baryons via the Z-boson decay process \begin{document}$ Z\to \Xi_{bQ}+\bar b +\bar Q $\end{document} with a \begin{document}$ Q= (c,b) $\end{document} quark under the NRQCD factorization approach. After considering the contribution from the diquark states \begin{document}$ \langle bc\rangle[^3S_1]_{\bar 3/6} $\end{document}, \begin{document}$ \langle bc\rangle[^1S_0]_{\bar 3/6} $\end{document}, \begin{document}$ \langle bb\rangle [^1S_0]_6 $\end{document}, and \begin{document}$ \langle bb\rangle[^3S_1]_{\bar 3} $\end{document}, the calculated branching fractions are \begin{document}$ {\cal B}(Z\to\Xi_{bc}+X) = 3.595\times 10^{-5} $\end{document} and \begin{document}$ {\cal B}(Z\to\Xi_{bb}+X) = 1.213\times 10^{-6} $\end{document}. Furthermore, the \begin{document}$ \Xi_{bc} $\end{document} and \begin{document}$ \Xi_{bb} $\end{document} production events are predicted to be of the order of \begin{document}$ 10^4 $\end{document} and \begin{document}$ 10^3 $\end{document} at the LHC collider, and the order of \begin{document}$ 10^7 $\end{document} and \begin{document}$ 10^6 $\end{document} for the CEPC collider. We then estimate the production ratio for \begin{document}$ Z\to c\bar c(b\bar b)\to\Xi^{+,0}_{bc}+X $\end{document} with \begin{document}$ \Xi^{+,0}_{bc} \to \Lambda^+_c $\end{document} in Z-boson decay, that is, \begin{document}$ {\cal R}(Z\to c\bar c\to\Xi^{+,0}_{bc}+X) \sim {\cal O}(10^{-6}) $\end{document} and \begin{document}$ {\cal R}(Z\to b\bar b\to\Xi^{+,0}_{bc}+X) \sim {\cal O}(10^{-5}) $\end{document}, respectively. Finally, we present the differential decay widths of \begin{document}$ \Xi_{bc} $\end{document} and \begin{document}$ \Xi_{bb} $\end{document} with respect to \begin{document}$ s_{23} $\end{document} and z distributions and analyze the uncertainties.
Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model
Ya-Peng Zhao, Chao-Yong Wang, Shu-Yu Zuo, Cheng-Ming Li
2023, 47(5): 053103. doi: 10.1088/1674-1137/acbf2a
In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for \begin{document}$ q<1.15 $\end{document}, CEP moves in the direction of lower temperature and larger quark chemical potential. However, for \begin{document}$ q>1.15 $\end{document}, CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance (\begin{document}$ \sigma^{2} $\end{document}), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for \begin{document}$ \sqrt{S_{NN}}>19.6\ \mathrm{GeV} $\end{document}, when q is set to \begin{document}$ 1.07 $\end{document}.
Revisiting D-meson twist-2, 3 distribution amplitudes
Tao Zhong, Dong Huang, Hai-Bing Fu
2023, 47(5): 053104. doi: 10.1088/1674-1137/acc1cb
Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of \begin{document}$ {\cal{R}}(D) $\end{document} of the semileptonic decay \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}, researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document} , and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document} are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}. Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document}, and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document}. New sum rule formulae for the \begin{document}$\xi $\end{document}-moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ-moments via the least squares method.
D-wave excited ${\boldsymbol{ cs}\bar{\boldsymbol c}\bar{\boldsymbol s}} $ tetraquark states with ${ \boldsymbol{J^{PC}}=\bf 1^{\bf ++}} $ and ${\bf 1^{\bf +-}} $
Zi-Yan Yang, Wei Chen
2023, 47(5): 053105. doi: 10.1088/1674-1137/acbf2c
We study the mass spectra of D-wave excited \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark states with \begin{document}$ J^{PC}=1^{++} $\end{document} and \begin{document}$ 1^{+-} $\end{document} in both symmetric \begin{document}$ \mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}} $\end{document} and antisymmetric \begin{document}$ \bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}} $\end{document} color configurations using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark interpolating currents in various excitation structures with \begin{document}$(L_\lambda,L_\rho\{l_{\rho_1},l_{\rho_2}\})=(2,0\{0,0\}),\,(1,1\{1,0\}),\,(1,1\{0,1\}),\,(0,2\{1,1\}),\,(0,2\{2,0\}),\,(0,2\{0,2\})$\end{document}. Our results support the interpretation of the recently observed \begin{document}$ X(4685) $\end{document} resonance as a D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark state with \begin{document}$ J^{PC}=1^{++} $\end{document} in the \begin{document}$ (2,0\{0,0\}) $\end{document} or \begin{document}$ (0,2\{2,0\}) $\end{document} excitation mode, although some other possible excitation structures cannot be excluded exhaustively within theoretical errors. Moreover, our results provide the mass relations \begin{document}$ 6_{\rho\rho}<3_{\lambda\lambda}<3_{\lambda\rho}<3_{\rho\rho} $\end{document} and \begin{document}$ 6_{\rho\rho}<3_{\lambda\lambda}<6_{\lambda\lambda}< 3_{\rho\rho} $\end{document} for the positive and negative \begin{document}$ \mathbb{C} $\end{document}-parity D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquarks, respectively. We suggest searching for these possible D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquarks in both the hidden-charm channels \begin{document}$ J/\psi\phi $\end{document} and \begin{document}$ \eta_c\phi $\end{document}, as well as open-charm channels such as \begin{document}$ D_s\bar{D}_s^* $\end{document} and \begin{document}$ D_{s}\bar{D}_{s1}^* $\end{document} .
One-loop formulas for Hlνl for l = e, µ, τ in 't Hooft-Veltman gauge
Dzung Tri Tran, Khiem Hong Phan
2023, 47(5): 053106. doi: 10.1088/1674-1137/acc1cf
In this paper, we present analytical results for one-loop contributions to the decay processes \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} (for \begin{document}$ l = e, \mu, \tau $\end{document}). The calculations are performed within the Standard Model framework in the 't Hooft-Veltman gauge. One-loop form factors are then written in terms of scalar one-loop functions in the standard notations of \begin{document}$ {\tt LoopTools}$\end{document}. As a result, one-loop decay rates for the decay channels can be evaluated numerically by using the package. Furthermore, we analyze the signals of \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} via the production processes \begin{document}$ e^-e^+ \rightarrow ZH^* \rightarrow Z (H^* \rightarrow Z \nu_l\bar{\nu}_l) $\end{document}, including the initial beam polarizations at future lepton colliders. The Standard Model backgrounds, such as the processes \begin{document}$ e^-e^+ \rightarrow \nu_l\bar{\nu}_l ZZ $\end{document}, are also examined in this study. Numerical results indicate that one-loop corrections make contributions of approximately 10% to the decay rates. These are sizeable contributions and should be taken into account at future colliders. We show that the signals \begin{document}$ H\rightarrow Z\nu_l\bar{\nu}_l $\end{document} are clearly visible at the center-of-mass energy \begin{document}$ \sqrt{s}=250 $\end{document} GeV and are difficult to probe in higher-energy regions owing to the dominant backgrounds.
Production of $ {\boldsymbol{d}_{\boldsymbol{N\Omega}}} $ dibaryon in kaon induced reactions
Jing Liu, Qi-Fang Lü, Chun-Hua Liu, Dian-Yong Chen, Yu-Bing Dong
2023, 47(5): 053107. doi: 10.1088/1674-1137/acc44c
In this paper, we propose to investigate the \begin{document}$ d_{N\Omega} $\end{document} dibaryon production in the \begin{document}$ K^- p \rightarrow d_{N\Omega} \bar{\Xi}^0 $\end{document} process by utilizing a kaon beam with a typical momentum of approximately 10 GeV, which may be available at COMPASS, OKA@U-70, and SPS@CERN. The cross sections for \begin{document}$ K^- p \rightarrow d_{N\Omega} \bar{\Xi}^0 $\end{document} are estimated, and in particular, the magnitude of the cross sections is evaluated to be several hundred nanobarns at \begin{document}$ P_K=20 $\end{document} GeV. Considering that the \begin{document}$ d_{N\Omega} $\end{document} dibaryon dominantly decays into \begin{document}$ \Xi \Lambda $\end{document} and \begin{document}$ \Xi \Sigma $\end{document}, we also estimate the cross sections for \begin{document}$ K^- p \to \Xi^0 \Lambda \bar{\Xi}^0 $\end{document} and \begin{document}$ K^- p \to $\end{document}\begin{document}$ \Xi^- \Sigma^+ \bar{\Xi}^0 $\end{document}, where the \begin{document}$ d_{N\Omega} $\end{document} dibaryon can be observed in the invariant mass distributions of \begin{document}$ \Xi^0 \Lambda $\end{document} and \begin{document}$ \Xi^- \Sigma^+ $\end{document}, respectively.
Photo-production of lowest ${\boldsymbol\Sigma^{*}_{\bf 1/2^-}}$ state within the Regge-effective Lagrangian approach
Yun-He Lyu, Han Zhang, Neng-Chang Wei, Bai-Cian Ke, En Wang, Ju-Jun Xie
2023, 47(5): 053108. doi: 10.1088/1674-1137/acc4ab
Because the lowest \begin{document}$ \Sigma^{*} $\end{document} state with quantum numbers spin-parity \begin{document}$ J^{P} =1/2^{-} $\end{document} is far from being established experimentally and theoretically, we perform a theoretical study on the \begin{document}$ \Sigma^*_{1/2^-} $\end{document} photo-production within the Regge-effective Lagrangian approach. Considering that \begin{document}$ \Sigma^*_{1/2^-} $\end{document} couples to the \begin{document}$ \bar{K}N $\end{document} channel, we study the contributions from the t-channel K exchange diagram. Moreover, the contributions from the t-channel \begin{document}$ K^* $\end{document} exchange, s-channel nucleon pole, u-channel Σ exchange, and contact term are considered. The differential and total cross sections of the process \begin{document}$ \gamma n \to K^{+}\Sigma^{*-}_{1/2^-} $\end{document} are predicted with our model parameters. The results should help in experimentally searching for the \begin{document}$ \Sigma^*_{1/2^-} $\end{document} state in the future.
Reaction 55Mn + 159Tb : preparation for the synthesis of new elements
Lixin Chen, Suyang Xu, Zhiyuan Zhang, Jianguo Wang, Minghui Huang, Mingming Zhang, Long Ma, Huabin Yang, Chunli Yang, Xiaolei Wu, Houbing Zhou, Zhen Zhao, Xinyuan Huang, Hao Zhou, Xu Zhang, Luchong Sun, Zongchi Li, Zaiguo Gan
2023, 47(5): 054001. doi: 10.1088/1674-1137/acb9e2
The complete fusion reaction of \begin{document}$^{55}$\end{document}Mn + \begin{document}$^{159}$\end{document}Tb was studied on the gas-filled recoil separator SHANS2. Nineteen ER - α\begin{document}$_{1}$\end{document} - α\begin{document}$_{2}$\end{document} decay chains from \begin{document}$^{210}$\end{document}Th produced from the 4n evaporation channel were observed. The α-particle energy and half-life of \begin{document}$^{210}$\end{document}Th were determined as 7922(14) keV and 14(4) ms, respectively. In addition, the decay properties of \begin{document}$E_{\alpha}$\end{document} = 7788(14) keV and \begin{document}$T_{1/2}$\end{document} = 36\begin{document}$^{+15}_{-8}$\end{document} ms were obtained for \begin{document}$^{211}$\end{document}Th. The measured α decay properties of \begin{document}$^{210}$\end{document}Th and \begin{document}$^{211}$\end{document}Th were consistent with literature data. The cross sections were measured to be 0.59\begin{document}$^{+0.25}_{-0.23}$\end{document} nb and 0.19\begin{document}$^{+0.12}_{-0.09}$\end{document} nb for \begin{document}$^{210}$\end{document}Th and \begin{document}$^{211}$\end{document}Th, respectively. The equilibrium charge state of the recoiled nucleus \begin{document}$^{210}$\end{document}Th was determined experimentally. The new data were helpful for estimating the equilibrium charge states of elements 119 and 120, which could be produced via the \begin{document}$^{240}$\end{document}Pu(\begin{document}$^{55}$\end{document}Mn, 3n)\begin{document}$^{292}$\end{document}119 and \begin{document}$^{243}$\end{document}Am(\begin{document}$^{55}$\end{document}Mn, 3n)\begin{document}$^{295}$\end{document}120 reactions, respectively.
Determining the nuclear temperature dependence on source neutron-proton asymmetry in heavy-ion reactions at intermediate energy
Guofeng Qu, Yu Huang, Hua Zheng, Xingquan Liu, R. Wada, Weiping Lin, Meirong Huang, Jifeng Han, Peipei Ren, Zhenlei Yang, Xin Zhang, Qiangzhong Leng
2023, 47(5): 054002. doi: 10.1088/1674-1137/acbd91
In this article, we investigate the dependence of nuclear temperature on emitting source neutron-proton (\begin{document}$ N/Z $\end{document}) asymmetry with light charged particles (LCPs) and intermediate mass fragments (IMFs) generated from intermediate-velocity sources in thirteen reaction systems with different \begin{document}$ N/Z $\end{document} asymmetries, \begin{document}$ ^{64} \rm{Zn} $\end{document} on \begin{document}$ ^{112} \rm{Sn} $\end{document}, and \begin{document}$ ^{70} \rm{Zn} $\end{document}, \begin{document}$ ^{64} \rm{Ni} $\end{document} on \begin{document}$ ^{112,124} \rm{Sn} $\end{document}, \begin{document}$ ^{58,64} \rm{Ni} $\end{document}, \begin{document}$ ^{197} \rm{Au} $\end{document}, and \begin{document}$ ^{232} \rm{Th} $\end{document} at 40 MeV/nucleon. The apparent temperature values of LCPs and IMFs from different systems are deduced from the measured yields using two helium-related and eight carbon-related double isotope ratio thermometers, respectively. Then, the sequential decay effect on the experimental apparent temperature deduction with the double isotope ratio thermometers is quantitatively corrected explicitly with the aid of the quantum statistical model. The present treatment is an improvement compared to our previous studies in which an indirect method was adopted to qualitatively consider the sequential decay effect. A negligible \begin{document}$ N/Z $\end{document} asymmetry dependence of the real temperature after the correction is quantitatively addressed in heavy-ion reactions at the present intermediate energy, where a change of 0.1 units in source \begin{document}$ N/Z $\end{document} asymmetry corresponds to an absolute change in temperature of an order of 0.03 to 0.29 MeV on average for LCPs and IMFs. This conclusion is in close agreement with that inferred qualitatively via the indirect method in our previous studies.
Open quantum system approach for heavy quark thermalization
Zhuoxuan Xie, Baoyi Chen
2023, 47(5): 054101. doi: 10.1088/1674-1137/acbc0f
We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schrödinger equation (SSE) from the full Schrödinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.
Z0 boson associated b-jet production in high-energy nuclear collisions
Sa Wang, Wei Dai, Ben-Wei Zhang, Enke Wang
2023, 47(5): 054102. doi: 10.1088/1674-1137/acc1ca
The production of vector boson tagged heavy quark jets potentially provides new tools to probe the jet quenching effect. In this paper, we present the first theoretical study on the angular correlations (\begin{document}$ \Delta\phi_{bZ} $\end{document}), transverse momentum imbalance (\begin{document}$ x_{bZ} $\end{document}), and nuclear modification factor (\begin{document}$ I_{AA} $\end{document}) of \begin{document}$ Z^0 $\end{document} boson tagged b-jets in heavy-ion collisions, which was performed using a Monte Carlo transport model. We find that the medium modification of the \begin{document}$ \Delta\phi_{bZ} $\end{document} for \begin{document}$ Z^0$\end{document} + b-jet has a weaker dependence on \begin{document}$ \Delta\phi_{bZ} $\end{document} than that for \begin{document}$ Z^0$\end{document} + jet, and the modification patterns are sensitive to the initial jet \begin{document}$ p_T $\end{document} distribution. Additionally, with the high purity of the quark jet in \begin{document}$ Z^0$\end{document} + (b-) jet production, we calculate the momentum imbalance \begin{document}$ x_{bZ} $\end{document} and the nuclear modification factor \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions. We observe a smaller \begin{document}$ \Delta \langle x_{jZ} \rangle $\end{document} and larger \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions relative to those of \begin{document}$ Z^0$\end{document} + jet, which may be an indication of the mass effect of jet quenching and can be tested in future measurements.
Microscopic study of neutron-induced fission process of 239Pu via zero- and finite-temperature density functional theory
Yong-Jing Chen, Yang Su, Li-Le Liu, Guoxiang Dong, Zhigang Ge, Nengchuan Shu, Xiaobao Wang
2023, 47(5): 054103. doi: 10.1088/1674-1137/acbe2c
To study the neutron-induced fission of \begin{document}$ ^{239} $\end{document}Pu, potential energy surface (PES) calculations were performed using zero and finite-temperature density functional theory (FT-DFT) with the Skyrme force. The energy of the incident neutron was simulated by the temperature of the FT-DFT. The variations of the least-energy fission path, fission barrier, total kinetic energy, scission line, and mass distribution of fission fragments with the incident neutron energy were analyzed. It was learned that an increase in the temperature lowers the barrier height, the isomeric-state energy, and the ridge between symmetric and asymmetric fission valleys. Additionally, the gaps of the single particle levels become smaller with an increase in the temperature. As the temperature increases, the pre-fission region shrinks, and the scission occurs at smaller deformation around the symmetric fission channel. At low temperatures, the pairing correlations in the collective space are similar to those in zero-temperature DFT, and when the temperature is \begin{document}$ T> $\end{document} 0.3 MeV, the pairing gaps decrease rapidly. Two different methods were used to calculate the fission yields of the neutron-induced fission \begin{document}$ ^{239} $\end{document}Pu (n, f) with different incident neutron energies, in the framework of time-dependent generator coordinate method (TDGCM). One way to calculate the fission yield of \begin{document}$ ^{239} $\end{document}Pu (n, f) is to solve the collective equation of the TDGCM by using the PES from the FT-DFT with the corresponding temperature. The other involves using the PES from the zero-temperature DFT and adjusting the initial collective energy of the wave packet in the TDGCM according to the incident neutron energy. For the cases of the lower incident neutron energies, these two methods gave similar results and reproduced the experimental peak and width of fission fragment distribution. However, for the highest incident neutron energy considered in this study, the results from the TDGCM using the PES from zero-temperature DFT deviated explicitly from the experimental data, whereas those obtained by using the PES from FT-DFT remained close to the experimental data. This indicated that, with the increase in the incident neutron energy, the shell structure of the compound nuclei changed explicitly; thus, it may not be effective to use the PES from zero-temperature to perform the fission dynamic calculation.
Solving Schrodinger equations using a physically constrained neural network
Kai-Fang Pu, Han-Lin Li, Hong-Liang Lü, Long-Gang Pang
2023, 47(5): 054104. doi: 10.1088/1674-1137/acc518
Deep neural networks (DNNs) and auto differentiation have been widely used in computational physics to solve variational problems. When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization, various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency. We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function (CDF) \begin{document}$F(x) = \int_{-\infty}^{x} \psi^*\psi {\rm d}x'$\end{document}. Using this constrained neural network to represent the variational wave function, we solve Schrodinger equations using auto-differentiation and stochastic gradient descent (SGD) by minimizing the violation of the trial wave function \begin{document}$ \psi(x) $\end{document} to the Schrodinger equation. For several classical problems in quantum mechanics, we obtain their ground state wave function and energy with very low errors. The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.
Anisotropic strange quark star in Finch-Skea geometry and its maximum mass for non-zero strange quark mass (ms ≠ 0)
B. Das, K. B. Goswami, A. Saha, P. K. Chattopadhyay
2023, 47(5): 055101. doi: 10.1088/1674-1137/acb90f
A class of relativistic astrophysical compact objects is analyzed in the modified Finch-Skea geometry described by the MIT bag model equation of state of interior matter, \begin{document}$ p=\dfrac{1}{3}\left(\rho-4B\right) $\end{document}, where B is known as the bag constant. B plays an important role in determining the physical features and structure of strange stars. We consider the finite mass of the strange quark (\begin{document}$ m_{s} \neq 0 $\end{document}) and study its effects on the stability of quark matter inside a star. We note that the inclusion of strange quark mass affects the gross properties of the stellar configuration, such as maximum mass, surface red-shift, and the radius of strange quark stars. To apply our model physically, we consider three compact objects, namely, (i) VELA X-1, (ii) 4U 1820-30, and (iii) PSR J 1903+327, which are thought to be strange stars. The range of B is restricted from 57.55 to \begin{document}$B_{\rm stable}$\end{document} (\begin{document}$\rm MeV/fm^{3}$\end{document}), for which strange matter might be stable relative to iron (\begin{document}$^{56}{\rm Fe}$\end{document}). However, we also observe that metastable and unstable strange matter depend on B and \begin{document}$ m_{s} $\end{document}. All energy conditions hold well in this approach. Stability in terms of the Lagrangian perturbation of radial pressure is studied in this paper.
Gauging universe expansion via scalar fields
Devanarayanan Rajeeb Kumar, S.D. Pathak, Vikash Kumar Ojha
2023, 47(5): 055102. doi: 10.1088/1674-1137/acc0f2
In this study, we investigate the expansion of the FRLW universe in the open, closed, and flat geometries. The universe is dominated by a scalar field (spatially homogeneous) as a source of dark energy. We consider the three different classes of scalar fields – quintessence, tachyonic, and phantom field – for our analysis. A mathematical analysis is carried out by considering these three scalar fields with exponential and power-law potentials. Both potentials give exponential expansion in the open, closed, and flat FRLW universes. It is found that quintessence, tachyonic, and phantom scalar fields are indistinguishable under the slow roll approximation.
Gravastar in the framework of symmetric teleparallel gravity
Sneha Pradhan, Sanjay Mandal, P.K. Sahoo
2023, 47(5): 055103. doi: 10.1088/1674-1137/acc1ce
We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in \begin{document}$ f(Q) $\end{document} gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of \begin{document}$ f(Q) $\end{document} gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.
Primordial black holes and third order scalar induced gravitational waves
Zhe Chang, Yu-Ting Kuang, Xukun Zhang, Jing-Zhi Zhou
2023, 47(5): 055104. doi: 10.1088/1674-1137/acc649
The process of primordial black hole (PBH) formation is inevitably accompanied by scalar induced gravitational waves (SIGWs). The strong correlation between PBH and SIGW signals may offer a promising approach to detecting PBHs in upcoming gravitational wave experiments, such as the Laser Interferometer Space Antenna (LISA). We investigate third order SIGWs during a radiation-dominated era in the case of the monochromatic primordial power spectrum \begin{document}$ \mathcal{P}_{\zeta}=A_{\zeta}k_*\delta\left(k-k_*\right) $\end{document}. For LISA observations, the relationships between the signal-to-noise ratio (SNR) and monochromatic primordial power spectrum are studied systematically, revealing that the effects of third order SIGWs extend the cutoff frequency from \begin{document}$ 2f_* $\end{document} to \begin{document}$ 3f_* $\end{document} and lead to an approximately 200% increase in the SNR for the frequency band from \begin{document}$ 10^{-5} $\end{document}Hz to \begin{document}$ 1.6\times 10^{-3} $\end{document}Hz, corresponding to PBHs with masses in the range \begin{document}$4\times 10^{-12}M_{\odot} \sim 10^{-7}M_{\odot}$\end{document}. We find that there is a critical value, \begin{document}$ A_*=1.76\times 10^{-2} $\end{document}, for the amplitude of the monochromatic primordial power spectra, such that when \begin{document}$ A_{\zeta}>A_* $\end{document}, the energy density of third order SIGWs is larger than that of second order SIGWs.
Entropies of the various components of the universe
Hao Yu, Yu-Xiao Liu, Jin Li
2023, 47(5): 055105. doi: 10.1088/1674-1137/acc2ad
In this study, we investigate the entropies of photons, ideal gas-like dust (baryonic matter), and a special kind of dark energy in the context of cosmology. When these components expand freely with the universe, we calculate the entropy and specific entropy of each component from the perspective of statistics. Under specific assumptions and conditions, the entropies of these components can satisfy the second law of thermodynamics independently. Our calculations show that the specific entropy of matter cannot be a constant during the expansion of the universe, except for photons. When these components interact with the space-time background, particle production (annihilation) can occur. We study the influence of the interaction on the entropies of these components and obtain the conditions guaranteeing that the entropy of each component satisfies the second law of thermodynamics.
Null test for cosmic curvature using Gaussian process
Peng-Ju Wu, Jing-Zhao Qi, Xin Zhang
2023, 47(5): 055106. doi: 10.1088/1674-1137/acc647
The cosmic curvature \begin{document}$ \Omega_{K,0} $\end{document}, which determines the spatial geometry of the universe, is an important parameter in modern cosmology. Any deviation from \begin{document}$ \Omega_{K,0}=0 $\end{document} would have a profound impact on the primordial inflation paradigm and fundamental physics. In this work, we adopt a cosmological model-independent method to test whether \begin{document}$ \Omega_{K,0} $\end{document} deviates from zero. We use the Gaussian process to reconstruct the reduced Hubble parameter \begin{document}$ E(z) $\end{document} and the derivative of the distance \begin{document}$ D'(z) $\end{document} from observational data and then determine \begin{document}$ \Omega_{K,0} $\end{document} with a null test relation. The cosmic chronometer (CC) Hubble data, baryon acoustic oscillation (BAO) Hubble data, and supernovae Pantheon sample are considered. Our result is consistent with a spatially flat universe within the domain of reconstruction \begin{document}$ 0<z<2.3 $\end{document}, at the \begin{document}$ 1\sigma $\end{document} confidence level. In the redshift interval \begin{document}$ 0<z<1 $\end{document}, the result favors a flat universe, while at \begin{document}$ z>1 $\end{document}, it tends to favor a closed universe. In this sense, there is still a possibility for a closed universe. We also carry out the null test of the cosmic curvature at \begin{document}$ 0<z<4.5 $\end{document} using the simulated gravitational wave standard sirens, CC+BAO, and redshift drift Hubble data. The result indicates that in the future, with the synergy of multiple high-quality observations, we can tightly constrain the spatial geometry or exclude the flat universe.