Chinese Physics C

2024-10 Contents

2024, 48(10): 1-2.

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Abstract:

CP violation of baryon decays with Nπ rescatterings

Jian-Peng Wang, Fu-Sheng Yu

2024, 48(10): 101001. doi: 10.1088/1674-1137/ad75f4

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Abstract:
There is a long-standing puzzle that the CP violation (CPV) in the baryon systems has never been well established in experiments, while the CPV of mesons have been observed by decades. In this paper, we propose that the CPV of baryon decays can be generated with the rescatterings of a nucleon and a pion into some final states, i.e.

\begin{document}$N\pi\to N\pi$\end{document}

or

\begin{document}$N\pi\pi$\end{document}

. Benefited by the fruitful data of

\begin{document}$N\pi$\end{document}

scatterings, we can model-independently analyse the strong phases of

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

-baryon decays using the partial wave amplitudes of

\begin{document}$N\pi$\end{document}

scatterings. Avoiding the most difficult problem of non-perturbative dynamics, it makes a great advantage to predict the CPV of baryon decays with a relatively reliable understanding of the decay dynamics. We study the processes of

\begin{document}$\Lambda_b^0\to (p\pi^+\pi^-)h^-$\end{document}

and

\begin{document}$(p\pi^0)h^-$\end{document}

with

\begin{document}$h=\pi$\end{document}

or

\begin{document}$K$\end{document}

. It is found that the global CPV of the above processes in the invariant mass regions of

\begin{document}$N\pi$\end{document}

scatterings are at the order of several percent. More importantly, the local CPV in some regions of the Dalitz plots can reach the order of 10%, or be even larger. Considering the predicted results and the experimental data samples, we strong suggest to measure the CPV of

\begin{document}$\Lambda_b^0\to (p\pi^+\pi^-)K^-$\end{document}

, which has a large possibility to achieve the first observation of CPV in the baryon system.

Searching for ⁷⁶Ge neutrinoless double beta decay with the CDEX-1B experiment

Bing-Tao Zhang, Jun-Zheng Wang, Li-Tao Yang, Qian Yue, Ke-Jun Kang, Yuan-Jing Li, Hai-Peng An, C. Greeshma, Jian-Ping Chang, Yun-Huan Chen, Jian-Ping Cheng, Wen-Han Dai, Zhi Deng, Chang-Hao Fang, Xin-Ping Geng, Hui Gong, Qiu-Ju Guo, Xu-Yuan Guo, Li He, Sheng-Ming He, Jin-Wei Hu, Han-Xiong Huang, Tu-Chen Huang, Hai-Tao Jia, Xi Jiang, S. Karmakar, Hao-Bin Li, Jian-Min Li, Jin Li, Qian-Yun Li, Ren-Ming-Jie Li, Xue-Qian Li, Yu-Lan Li, Yi-Fan Liang, Bin Liao, Fong-Kay Lin, Shin-Ted Lin, Jia-Xuan Liu, Shu-Kui Liu, Yan-Dong Liu, Yu Liu, Yuan-Yuan Liu, Zhong-Zhi Liu, Hao Ma, Yu-Cai Mao, Qi-Yuan Nie, Jin-Hua Ning, Hui Pan, Ning-Chun Qi, Jie Ren, Xi-Chao Ruan, Ze She, Manoj Kumar Singh, Tian-Xi Sun, Chang-Jian Tang, Wei-You Tang, Yang Tian, Guang-Fu Wang, Li Wang, Qing Wang, Yu-Feng Wang, Yun-Xiang Wang, Henry-Tsz-King Wong, Shi-Yong Wu, Yu-Cheng Wu, Hao-Yang Xing, Rui Xu, Yin Xu, Tao Xue, Yu-Lu Yan, Nan Yi, Chun-Xu Yu, Hai-Jun Yu, Jian-Feng Yue, Ming Zeng, Zhi Zeng, Feng-Shou Zhang, Lei Zhang, Zhen-Hua Zhang, Zhen-Yu

2024, 48(10): 103001. doi: 10.1088/1674-1137/ad597b

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Abstract:
We operated a p-type point contact high purity germanium (PPCGe) detector (CDEX-1B, 1.008 kg) in the China Jinping Underground Laboratory (CJPL) for 500.3 days to search for neutrinoless double beta (

\begin{document}$ {0\nu\beta\beta} $\end{document}

) decay of ⁷⁶Ge. A total of 504.3 kg

\begin{document}$ \cdot $\end{document}

day effective exposure data was accumulated. The anti-coincidence and the multi/single-site event (MSE/SSE) discrimination methods were used to suppress the background in the energy region of interest (ROI, 1989–2089 keV for this work) with a factor of 23. A background level of 0.33 counts/ (keV

\begin{document}$ \cdot $\end{document}

kg

\begin{document}$ \cdot $\end{document}

yr) was realized. The lower limit on the half life of ⁷⁶Ge

\begin{document}$ {0\nu\beta\beta} $\end{document}

decay was constrained as

\begin{document}$T_{1/2}^{0\nu}\ > \ {1.0}\times $\end{document}

\begin{document}$ 10^{23}\ \rm yr\ (90{\text{%}} \ C.L.) $\end{document}

, corresponding to the upper limits on the effective Majorana neutrino mass:

\begin{document}$ \langle m_{\beta\beta}\rangle < $\end{document}

3.2–7.5

\begin{document}$ \ \mathrm{eV} $\end{document}

.

Building imaginary-time thermal field theory with artificial neural networks

Tian Xu, Lingxiao Wang, Lianyi He, Kai Zhou, Yin Jiang

2024, 48(10): 103101. doi: 10.1088/1674-1137/ad5f80

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In this paper, we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks (ANNs). The actions are estimated by learning system configurations governed by the Boltzmann factor,

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

, at different temperatures within the imaginary time formalism of thermal field theory. Specifically, we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method. Continuous-mixture autoregressive networks (CANs) enable the construction of accurate effective actions with tractable probability density estimation. Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles. This capability is especially valuable for detailed exploration of phase diagrams.

Searches for multi-Z boson productions and anomalous gauge boson couplings at a muon collider

Ruobing Jiang, Chuqiao Jiang, Alim Ruzi, Tianyi Yang, Yong Ban, Qiang Li

2024, 48(10): 103102. doi: 10.1088/1674-1137/ad5661

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Abstract:
Multi-boson productions can be exploited as novel probes either for standard model precision tests or new physics searches, and have become a popular research topic in ongoing LHC experiments and future collider studies, including those for electron–positron and muon–muon colliders. In this study, we focus on two examples, i.e.,

\begin{document}$ {\text{Z}} {\text{Z}} {\text{Z}} $\end{document}

direct productions through

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

annihilation at a

\begin{document}$ 1\, {\text{TeV}} $\end{document}

muon collider, and

\begin{document}$ {\text{Z}} {\text{Z}} $\end{document}

productions through vector boson scattering (VBS) at a

\begin{document}$ 10\, {\text{TeV}} $\end{document}

muon collider, with an integrated luminosity of

\begin{document}$10\; \text{ab}^{-1}$\end{document}

. Various channels are considered, including

\begin{document}$ {\text{Z}} {\text{Z}} {\text{Z}} \rightarrow 4\ell2\nu $\end{document}

and

\begin{document}$ {\text{Z}} {\text{Z}} {\text{Z}} \rightarrow 4\ell $\end{document}

+2jets. The expected significance on these multi-Z boson production processes is reported based on a detailed Monte Carlo study and signal background analysis. Sensitivities on anomalous gauge boson couplings are also presented.

Ground states and first radial excitations of vector tetraquark states with explicit P-waves via QCD sum rules

Zhi-Gang Wang

2024, 48(10): 103103. doi: 10.1088/1674-1137/ad5ae5

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Abstract:
In this study, we chose the diquark-antidiquark type four-quark currents with an explicit P-wave between the diquark and antidiquark pairs to study the ground states and first radial excitations of the hidden-charm tetraquark states with quantum numbers

\begin{document}$J^{PC}=1^{--}$\end{document}

. We also obtained the lowest vector tetraquark masses and made possible assignments of the existing

\begin{document}$Y$\end{document}

states. There indeed exists a hidden-charm tetraquark state with

\begin{document}$J^{PC}=1^{--}$\end{document}

at an energy of approximately 4.75 GeV as the first radial excitation that accounts for the BESIII data.

B_c meson and its scalar cousin with QCD sum rules

Zhi-Gang Wang

2024, 48(10): 103104. doi: 10.1088/1674-1137/ad5a71

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Abstract:
In this study, we use the optical theorem to calculate the next-to-leading order corrections to the QCD spectral densities directly in the QCD sum rules for the pseudoscalar and scalar B_c mesons. We use experimental data for guidance to perform an updated analysis. We obtain the masses and, in particular, decay constants, which are the fundamental input parameters in high energy physics. Ultimately, we obtain the pure leptonic decay widths, which can be compared with experimental data in the future.

Testing Bell inequality through ${\boldsymbol h{\bf\rightarrow}\boldsymbol\tau\boldsymbol\tau }$ at CEPC

Kai Ma, Tong Li

2024, 48(10): 103105. doi: 10.1088/1674-1137/ad62d8

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The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future

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

colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through

\begin{document}$ h{\rightarrow} \tau\tau $\end{document}

at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we consider the detector effects of CEPC including uncertainties for tracks and jets from Z boson in the production of

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

. Necessary reconstruction approaches are described to measure quantum entanglement between

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

and

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

. Finally, we show the sensitivity of CEPC to Bell inequality violation for the two methods.

Probing inelastic signatures of dark matter detection via polarized nucleus

Zai Yun, Junwei Sun, Bin Zhu, Xuewen Liu

2024, 48(10): 103106. doi: 10.1088/1674-1137/ad6416

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We investigate the inelastic signatures of dark matter-nucleus interactions, explicitly focusing on the ramifications of polarization, dark matter splitting, and the Migdal effect. Direct detection experiments, crucial for testing the existence of dark matter, encounter formidable obstacles, such as indomitable neutrino backgrounds and elusive determination of dark matter spin. To overcome these challenges, we explore the potential of polarized-target dark matter scattering, examining the impact of nonvanishing mass splitting, and the role of the Migdal effect in detecting dark matter. Our analysis demonstrates the valuable utility of the polarized triple-differential event rate as an effective tool for examining inelastic dark matter. It enables us to investigate angular and energy dependencies, providing valuable insights into the scattering process.

Effects of family non-universal Z ′ model in angular observables of ${\boldsymbol B {\bf\to} (\boldsymbol\rho, {\boldsymbol a}_{\bf 1})\boldsymbol\mu^+\boldsymbol\mu^- }$ decays

Nimra Farooq, Marwah Zaki, M. Ali Paracha, Faisal Munir Bhutta

2024, 48(10): 103107. doi: 10.1088/1674-1137/ad5e65

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We present the angular distribution of the four-fold

\begin{document}$ B\to\rho (\to\pi\pi)\mu^{+}\mu^{-} $\end{document}

and

\begin{document}$ B\to a_{1}(\to\rho_{\parallel, \perp}\pi)\mu^{+}\mu^{-} $\end{document}

decays in the Standard Model and family non-universal

\begin{document}$ Z^{\prime} $\end{document}

model. At the quark level, these decays are governed by the

\begin{document}$ b\to d\mu^{+}\mu^{-} $\end{document}

transition. Along with different angular observables, we provide predictions of differential branching ratios, forward-backward asymmetry, and longitudinal polarization fractions of

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

and

\begin{document}$ a_{1} $\end{document}

mesons. Our analysis shows that the signatures of the family non-universal

\begin{document}$ Z^{\prime} $\end{document}

model are more distinct in the observables associated with the

\begin{document}$ B\to\rho(\to\pi\pi)\mu^{+}\mu^{-} $\end{document}

decay than in those associated with the

\begin{document}$ B\to a_{1}(\to\rho_{\parallel, \perp}\pi)\mu^{+}\mu^{-} $\end{document}

decay. Future measurements of the predicted angular observables, both at current and future high energy colliders, will provide useful complementary data required to clarify the structure of the family non-universal

\begin{document}$ Z^{\prime} $\end{document}

model in

\begin{document}$ |\Delta b| $\end{document}

=

\begin{document}$ |\Delta d|=1 $\end{document}

processes.

Radiative leptonic decay of heavy quarkonia

Junle Pei, Xinchou Lou, Yaquan Fang, Jinfei Wu, Manqi Ruan

2024, 48(10): 103108. doi: 10.1088/1674-1137/ad6552

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In this study, the properties of heavy quarkonia X are examined by treating them as bound states of Q and

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

at the leading-order level within the non-relativistic quantum chromodynamics (NRQCD) framework, where Q represents either a charm or bottom quark. The branching ratios for the radiative leptonic decays

\begin{document}$ X\rightarrow \gamma l^{+} l^{-} $\end{document}

are revisited, and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of X. Furthermore, we apply Lorentz transformations from the rest frame of X to the center-of-mass frame of

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

to establish the connection between the widths

\begin{document}$ {\Gamma_{X \rightarrow \gamma l^{+} l^{-}}} $\end{document}

and

\begin{document}$ {\Gamma_{X \rightarrow l^{+} l^{-}}} $\end{document}

. The comparison of the connection to those documented in literature (divided by

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

) for various X states, such as

\begin{document}$ J/\Psi $\end{document}

,

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

,

\begin{document}$ \Upsilon(1S) $\end{document}

, and

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

, shows relative differences typically around or below 10%, comparable to the next-to-leading order corrections of

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

and

\begin{document}$ O(v^4) $\end{document}

. However, we observe a significant disparity in the ratio between

\begin{document}$ {\Gamma_{\Psi(2S) \to \gamma \tau^+ \tau^-}} $\end{document}

and

\begin{document}$ {\Gamma_{\Psi(2S) \to \tau^+ \tau^-}} $\end{document}

, with our prediction being four times larger than those in literature. The outcomes derived from this study have practical implications in describing the quantum electrodynamics radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and searches for new physics.

Chromomagnetic dipole moments of light quarks in the bestest little Higgs model

T. Cisneros-Pérez, E. Cruz-Albaro, A. Y. Ojeda-Castañeda, S. E. Solís-Núñez

2024, 48(10): 103109. doi: 10.1088/1674-1137/ad62d9

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In this study, we investigated the anomalous Chromomagnetic Dipole Moment (CMDM), denoted as

\begin{document}$\hat{\mu}_{q}^{\rm BLHM}$\end{document}

, of light quarks

\begin{document}$q=(u, c, d, s, b)$\end{document}

within the framework of the Bestest Little Higgs Model (BLHM) as an extension of the Standard Model (SM). Our investigation encompassed novel interactions among the light quarks, heavy quark B, and heavy bosons

\begin{document}$(W^{\prime\pm}, H^{\pm}, \phi^{\pm}, \eta^{\pm})$\end{document}

, incorporating the extended Cabibbo-Kobayashi-Maskawa (CKM) matrix characteristic of the BLHM. We thoroughly explored the permissible parameter space, yielding a spectrum of CMDM values ranging from

\begin{document}$ 10^{-10} $\end{document}

to

\begin{document}$ 10^{-3} $\end{document}

.

Masses and decays of triply-heavy pentaquarks

Chang-Le Liu, Wen-Xuan Zhang, Duo-Jie Jia

2024, 48(10): 103110. doi: 10.1088/1674-1137/ad595a

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In this study, we analyzed masses and decays of triply-heavy pentaquarks

\begin{document}$QQQn\bar{n}~(Q=b,c)$\end{document}

in the unified MIT bag model. We construct the color-spin wave functions of the triply-heavy pentaquarks and use the numerical variational method to compute all the ground-state masses of these systems. By excluding the scattering states in configuration spsce, we computed the decay width ratios of each decay channel relative to the maximum width for the compact pentaquark states, obtaining the main decay modes of the triply-heavy pentaquark systems.

Estimating the production of dark photons with η decay in high-energy collisions

Wei Kou, Xurong Chen

2024, 48(10): 103111. doi: 10.1088/1674-1137/ad6752

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We propose searching for dark photon signals in the decay channel of η mesons, specifically through the leptonic decay (

\begin{document}$A^\prime \to e^+e^-(\mu^+\mu^-)$\end{document}

) observable in photon-photon interactions during ultra-peripheral heavy-ion collisions. We estimate the total cross-section for dark photon production in ultra-peripheral PbPb collisions at current and future hadron colliders. Our findings support the potential for detecting dark photon signals at the LHC, High-Luminosity LHC, High-Energy LHC, and Future Circular Collider.

Cross section measurement for the ²³²Th(n, f ) reaction in the 4.50−5.40 MeV region using a time projection chamber

Haofan Bai, Han Yi, Yankun Sun, Yiwei Hu, Jie Liu, Zepeng Wu, Cong Xia, Wenkai Ren, Wentian Cao, Tieshuan Fan, Guohui Zhang, Ruirui Fan, Yang Li, Wei Jiang, Yonghao Chen, You Lv, Changjun Ning, Weihua Jia, Zhiyong Zhang, Haolei Chen, Zhen Chen, Maoyuan Zhao, Changqing Feng, Shubin Liu

2024, 48(10): 104001. doi: 10.1088/1674-1137/ad5ae6

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Accurate cross sections of neutron induced fission reactions are required in the design of advanced nuclear systems and the development of fission theory. Time projection chambers (TPCs), with their track reconstruction and particle identification capabilities, are considered the best detectors for high-precision fission cross section measurements. The TPC developed by the back-streaming white neutron source (Back-n) team of the China Spallation Neutron Source (CSNS) was used as the fission fragment detector in measurements. In this study, the cross sections of the ²³²Th(n, f) reaction at five neutron energies in the 4.50−5.40 MeV region were measured. The fission fragments and α particles were well identified using our TPC, which led to a higher detection efficiency of the fission fragments and smaller uncertainty of the measured cross sections. Ours is the first measurement of the ²³²Th(n, f) reaction using a TPC for the detection of fission fragments. With uncertainties less than 5%, our cross sections are consistent with the data in different evaluation libraries, including JENDL-4.0, ROSFOND-2010, CENDL-3.2, ENDF/B-VIII.0, and BROND-3.1, whose uncertainties can be reduced after future improvement of the measurement.

New measurement of the neutron-induced total cross-sections of ^natCr in a wide energy range on the Back-n at CSNS

Baoqian Li, Min Xiao, Yonghao Chen, Jieming Xue, Xinxiang Li, Han Yi, Pinjing Cheng, Rong Liu, Yiwei Yang, Zijie Han, Dajun Zhao, Haoqiang Wang, Jirong Zhao, Peng Luan, Jing Liu, Zijun Liu, Chaomin Chen, Wen Luo, Bo Zheng, Song Feng

2024, 48(10): 104002. doi: 10.1088/1674-1137/ad66c0

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The neutron total cross-section of

\begin{document}$ ^{\mathrm{nat}} $\end{document}

Cr plays a crucial role in new nuclear engineering design and fundamental science. A new measurement of the neutron-induced total cross-sections of

\begin{document}$ ^{\mathrm{nat}} $\end{document}

Cr was performed using the transmission method on the back-streaming white neutron beamline (Back-n) at the China Spallation Neutron Source (CSNS). The neutron energy was determined using the time-of-flight technique. The neutron total cross-sections of

\begin{document}$ ^{\mathrm{nat}} $\end{document}

Cr were obtained across a broad energy range (0.3 eV−20 MeV) in one experiment for the first time. The resulting effective total cross-sections were compared with the existing experimental data in different energy ranges, which revealed good agreement with the evaluated libraries. Theoretical calculation of the total cross-section in the energy range of 1.5 to 20 MeV was then conducted using TALYS-1.96 and compared with the present results. The measurement provides a high-quality total cross-section of

\begin{document}$ ^{\mathrm{nat}} $\end{document}

Cr, including detailed uncertainty data across a wide energy range, offering a valuable reference for nuclear data re-evaluation and nuclear engineering design.

Description of moment of inertia and the interplay between anti-pairing and pairing correlations in ²⁴⁴Pu and ²⁴⁸Cm

Anshul Dadwal, Xiao-Tao He

2024, 48(10): 104101. doi: 10.1088/1674-1137/ad57a6

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A variable moment of inertia (VMI) inspired interacting boson model (IBM), which includes many-body interactions and a perturbation possessing

\begin{document}$S O $\end{document}

(5) (or

\begin{document}$S U $\end{document}

(5)) symmetry, is used to investigate the rotational bands of the

\begin{document}$ A\sim 250 $\end{document}

mass region. A novel modification is introduced, extending the Arima coefficient to the third order. This study is dedicated to the quantitative analysis of evolving trends in intraband γ-transition energy as well as the kinematic and dynamic moments of inertia (MoIs) within the rotational bands of

\begin{document}$ ^{244} $\end{document}

Pu and

\begin{document}$ ^{248} $\end{document}

Cm. The computed outcomes exhibit an exceptional degree of agreement with experimental observations across various conditions. The significance of including a higher-order Arima coefficient is further examined by contrasting it with the previously proposed model. The calculated results demonstrate the significance of both the anti-pairing and pairing effects in the evolution of the dynamic MoI. Additionally, these insights reveal the importance of a newly introduced parameter in accurately depicting complex nuclear behaviors, such as back-bending, up-bending, and downturn in the MoI.

Collective flow and fluid behavior in p/d/³He+Au collisions at ${ \sqrt{\boldsymbol s_{\boldsymbol NN}} \bf = 200}$ GeV

Zeming Wu, Baochi Fu, Shujun Zhao, Runsheng Liu, Huichao Song

2024, 48(10): 104102. doi: 10.1088/1674-1137/ad5ae8

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By varying the intrinsic initial geometry, p/d/³He+Au collisions at the Relativistic Heavy Ion Collider (RHIC) provide a unique opportunity to understand the collective behavior and probe possible sub-nucleon fluctuations in small systems. In this study, we employed the hybrid model

\begin{document}$ {\mathrm{iEBE-VISHNU}}$\end{document}

under TRENTo initial conditions to study the collective flow and fluid behavior in p/d/³He+Au collisions. With fine-tuned parameters,

\begin{document}$ {\mathrm{iEBE-VISHNU}}$\end{document}

can describe the

\begin{document}$ v_2(p_T) $\end{document}

and

\begin{document}$ v_3(p_T) $\end{document}

data from the PHENIX and STAR collaborations. However, for certain parameter sets with initial sub-nucleon fluctuations, the hydrodynamic simulations already go beyond their limits with an average Knudsen number

\begin{document}$ \langle K_n \rangle $\end{document}

clearly larger than unity. Our calculations demonstrate that, for a meaningful evaluation of the fluid behavior in small systems, model simulations must also pay attention to the validity range of hydrodynamics.

Angular distribution of products in multinucleon transfer reactions

Xian-Kai Le, Kuan Fan, Feng-Zhu Xing, Shu-Qing Guo, Nan Wang

2024, 48(10): 104103. doi: 10.1088/1674-1137/ad5e66

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Abstract:
A method based on the dinuclear system (DNS) is proposed to describe the angular distribution of products in multinucleon transfer (MNT) reactions. By considering fluctuation effects, the angular distributions of reactions involving ¹³⁶Xe+²⁰⁸Pb, ¹³⁶Xe+²⁰⁹Bi, ⁸⁶Kr+¹⁶⁶Er,⁸⁴Kr+²⁰⁹Bi, and ⁸⁴Kr+²⁰⁸Pb are examined, demonstrating good agreement with experimental data. Moreover, the double differential cross-sections (

\begin{document}${\rm d}{\sigma }^{2}/{{\rm d}l}_{i}{\rm d}\mathrm{\Theta }$\end{document}

and

\begin{document}${\rm d}{\sigma }^{2}/{\rm d}Z{\rm d}\mathrm{\Theta }$\end{document}

) of reactions ¹³⁶Xe+²⁰⁸Pb and ¹³⁶Xe+²⁰⁹Bi are analyzed to explore the mechanism of angular distribution in MNT reactions. Additionally, the optimal angles for detecting N=126 isotopes are determined via an analysis on the influence of proton and neutron numbers of the projectiles on the angular distribution of the N=126 isotopic line. The results of this study can provide valuable insights for experimental detection.

High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions

Ayushi Awasthi, Arushi Sharma, Ishwar Kant, O. S. K. S. Sastri

2024, 48(10): 104104. doi: 10.1088/1674-1137/ad5d63

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Abstract:
The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference. The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^th order Runge-kutta method. We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input. Leveraging a machine learning-based genetic algorithm, we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts. Our approach yields inverse potentials for both single and multi-channel scattering, achieving convergence to a mean-squared error

\begin{document}$ \leq 10^{-3} $\end{document}

. The resulting scattering lengths "

\begin{document}$ a_0 $\end{document}

" and effective ranges "r" for

\begin{document}$ ^3S_1 $\end{document}

and

\begin{document}$ ^1S_0 $\end{document}

states, expressed as [

\begin{document}$ a_0 $\end{document}

, r], are found to be [5.445(5.424), 1.770(1.760)]

\begin{document}$\rm fm$\end{document}

and [–23.741(–23.749), 2.63(2.81)]

\begin{document}$\rm fm$\end{document}

, respectively; these values are in excellent agreement with experimental ones. Furthermore, the calculated total scattering cross-sections are highly consistent with their experimental counterparts, having a percentage error of less than 1%. This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

Wei Zhang, Jin-Ke Huang, Ting-Ting Sun, Jing Peng, Shuang-Quan Zhang

2024, 48(10): 104105. doi: 10.1088/1674-1137/ad62dd

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The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are examined using the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic-like evolution for the ground state shapes is shown with respect to the neutron number, i.e., spherical shapes at shell closures

\begin{document}$ N= $\end{document}

126, 184, 258, and prolate dominated shapes between them. Analogous to the shape evolution, the inner fission barriers also exhibit a periodic-like behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect on the inner fission barrier is evaluated using triaxial relativistic mean field calculations combined with a simple BCS method for pairing. When the triaxial correction is included, the inner barrier heights show good consistency with available empirical data. Additionally, the evolution from the proton to the neutron drip line aligns with results from the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus

\begin{document}$ ^{318} $\end{document}

U which may play a role of fission recycling in astrophysical r-process nucleosynthesis.

Anisotropic pressure effect on central EOS of PSR J0740+6620 in the light of dimensionless TOV equation

Zhihao Yang, Dehua Wen

2024, 48(10): 104106. doi: 10.1088/1674-1137/ad62d7

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It is generally agreed upon that the pressure inside a neutron star is isotropic. However, a strong magnetic field or superfluidity suggests that the pressure anisotropy may be a more realistic model. We derived the dimensionless TOV equation for anisotropic neutron stars based on two popular models, namely, the BL and H models, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass

\begin{document}$M_{\rm max}$\end{document}

and its corresponding radius

\begin{document}$R_{M\rm max}$\end{document}

can also be expressed linearly by a combination of radial central pressure

\begin{document}$p_{\rm rc}$\end{document}

and central energy density

\begin{document}$ \varepsilon_{c} $\end{document}

, which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of

\begin{document}$\lambda_{\rm BL}$\end{document}

(

\begin{document}$ \lambda_{H} $\end{document}

), which controls the magnitude of the difference between the transverse pressure and radial pressure. Combining with observational data of PSR J0740+6620 and comparing to the extracted EOS based on an isotropic neutron star, it is shown that in the BL model, for

\begin{document}$\lambda_{\rm BL}$\end{document}

= 0.4, the extracted central energy density

\begin{document}$ \varepsilon_{c} $\end{document}

changed from 546 − 1056 MeV/fm³ to 510 − 1005 MeV/fm³, and the extracted radial central pressure

\begin{document}$p_{\rm rc}$\end{document}

changed from 87 − 310 MeV/fm³ to 76 − 271 MeV/fm³. For

\begin{document}$\lambda_{\rm BL}$\end{document}

= 2, the extracted

\begin{document}$ \varepsilon_{c} $\end{document}

and

\begin{document}$p_{\rm rc}$\end{document}

changed to 412 − 822 MeV/fm³ and 50 − 165 MeV/fm³, respectively. In the H model, for

\begin{document}$ \lambda_{H} $\end{document}

= 0.4, the extracted

\begin{document}$ \varepsilon_{c} $\end{document}

changed to 626 − 1164 MeV/fm³, and the extracted

\begin{document}$p_{\rm rc}$\end{document}

changed to 104 − 409 MeV/fm³. For

\begin{document}$ \lambda_{H} $\end{document}

= 2, the extracted

\begin{document}$ \varepsilon_{c} $\end{document}

decreased to 894 − 995 MeV/fm³, and the extracted

\begin{document}$p_{\rm rc}$\end{document}

changed to 220 − 301 MeV/fm³.

Dependence of thermodynamic quantities at freeze-out on pseudorapidity and collision energy in p-p collisions at LHC energies

Murad Badshah, Yahia A.H. Obaidat, Haifa I. Alrebdi, M. Waqas, Muhammad Ajaz, Refka Ghodhbani

2024, 48(10): 104107. doi: 10.1088/1674-1137/ad62da

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Abstract:
The transverse momentum distributions of charged hadrons produced in proton-proton collisions at center-of-mass energies (

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

) of 0.9 TeV and 2.36 TeV, as measured by the CMS detector at the Large Hadron Collider (LHC), have been analyzed within various pseudorapidity classes utilizing the thermodynamically consistent Tsallis distribution. The fitting procedure resulted in the key parameters, namely, effective temperature (T), non-extensivity parameter (q), and kinetic freezeout volume (V). Additionally, the mean transverse momentum (

\begin{document}$ \langle p_T\rangle $\end{document}

) and initial temperature (T_i) of the particle source are determined through the fit function and string percolation method, respectively. An alternative method is employed to calculate the kinetic freezeout temperature (

\begin{document}$ T_0 $\end{document}

) and transverse flow velocity (

\begin{document}$ \beta_T $\end{document}

) from T. Furthermore, thermodynamic quantities at the freezeout, including energy density (ε), particle density (n), entropy density (s), pressure (P), and squared speed of sound (

\begin{document}${C_s}^2$\end{document}

), are computed using the extracted T and q. It is also observed that, with a decrease in pseudorapidity, all thermodynamic quantities except V and q increase. This trend is attributed to greater energy transfer along the mid pseudorapidity. q increases towards higher values of pseudorapidity, indicating that particles close to the beam axis are far from equilibrium. Meanwhile, V remains nearly independent of pseudorapidity. The excitation function of these parameters (q) shows a direct (inverse) correlation with collision energy. The ε, n, s, and P show a strong dependence on collision energies at low pseudorapidities. Explicit verification of the thermodynamic inequality

\begin{document}$\varepsilon \geqslant 3 P$\end{document}

suggests the formation of a highly dense droplet-like Quark-Gluon Plasma (QGP). Additionally, the inequality

\begin{document}$T_i > T > T_0$\end{document}

is explicitly confirmed, aligning with the evolution of the produced fireball.

A simple model for two-proton radioactivity

Jie-Dong Jiang, Xiao Liu, Dong-Meng Zhang, Ming Li, Xi-Jun Wu, Xiao-Hua Li

2024, 48(10): 104108. doi: 10.1088/1674-1137/ad6417

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Abstract:
In this work, considering the preformation factor of the emitted two protons in parent nucleus

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

and the effect of the parent nucleus deformation, based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition, we improve a simple phenomenological model proposed by Bayrak [J. Phys. G: 47, 025102 (2020)] to systematically study

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

radioactivity half-lives. This model contains two adjustable parameters

\begin{document}$ V_0 $\end{document}

and

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

, which are related to the depth of nuclear potential and effect of deformation. The calculated results show that this model can effectively reproduce the experimental data with a corresponding root-mean-square (RMS) standard deviation of σ = 0.683. For comparison, we include the Gamow-like model (GLM) proposed by Liu et al. [Chin. Phys. C 45, 044110 (2021)], generalized liquid drop model (GLDM) proposed by Cui et al. [Phys. Rev. C 101, 014301 (2020)], effective liquid drop model (ELDM) proposed by M. Gonalves et al. [Phys. Lett. B 774, 14 (2017)], two-potential approach with Skyrme-Hartree-Fock (TPASHF) proposed by Pan et al. [Chin. Phys. C 45, 124104 (2021)], phenomenological model with a screened electrostatic barrier (SEB) propoesed by Zou et al. [Chin. Phys. C 45, 104101 (2021)], unified fission model (UFM) proposed by Xing et al. [Chin. Phys. C 45, 124105 (2021)], Coulomb and proximity potential model for deformed nuclei (CPPMDN) proposed by Santhosh [Phys. Rev. C 104, 064613 (2021)], two-parameter empirical formula proposed by Liu et al. [Chin. Phys. C 45, 024108 (2021)], and four-parameter empirical formula proposed by Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)]. In addition, we use this model to predict the

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

radioactive half-lives of some possible potential nuclei whose

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

radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020.

Generating Baikal-GVD high energy cascade-like neutrino events with a GEANT4-based simulation toolkit

Zike Wang, A.D. Avrorin, Zhen Cao, Mingjun Chen, Peiyuan Chu, Zh.-A.M. Dzhilkibaev, Bo Gao, Tianqi Huang, Jiali Liu, Ying Qi, Xiaohao You, D.N. Zaborov

2024, 48(10): 105001. doi: 10.1088/1674-1137/ad5bd4

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Abstract:
Using the GEANT4 and Cosmic Ray Monte Carlo (CRMC) software packages, we developed a new simulation toolkit for astrophysical neutrino telescopes. By configuring the Baikal-GVD detector and comparing the vertex position and direction of incident particles, as well as the channel-by-channel signals, to the events detected by Baikal-GVD, we successfully generated 13 high-energy cascade neutrino events with the toolkit. Our analysis revealed a systematic offset between the reconstructed shower position and the true interaction position, with a distance close to the scale of the shower maximum of −0.54±1.29 m. We achieved a good linear relationship between the photoelectron number of neutrino events obtained by simulation and the real data measured by Baikal-GVD. The simulation toolkit could serve as a reliable basis for studying the performance of astrophysical neutrino telescopes.

Newtonian limit of Einstein equation with a cosmological constant

Li-Fang Li, Zhoujian Cao, Xiaokai He

2024, 48(10): 105101. doi: 10.1088/1674-1137/ad5f81

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Abstract:
Traditionally, the cosmological constant has been viewed as dark energy that mimics matter with negative energy. Given that matter with negative energy provides a repulsive force, which fundamentally differs from typical gravitational forces, it has been believed that the cosmological constant effectively contributes a repulsive force. However, it is important to note that the concept of gravitational force is valid only within the framework of Newtonian dynamics. In this study, we demonstrate that the traditional understanding of the gravitational force contributed by the cosmological constant is not entirely correct. Our approach involves investigating the Newtonian limit of the Einstein equation with a cosmological constant. The subtleties involved in this analysis are discussed in detail. Interestingly, we find that the effect of the cosmological constant on Newtonian gravity is an attractive force rather than a repulsive one for ordinary matter. As expected, this corrective force is negligibly small. However, our findings may offer a way to distinguish between dark energy and the cosmological constant, as one contributes a repulsive force while the other contributes an attractive force.

Inferring the spin distribution of binary black holes using deep learning

Li Tang, Xi-Long Fan

2024, 48(10): 105102. doi: 10.1088/1674-1137/ad62db

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Abstract:
The spin characteristics of black holes offer valuable insights into the evolutionary pathways of their progenitor stars. This is crucial for understanding the broader population properties of black holes. Traditional hierarchical Bayesian inference techniques employed to discern these properties often demand substantial time, and consensus regarding the spin distribution of binary black hole (BBH) systems remains elusive. In this study, leveraging observations from GWTC-3, we adopted a machine learning approach to infer the spin distribution of black holes within BBH systems. Specifically, we developed a deep neural network (DNN) and trained it using data generated from a Beta distribution. Our training strategy, involving the segregation of data into 10 bins, not only expedites model training but also enhances the versatility and adaptability of the DNN to accommodate the growing volume of gravitational wave observations. Utilizing Monte Carlo-bootstrap (MC-bootstrap) to generate observation-simulated samples, we derived spin distribution parameters:

\begin{document}$\alpha=1.3^{+0.25}_{-0.18},\;\beta=1.70^{+0.24}_{-0.29}$\end{document}

for the larger BH sample and

\begin{document}$\alpha=1.37^{+0.31}_{-0.20},\;\beta=1.63^{+0.30}_{-0.20}$\end{document}

for the smaller BH sample. Within our constraints, the distributions of component spin magnitudes suggest the likelihood of both black holes in the BBH merger possessing non-zero spin.

The ring-shaped shadow of a rotating naked singularity with a complete photon sphere

Mingzhi Wang, Guanghai Guo, Pengfei Yan, Songbai Chen, Jiliang Jing

2024, 48(10): 105103. doi: 10.1088/1674-1137/ad5660

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Abstract:
We investigate the shadows of the Konoplya-Zhidenko naked singularity. In the spacetime of the Konoplya-Zhidenko naked singularity, not only an unstable retrograde light ring (LR) but also an unstable prograde LR exists, leading to the formation of a complete photon sphere (PS). Due to the absence of an event horizon, a dark disc-shaped shadow does not appear; instead, a ring-shaped shadow is observed. The ring-shaped shadow appears as an infinite number of relativistic Einstein rings in the image of the naked singularity. For some parameter values, only the unstable retrograde LR exists, resulting in an incomplete unstable PS and thus giving rise to an arc-shaped shadow for the Konoplya-Zhidenko naked singularity. The shadow of the Konoplya-Zhidenko naked singularity gradually shifts to the right as the rotation parameter a increases and gradually becomes smaller as the deformation parameter

\begin{document}$ |\eta| $\end{document}

increases. Moreover, stable LRs and stable photon spherical orbits can exist in the Konoplya-Zhidenko naked singularity spacetime, but they have no effect on the image of the naked singularity. This study demonstrates that a rotating naked singularity can exhibit not only an arc-shaped shadow but also a ring-shaped shadow.

2024 Vol. 48, No. 10