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《中国物理C》（英文）编辑部

2024年10月30日

2021 Vol. 45, No. 5

column

PARTICLES AND FIELD
NUCLEAR PHYSIC
PARTICLE AND NUCLEAR ASTROPHYSICS AND COSMOLOGY

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PARTICLES AND FIELD

Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment

Yao Fu, Siqi Yang, Minghui Liu, Liang Han, Tie-Jiun Hou, Carl Schmidt, Chen Wang, C.-P. Yuan

2021, 45(5): 053001. doi: 10.1088/1674-1137/abe36d

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Abstract:
We investigate the parton distribution function (PDF) uncertainty in the measurement of the effective weak mixing angle

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

at the CERN Large Hadron Collider (LHC). The PDF-induced uncertainty is large in proton-proton collisions at the LHC due to the dilution effect. The measurement of the Drell-Yan forward-backward asymmetry (

\begin{document}$A_{\rm FB}$\end{document}

) at the LHC can be used to reduce the PDF uncertainty in the

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

measurement. However, when including the full mass range of lepton pairs in the

\begin{document}$A_{\rm FB}$\end{document}

data analysis, the correlation between the PDF updating procedure and the

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

extraction leads to a sizable bias in the obtained

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

value. From our studies, we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the Z-pole region, while most of the sensitivity in reducing the PDF uncertainty remains. Furthermore, the lepton charge asymmetry in the W boson events as a function of the rapidity of the charged leptons,

\begin{document}$A_\pm(\eta_\ell)$\end{document}

, is known to be another observable which can be used to reduce the PDF uncertainty in the

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

measurement. The constraint from

\begin{document}$A_\pm(\eta_\ell)$\end{document}

is complementary to that from

\begin{document}$A_{\rm FB}$\end{document}

, and thus no bias affects the

\begin{document}$\sin^2 \theta _{{\rm{eff}}}^{\ell}$\end{document}

extraction. The studies are performed using the error PDF Updating Method Package (ePump), which is based on Hessian updating methods. In this article, the CT14HERA2 PDF set is used as an example.

Simulation of neutron-tagged deep inelastic scattering at EicC

Gang Xie, Meng-Yang Li, Cheng-Dong Han, Rong Wang, Xurong Chen

2021, 45(5): 053002. doi: 10.1088/1674-1137/abe8cf

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Abstract:
Measuring the pionic structure function is of high interest, as it provides a new area for understanding the strong interaction among quarks and testing QCD predictions. To this end, we investigate the feasibility and expected impact of a possible experiment at EicC (Electron-ion collider in China). We show the simulation results on the statistical precision of an EicC measurement, based on the model of leading neutron tagged DIS process and the parton distribution functions of the pion from JAM18 global analysis. The simulation shows that at EicC, the kinematics cover the

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

range from 0.01 to 1, and the

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

range from 1 to 50 GeV

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

, within the acceptable statistical uncertainty. Assuming an integrated luminosity of 50 fb

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

, in the low-

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

region (

\begin{document}$<10$\end{document}

GeV

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

), the Monte Carlo data show that the suggested measurement in the whole

\begin{document}$x_{\rm{\pi}}$\end{document}

range reaches very high precision (

\begin{document}$<3$\end{document}

%). To perform such an experiment, only the addition of a far-forward neutron calorimeter is needed.

Feasibility study of CP violation in ${{{\mathit{\boldsymbol{\tau^-}}}} {\mathit{\boldsymbol{\rightarrow K_{S}}}\pi^{-} \nu_{\tau}}}$ decays at the Super Tau Charm Facility

Haoyu Sang, Xiaodong Shi, Xiaorong Zhou, Xianwei Kang, Jianbei Liu

2021, 45(5): 053003. doi: 10.1088/1674-1137/abeb07

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Abstract:
We report a feasibility study for violation in

\begin{document}$\tau^{-}\rightarrow K_{S}\pi^{-} \nu_{\tau}$\end{document}

decays at a Super Tau Charm Facility (STCF). With an expected luminosity of 1 ab

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

collected by STCF per year at a center-of-mass energy of 4.26 GeV, the statistical sensitivity for CP violation is determined to be of order

\begin{document}$9.7\times10^{-4}$\end{document}

by measuring the decay-rate difference between

\begin{document}$\tau^{+}\rightarrow K_{S}\pi^{+}\bar{\nu}_{\tau}$\end{document}

and

\begin{document}$\tau^{-}\rightarrow K_{S}\pi^{-} \nu_{\tau}$\end{document}

. The analysis is performed using a reliable fast simulation software package, which can describe the detector responses properly and vary the responses flexibly for further optimization. Moreover, the energy-dependent efficiencies for reconstructing

\begin{document}$\tau^{-}\rightarrow K_{S}\pi^{-} \nu_{\tau}$\end{document}

are presented. The expected CP sensitivity is proportional to

\begin{document}$1/\sqrt{\cal{L}}$\end{document}

in the energy region from 4.0 to 5.0 GeV. The sensitivity of CP violation is of order

\begin{document}$3.1\times10^{-4}$\end{document}

with 10 ab

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

integrated luminosity, which is equivalent to ten years' data taking in this energy region at STCF.

$ { \bar{\mathit{\boldsymbol{B}}}\to{ {X_s \gamma }}}$ in BLMSSM

Jian-Bin Chen, Meng Zhang, Li-Li Xing, Tai-Fu Feng, Shu-Min Zhao, Ke-Sheng Sun

2021, 45(5): 053101. doi: 10.1088/1674-1137/abe36b

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Applying the effective Lagrangian method, we study the flavor changing neutral current process

\begin{document}$b\to s\gamma$\end{document}

within the minimal supersymmetric extension of the Standard Model, where baryon and lepton numbers are local gauge symmetries. Constraints on the parameters are investigated numerically with the experimental data for the branching ratio of

\begin{document}$\bar{B}\to X_s\gamma$\end{document}

. Additionally, we present the corrections to direct CP-violation in

\begin{document}$\bar{B}\rightarrow X_s\gamma$\end{document}

and time-dependent CP-asymmetry in

\begin{document}$B\rightarrow K^*\gamma$\end{document}

. With appropriate assumptions on the parameters, we find the direct CP-violation

\begin{document}$A_{\rm CP}$\end{document}

is very small, while one-loop contributions to

\begin{document}$S_{K^*\gamma}$\end{document}

can be significant.

Categorization of two-loop Feynman diagrams in the $ {{\cal O}{\mathit{\boldsymbol{(\alpha^2)}}}} $ correction to $ {{\mathit{\boldsymbol{e^+}}}{{\mathit{\boldsymbol{e^-}}}} {\mathit{\boldsymbol{\rightarrow ZH}}}} $

Zhao Li, Yefan Wang, Quan-feng Wu

2021, 45(5): 053102. doi: 10.1088/1674-1137/abe84d

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The

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

process is the dominant process for the Higgs boson production at the future Higgs factory. In order to match the analysis on the Higgs properties with highly precise experiment data, it will be crucial to include the theoretical prediction to the full next-to-next-to-leading order electroweak effect in the production rate

\begin{document}$ \sigma(e^+e^-\rightarrow ZH) $\end{document}

. In this inspiring work, we categorize the two-loop Feynman diagrams of the

\begin{document}$ {\cal O}(\alpha^2) $\end{document}

correction to

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

into 6 categories according to relevant topological structures. Although 25377 diagrams contribute to the

\begin{document}$ {\cal O}(\alpha^2) $\end{document}

correction in total, the number of the most challenging diagrams with seven denominators is 2250, which contain only 312 non-planar diagrams with 155 independent types. This categorization could be a valuable reference for the complete calculation in future.

Properties of the P_c(4312) pentaquark and its bottom partner

K. Azizi, Y. Sarac, H. Sundu

2021, 45(5): 053103. doi: 10.1088/1674-1137/abe8ce

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We present an analysis of the newly observed pentaquark

\begin{document}$P_c(4312)^+$\end{document}

to shed light on its quantum numbers. To do that, the QCD sum rules approach is used. The measured mass of this particle is close to the

\begin{document}$\Sigma_c^{++}\bar{D}^-$\end{document}

threshold and has a small width, which supports the possibility of its being a molecular state. We consider an interpolating current in a molecular form and analyze both the positive and negative parity states with spin-

\begin{document}${1}/{2}$\end{document}

. We also consider the bottom counterpart of the state with similar molecular form. Our mass result for the charm pentaquark state supports that the quantum numbers of the observed state are consistent with

\begin{document}$J^P={1}/{2}^{-}$\end{document}

.

Phenomenological studies on ${{\bar{B}^0\rightarrow [K^-\pi^+]_{S/V}[\pi^+\pi^-]_{V/S} \rightarrow K^-\pi^+\pi^+\pi^-}}$ decay

Jing-Juan Qi, Zhen-Yang Wang, Zhu-Feng Zhang, Xin-Heng Guo

2021, 45(5): 053104. doi: 10.1088/1674-1137/abeb06

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Abstract:
Within the quasi-two-body decay model, we study the localized CP violation and branching fraction of the four-body decay

\begin{document}$\bar{B}^0\rightarrow [K^-\pi^+]_{S/V}[\pi^+\pi^-]_{V/S} \rightarrow K^-\pi^+\pi^-\pi^+$\end{document}

when the

\begin{document}$K^-\pi^+$\end{document}

and

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

pair invariant masses are

\begin{document}$0.35<m_{K^-\pi^+}<2.04 \; \mathrm{GeV}$\end{document}

and

\begin{document}$0<m_{\pi^-\pi^+}<1.06\; \mathrm{GeV}$\end{document}

, with the pairs being dominated by the

\begin{document}$\bar{K}^*_0(700)^0$\end{document}

,

\begin{document}$\bar{K}^*(892)^0$\end{document}

,

\begin{document}$\bar{K}^*(1410)^0$\end{document}

,

\begin{document}$\bar{K}^*_0(1430)$\end{document}

and

\begin{document}$\bar{K}^*(1680)^0$\end{document}

, and

\begin{document}$f_0(500)$\end{document}

,

\begin{document}$\rho^0(770)$\end{document}

,

\begin{document}$\omega(782)$\end{document}

and

\begin{document}$f_0(980)$\end{document}

resonances, respectively. When dealing with the dynamical functions of these resonances,

\begin{document}$f_0(500)$\end{document}

,

\begin{document}$\rho^0(770)$\end{document}

,

\begin{document}$f_0(980)$\end{document}

and

\begin{document}$\bar{K}^*_0(1430)$\end{document}

are modeled with the Bugg model, Gounaris-Sakurai function, Flatté formalism and LASS lineshape, respectively, while the others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters

\begin{document}$\rho_A\in[0,0.5]$\end{document}

and

\begin{document}$\phi_A\in[0,2\pi]$\end{document}

, our predicted results are

\begin{document}$\mathcal{A_{CP}}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in[-0.365,0.447]$\end{document}

and

\begin{document}$\mathcal{B}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in $\end{document}

\begin{document}$ [6.11,185.32]\times10^{-8}$\end{document}

, based on the hypothetical

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

structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the CP violating asymmetries and branching fractions of the two-body decays

\begin{document}$\bar{B}^0\rightarrow SV(VS)$\end{document}

and all the individual four-body decays

\begin{document}$\bar{B}^0\rightarrow SV(VS) \rightarrow K^-\pi^+\pi^-\pi^+$\end{document}

, respectively. Our theoretical results for the two-body decays

\begin{document}$\bar{B}^0\rightarrow \bar{K}^*(892)^0$\end{document}

\begin{document}$f_0(980)$\end{document}

,

\begin{document}$\bar{B}^0\rightarrow \bar{K}^*_0(1430)^0$\end{document}

\begin{document}$\omega(782)$\end{document}

,

\begin{document}$\bar{B}^0\rightarrow \bar{K}^*(892)^0f_0(980)$\end{document}

,

\begin{document}$\bar{B}^0\rightarrow $\end{document}

\begin{document}$ \bar{K}^*_0(1430)^0\rho$\end{document}

, and

\begin{document}$\bar{B}^0\rightarrow\bar{K}^*_0(1430)^0\omega$\end{document}

are consistent with the available experimental data, with the remaining predictions await testing in future high precision experiments.

Rescattering mechanism of weak decays of double-charm baryons

Jia-Jie Han, Hua-Yu Jiang, Wei Liu, Zhen-Jun Xiao, Fu-Sheng Yu

2021, 45(5): 053105. doi: 10.1088/1674-1137/abec68

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The doubly charmed baryon

\begin{document}$ \Xi_{cc}^{++} $\end{document}

was recently observed by LHCb via the decay processes of

\begin{document}$ \Xi_{cc}^{++}\to \Lambda_c^+ K^-\pi^+\pi^+ $\end{document}

and

\begin{document}$ \Xi_c^+\pi^+ $\end{document}

. These discovery channels were successfully predicted in a framework in which the short-distance contributions are calculated under the factorization hypothesis and the long-distance contributions are estimated using the rescattering mechanism for the final-state-interaction effects. In this paper, we illustrate the above framework in detail by systematic studies on the two-body baryonic decays

\begin{document}$ {\cal{B}}_{cc}\to{\cal{B}}_{c}P $\end{document}

involving the doubly charmed baryons

\begin{document}$ {\cal{B}}_{cc} = (\Xi_{cc}^{++} , \Xi_{cc}^+,\Omega_{cc}^+) $\end{document}

, the singly charmed baryons

\begin{document}$ {\cal{B}}_{c} = ({\cal{B}}_{\bar{3}}, {\cal{B}}_{6}) $\end{document}

and the light pseudoscalar mesons

\begin{document}$ P = (\pi,K,\eta_{1,8}) $\end{document}

.

NUCLEAR PHYSIC

Fusion reactions around the barrier for Be+²³⁸U

Bo Mei, Dimiter L. Balabanski, Wei Hua, Yu-Hu Zhang, Xiao-Hong Zhou, Cen-Xi Yuan, Jun Su

2021, 45(5): 054001. doi: 10.1088/1674-1137/abe36c

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Abstract:
Fusion-evaporation cross sections of

\begin{document}$^{238}$\end{document}

U(

\begin{document}$^{9}$\end{document}

Be, 5n)

\begin{document}$^{242}$\end{document}

Cm are measured over a wide energy range around the Coulomb barrier. These measured cross sections are compared with model calculations using two codes, namely HIVAP2 and KEWPIE2. HIVAP2 calculations overestimate the measured fusion-evaporation cross sections by a factor of approximately 3. In KEWPIE2 calculations, two approaches, namely the Wentzel-Kramers-Brillouin (WKB) approximation and the empirical barrier-distribution (EBD) method, are used for the capture probability; both of them properly describe the measured cross sections. Additionally, fusion cross sections of

\begin{document}$^{7,9}$\end{document}

Be+

\begin{document}$^{238}$\end{document}

U measured in two experiments are applied to constrain model calculations further through three codes, i.e., HIVAP2, KEWPIE2, and CCFULL. Parameters in these codes are also examined by comparison with measured fusion cross sections. All the comparisons indicate that the KEWPIE2 calculations using the WKB approximation agree well with the measured cross sections of both fusion reactions

\begin{document}$^{7,9}$\end{document}

Be+

\begin{document}$^{238}$\end{document}

U and the fusion-evaporation reaction

\begin{document}$^{238}$\end{document}

U(

\begin{document}$^{9}$\end{document}

Be, 5n)

\begin{document}$^{242}$\end{document}

Cm. Calculations using the fusion code CCFULL are also in good agreement with the measured fusion cross sections of

\begin{document}$^{7,9}$\end{document}

Be+

\begin{document}$^{238}$\end{document}

U.

The effect of hadronic scatterings on the measurement of vector meson spin alignments in heavy-ion collisions

Diyu Shen, Jinhui Chen, Zi-Wei Lin

2021, 45(5): 054002. doi: 10.1088/1674-1137/abe763

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Spin alignments of vector mesons and hyperons in relativistic heavy-ion collisions have been proposed as signals of global polarization. The STAR experiment first observed the

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

polarization. Recently, the ALICE collaboration measured the transverse momentum (

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

) and the collision centrality dependence of

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

, and

\begin{document}$\phi$\end{document}

spin alignments during Pb-Pb collisions at

\begin{document}$\sqrt {{s_{{\rm NN}}}}$\end{document}

= 2.76 TeV. A large signal is observed in the low

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

region of mid-central collisions for

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

, while the signal is much smaller for

\begin{document}$\phi$\end{document}

, and these have not been understood yet. Since vector mesons have different lifetimes and their decay products have different scattering cross sections, they suffer from different hadronic effects. In this paper, we study the effect of hadronic interactions on the spin alignment of

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

,

\begin{document}$\phi$\end{document}

, and

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

mesons in relativistic heavy-ion collisions with a multi-phase transport model. We find that hadronic scatterings lead to a deviation of the observed spin alignment matrix element

\begin{document}$\rho_{00}$\end{document}

away from the true value for

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

and

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

mesons (with a bigger effect on

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

) while the effect is negligible for the

\begin{document}$\phi$\end{document}

meson. The effect depends on the kinematic acceptance: the observed

\begin{document}$\rho_{00}$\end{document}

value is lower than the true value when the pseudorapidity (

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

) coverage is small, while there is little effect when the

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

coverage is large. Hence, this study provides valuable information to understand the vector meson spin alignment signals observed during the experiments.

Renormalizability of leading order covariant chiral nucleon-nucleon interaction

Chun-Xuan Wang, Li-Sheng Geng, Bingwei Long

2021, 45(5): 054101. doi: 10.1088/1674-1137/abe368

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Abstract:
In this work, we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering [Chin. Phys. C 42 (2018) 014103] at leading order. We show that unlike the Weinberg scheme, renormalizaion group invariance is satisfied in the

\begin{document}$^3P_{0}$\end{document}

channel. Another interesting feature is that the

\begin{document}$^1S_{0}$\end{document}

and

\begin{document}$^3P_{1}$\end{document}

channels are correlated. Fixing the relevant low energy constants by fitting to the

\begin{document}$^1S_{0}$\end{document}

phase shifts at

\begin{document}$T_\mathrm{lab.}=10$\end{document}

and 25 MeV with cutoff values

\begin{document}$\Lambda = 400-650$\end{document}

MeV, one can describe the

\begin{document}$^3P_{1}$\end{document}

phase shifts relatively well. In the limit of

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

, the

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

phase shifts become cutoff-independent, whereas the

\begin{document}$^3P_{1}$\end{document}

phase shifts do not. This is consistent with the Wigner bound and previous observations that the

\begin{document}$^{3}P_1$\end{document}

channel is best treated perturbatively. As for the

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

and

\begin{document}$^3S_{1}$\end{document}

-

\begin{document}$^3D_{1}$\end{document}

channels, renormalization group invariance is satisfied.

Production of bottomonium-like Z_b states in e-h and ultraperipheral h-h collisions

Xiao-Yun Wang, Wei Kou, Qing-Yong Lin, Ya-Ping Xie, Xurong Chen, Alexey Guskov

2021, 45(5): 054102. doi: 10.1088/1674-1137/abe3ec

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Abstract:
The photoproduction of the bottomonium-like states

\begin{document}$ Z_{b}(10610) $\end{document}

and

\begin{document}$ Z_{b}(10650) $\end{document}

via

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

scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of

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

states via the t-channel with

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

exchange. The numerical results show that the values of the total cross-sections of

\begin{document}$ Z_{b}(10610) $\end{document}

and

\begin{document}$ Z_{b}(10650) $\end{document}

can reach 0.09 nb and 0.02 nb, respectively, near the center-of-mass energy of 22 GeV. Experimental measurements and studies of the photoproduction of

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

states near the energy region around

\begin{document}$ W\simeq 22 $\end{document}

GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for

\begin{document}$ Z_{b}(10610) $\end{document}

production in electron-ion collisions (EIC) and ultraperipheral collisions (UPCs). The results show that a considerable number of

\begin{document}$ Z_{b}(10610) $\end{document}

events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for

\begin{document}$ \gamma p\rightarrow Z_{b}n $\end{document}

in

\begin{document}$ ep $\end{document}

and

\begin{document}$ pA $\end{document}

collisions via EICs and UPCs. The results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments in searching for bottomonium-like

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

states.

Nucleon-pair approximation with uncoupled representation

Y. Lei, Y. Lu, Y. M. Zhao

2021, 45(5): 054103. doi: 10.1088/1674-1137/abe3ed

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Abstract:
In this paper, we propose an approach to nucleon-pair approximation (NPA) with m-scheme bases, in which the collective nucleon pairs are represented in terms of antisymmetric matrices, and commutations between nucleon pairs are given using a matrix multiplication that avoids angular-momentum couplings and recouplings. Therefore the present approach significantly simplifies the NPA computation. Furthermore, it is formulated on the same footing with and without isospin.

Relative probabilities of breakup channels in reactions of ^6,7Li with ²⁰⁹Bi at energies around and above the Coulomb barrier

Yong-Jin Yao, Cheng-Jian Lin, Lei Yang, Nan-Ru Ma, Dong-Xi Wang, Gao-long Zhang, Guang-Xin Zhang, Hui-Ming Jia, Feng Yang, Fu-Peng Zhong, Pei-Wei Wen, Xiu-Bo Qin, Hong-Ming Zhao

2021, 45(5): 054104. doi: 10.1088/1674-1137/abe3ee

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Abstract:
Coincidence measurements of breakup fragments in reactions of

\begin{document}${^{6, 7}{\rm{Li}}}$\end{document}

with

\begin{document}${^{209}{\rm{Bi}}}$\end{document}

at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array. Through the Q values along with the relative energies of the breakup fragments, different breakup components (prompt breakups and delayed breakups) and different breakup modes (

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

,

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

,

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

, and

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

) are distinguished. A new breakup mode,

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

, is observed in

\begin{document}${^{6}{\rm{Li}}}$\end{document}

-induced reactions at energies above the Coulomb barrier. Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated. The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion, particularly for the above-barrier energies.

Systematic study of the Woods-Saxon potential parametersbetween heavy-ions

Lin Gan, Zhi-Hong Li, Hui-Bin Sun, Shi-Peng Hu, Er-Tao Li, Jian Zhong

2021, 45(5): 054105. doi: 10.1088/1674-1137/abe84f

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Abstract:
Experimental elastic scattering angular distributions of ¹¹B, ¹²C, and ¹⁶O + heavy-ions are used to study the Woods-Saxon potential parameters. Best fitted values of the diffuseness parameters are found for each system, and a linear relationship is expressed between the diffuseness parameters and

\begin{document}$A_1^{1/3}+A_2^{1/3}$\end{document}

. The correlation of the potential depth and radius parameters with

\begin{document}$A_1^{1/3}+A_2^{1/3}$\end{document}

is also revealed within the limitations of the diffuseness parameter formula. Because the incident energies of most of the analyzed reactions are below or around the Coulomb barrier, the energy dispersion relation between the real and imaginary potentials is considered in order to investigate the ratio between the imaginary and real potential well depths, resulting in an expression of

\begin{document}$W/V$\end{document}

. Within the limitation of the volume integrals calculated with the S

\begin{document}$\tilde{a}$\end{document}

o Paulo potential, parameterized formulas for the depth and radius parameters are obtained. The systematic Woods-Saxon potential parameters derived in the present work can reproduce not only the experimental data of elastic scattering angular distributions induced by ¹¹B, ¹²C, and ¹⁶O but also some elastic scattering induced by other heavy-ions.

Color-electric conductivity in a viscous quark-gluon plasma

Bing-feng Jiang, Shao-wu Shi, De-fu Hou, Jia-rong Li

2021, 45(5): 054106. doi: 10.1088/1674-1137/abe9a2

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Abstract:
Several different transport processes, such as heat, momentum, and charge transports, may occur simultaneously in a thermal plasma system. The corresponding transport coefficients are heat conductivity, shear viscosity, and electric conductivity. In the present study, we investigate the color-electric conductivity of the quark-gluon plasma (QGP) in the presence of shear viscosity, focusing on the connection between the charge transport and momentum transport. To achieve this goal, we solve the viscous chromohydrodynamic equations obtained from the QGP kinetic theory associated with the distribution function modified by shear viscosity. According to the solved color fluctuations of hydrodynamic quantities, we obtain the induced color current through which the color-electric conductivity is derived. Numerical analysis shows that the conductivity properties of the QGP are mainly demonstrated by the longitudinal part of the color-electric conductivity. Shear viscosity has an appreciable impact on real and imaginary parts of the color-electric conductivity in some frequency regions.

Proton-halo breakup dynamics for the breakup threshold in the ε₀ → 0 limit

B. Mukeru

2021, 45(5): 054107. doi: 10.1088/1674-1137/abe9a3

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Abstract:
Proton-halo breakup behavior in the

\begin{document}$ \varepsilon_0\to 0 $\end{document}

limit (where

\begin{document}$ \varepsilon_0 $\end{document}

is the ground-state binding energy) is studied around the Coulomb barrier in the

\begin{document}$ ^8{\rm{B}}+{}^{58}{\rm{Ni}} $\end{document}

reaction for the first time. For practical purposes, apart from the experimental

\begin{document}$ ^8{\rm{B}} $\end{document}

binding energy of 137 keV, three more arbitrarily chosen values (1, 0.1, 0.01 keV) are considered. It is first shown that the Coulomb barrier between the core and the proton prevents the

\begin{document}$ ^7{\rm{Be}}+p $\end{document}

system from reaching the state of an open proton-halo system, which, among other factors, would require the ground-state wave function to extend to infinity in the asymptotic region, as

\begin{document}$ \varepsilon_0\to 0 $\end{document}

. The elastic scattering cross section, which depends on the density of the ground-state wave function, is found to have a negligible dependence on the binding energy in this limit. The total, Coulomb and nuclear breakup cross sections are all reported to increase significantly from

\begin{document}$ \varepsilon_0 = 137 $\end{document}

to 1.0 keV, and converge to their maximum values as

\begin{document}$ \varepsilon_0\to 0 $\end{document}

. This increase is mainly understood as coming from a longer tail of the ground-state wave function for

\begin{document}$ \varepsilon_0\leqslant 1.0 $\end{document}

keV, compared to that for

\begin{document}$ \varepsilon_0 = 137 $\end{document}

keV. It is also found that the effect of the continuum-continuum couplings is to slightly delay the convergence of the breakup cross section. The analysis of the reaction cross section indicates a convergence of all the breakup observables as

\begin{document}$ \varepsilon_0\to 0 $\end{document}

. These results provide a better sense of the dependence of the breakup process on the breakup threshold.

The effects of pre-equilibrium emission and secondary decay on the determination of freeze-out volume at intermediate energies

Hui-Xiao Duan, Dong-Hai Zhang, Fan Zhang, Hai-Shun Wu

2021, 45(5): 054108. doi: 10.1088/1674-1137/abec39

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The effects of pre-equilibrium emission and secondary decay on the determination of the freeze-out volume are investigated using the isospin-dependent quantum molecular dynamics model accompanied by the statistical decay model GEMINI. Small-mass projectiles and large-mass targets with central collisions are studied at intermediate energies. It is revealed that the proton yields of pre-equilibrium emission are smaller than those of secondary decay. However, the determination of the freeze-out volume from the proton yields is more easily affected by pre-equilibrium emission. Moreover, the percentage of proton yields in the freeze-out stage is found to be approximately 50%.

Fission fragment mass yields of Th to Rf even-even nuclei

Krzysztof Pomorski, José M. Blanco, Pavel V. Kostryukov, Artur Dobrowolski, Bożena Nerlo-Pomorska, Michał Warda, Zhi-Gang Xiao, Yong-Jing Chen, Li-Le Liu, Jun-Long Tian, Xin-Yue Diao, Qiang-Hua Wu

2021, 45(5): 054109. doi: 10.1088/1674-1137/abec69

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Abstract:
Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.

PARTICLE AND NUCLEAR ASTROPHYSICS AND COSMOLOGY

Search for electron-antineutrinos associated with gravitational-wave events GW150914, GW151012, GW151226, GW170104, GW170608, GW170814, and GW170817 at Daya Bay

F. P. An, A. B. Balantekin, H. R. Band, M. Bishai, S. Blyth, G. F. Cao, J. Cao, J. F. Chang, Y. Chang, H. S. Chen, S. M. Chen, Y. Chen, Y. X. Chen, J. Cheng, Z. K. Cheng, J. J. Cherwinka, M. C. Chu, J. P. Cummings, O. Dalager, F. S. Deng, Y. Y. Ding, M. V. Diwan, T. Dohnal, J. Dove, M. Dvořák, D. A. Dwyer, J. P. Gallo, M. Gonchar, G. H. Gong, H. Gong, W. Q. Gu, J. Y. Guo, L. Guo, X. H. Guo, Y. H. Guo, Z. Guo, R. W. Hackenburg, S. Hans, M. He, K. M. Heeger, Y. K. Heng, A. Higuera, Y. K. Hor, Y. B. Hsiung, B. Z. Hu, J. R. Hu, T. Hu, Z. J. Hu, H. X. Huang, X. T. Huang, Y. B. Huang, P. Huber, D. E. Jaffe, K. L. Jen, X. L. Ji, X. P. Ji, R. A. Johnson, D. Jones, L. Kang, S. H. Kettell, S. Kohn, M. Kramer, T. J. Langford, J. Lee, J. H. C. Lee, R. T. Lei, R. Leitner, J. K. C. Leung, F. Li, J. J. Li, Q. J. Li, S. Li, S. C. Li, W. D. Li, X. N. Li, X. Q. Li, Y. F. Li, Z. B. Li, H. Liang, C. J. Lin, G. L. Lin, S. Lin, J. J. Ling, J. M. Link, L. Littenberg, B. R. Littlejohn, J. C. Liu, J. L. Liu, C. Lu, H. Q. Lu, J. S.

2021, 45(5): 055001. doi: 10.1088/1674-1137/abe84b

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The establishment of a possible connection between neutrino emission and gravitational-wave (GW) bursts is important to our understanding of the physical processes that occur when black holes or neutron stars merge. In the Daya Bay experiment, using the data collected from December 2011 to August 2017, a search was performed for electron-antineutrino signals that coincided with detected GW events, including GW150914, GW151012, GW151226, GW170104, GW170608, GW170814, and GW170817. We used three time windows of ±10, ±500, and ±1000 s relative to the occurrence of the GW events and a neutrino energy range of 1.8 to 100 MeV to search for correlated neutrino candidates. The detected electron-antineutrino candidates were consistent with the expected background rates for all the three time windows. Assuming monochromatic spectra, we found upper limits (90% confidence level) of the electron-antineutrino fluence of (1.13 − 2.44)×10¹¹ cm⁻² at 5 MeV to 8.0×10⁷ cm⁻² at 100 MeV for the three time windows. Under the assumption of a Fermi-Dirac spectrum, the upper limits were found to be (5.4 − 7.0)×10⁹ cm⁻² for the three time windows.

F. P. An, A. B. Balantekin, H. R. Band, M. Bishai, S. Blyth, G. F. Cao, J. Cao, J. F. Chang, Y. Chang, H. S. Chen, S. M. Chen, Y. Chen, Y. X. Chen, J. Cheng, Z. K. Cheng, J. J. Cherwinka, M. C. Chu, J. P. Cummings, O. Dalager, F. S. Deng, Y. Y. Ding, M. V. Diwan, T. Dohnal, J. Dove, M. Dvořák, D. A. Dwyer, J. P. Gallo, M. Gonchar, G. H. Gong, H. Gong, W. Q. Gu, J. Y. Guo, L. Guo, X. H. Guo, Y. H. Guo, Z. Guo, R. W. Hackenburg, S. Hans, M. He, K. M. Heeger, Y. K. Heng, A. Higuera, Y. K. Hor, Y. B. Hsiung, B. Z. Hu, J. R. Hu, T. Hu, Z. J. Hu, H. X. Huang, X. T. Huang, Y. B. Huang, P. Huber, D. E. Jaffe, K. L. Jen, X. L. Ji, X. P. Ji, R. A. Johnson, D. Jones, L. Kang, S. H. Kettell, S. Kohn, M. Kramer, T. J. Langford, J. Lee, J. H. C. Lee, R. T. Lei, R. Leitner, J. K. C. Leung, F. Li, J. J. Li, Q. J. Li, S. Li, S. C. Li, W. D. Li, X. N. Li, X. Q. Li, Y. F. Li, Z. B. Li, H. Liang, C. J. Lin, G. L. Lin, S. Lin, J. J. Ling, J. M. Link, L. Littenberg, B. R. Littlejohn, J. C. Liu, J. L. Liu, C. Lu, H. Q. Lu, J. S. Lu, K. B. Luk, X. B. Ma, X. Y. Ma, Y. Q. Ma, C. Marshall, D. A. Martinez Caicedo, K. T. McDonald, R. D. McKeown, Y. Meng, J. Napolitano, D. Naumov, E. Naumova, J. P. Ochoa-Ricoux, A. Olshevskiy, H. -R. Pan, J. Park, S. Patton, J. C. Peng, C. S. J. Pun, F. Z. Qi, M. Qi, X. Qian, N. Raper, J. Ren, C. Morales Reveco, R. Rosero, B. Roskovec, X. C. Ruan, H. Steiner, J. L. Sun, T. Tmej, K. Treskov, W. -H. Tse, C. E. Tull, B. Viren, V. Vorobel, C. H. Wang, J. Wang, M. Wang, N. Y. Wang, R. G. Wang, W. Wang, W. Wang, X. Wang, Y. Wang, Y. F. Wang, Z. Wang, Z. Wang, Z. M. Wang, H. Y. Wei, L. H. Wei, L. J. Wen, K. Whisnant, C. G. White, H. L. H. Wong, E. Worcester, D. R. Wu, F. L. Wu, Q. Wu, W. J. Wu, D. M. Xia, Z. Q. Xie, Z. Z. Xing, J. L. Xu, T. Xu, T. Xue, C. G. Yang, L. Yang, Y. Z. Yang, H. F. Yao, M. Ye, M. Yeh, B. L. Young, H. Z. Yu, Z. Y. Yu, B. B. Yue, S. Zeng, Y. Zeng, L. Zhan, C. Zhang, F. Y. Zhang, H. H. Zhang, J. W. Zhang, Q. M. Zhang, X. T. Zhang, Y. M. Zhang, Y. X. Zhang, Y. Y. Zhang, Z. J. Zhang, Z. P. Zhang, Z. Y. Zhang, J. Zhao, L. Zhou, H. L. Zhuang and J. H. Zou. Search For Electron-Antineutrinos Associated With Gravitational-Wave Events GW150914, GW151012, GW151226, GW170104, GW170608, GW170814, and GW170817 at Daya Bay[J]. Chinese Physics C. doi: 10.1088/1674-1137/abe84b.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Bing Tang

2021, 45(5): 055101. doi: 10.1088/1674-1137/abe369

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Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum J. Under the spatial perturbation, however, it is found that spatial chaos always occurs, independent of the perturbation amplitude.

Collisional Penrose process of 4D rotational Einstein-Gauss-Bonnet black holes

Yunlong Liu, Xiangdong Zhang

2021, 45(5): 055102. doi: 10.1088/1674-1137/abe36a

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The collisional Penrose process of massive spinning particles in a rotational Einstein-Gauss-Bonnet (EGB) black hole background is studied. By numerically solving the equations of motion for spinning particles, we find that the energy extraction efficiency increases monotonically with the decrease of the EGB coupling parameter

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

. Moreover, the efficiency

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

increases as the particle spin s grows. We also find that the energy extraction efficiency increases with the decrease of the EGB coupling parameter

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

. When the EGB coupling constant

\begin{document}$ \alpha=0$\end{document}

, our results reduce to the Kerr case, which has been investigated previously.

Bardeen black hole surrounded by perfect fluid dark matter

He-Xu Zhang, Yuan Chen, Tian-Chi Ma, Peng-Zhang He, Jian-Bo Deng

2021, 45(5): 055103. doi: 10.1088/1674-1137/abe84c

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We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter

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

as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius

\begin{document}$r_{+}^{C}$\end{document}

where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range

\begin{document}$0<r_{+}<r_{+}^{C}$\end{document}

. In addition, the critical radius

\begin{document}$r_{+}^{C}$\end{document}

increases with the magnetic charge g and decreases with the dark matter parameter

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

. Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter

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

, in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.

Sound velocity in dense stellar matter with strangeness and compact stars

Chengjun Xia, Zhenyu Zhu, Xia Zhou, Ang Li

2021, 45(5): 055104. doi: 10.1088/1674-1137/abea0d

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The phase state of dense matter in the intermediate density range (

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

1-10 times the nuclear saturation density) is both intriguing and unclear and can have important observable effects in the present gravitational wave era of neutron stars. As matter density increases in compact stars, the sound velocity is expected to approach the conformal limit (

\begin{document}$c_s/c=1/\sqrt{3}$\end{document}

) at high densities and should also fulfill the causality limit (

\begin{document}$c_s/c<1$\end{document}

). However, its detailed behavior remains a prominent topic of debate. It was suggested that the sound velocity of dense matter could be an important indicator of a deconfinement phase transition, where a particular shape might be expected for its density dependence. In this work, we explore the general properties of the sound velocity and the adiabatic index of dense matter in hybrid stars as well as in neutron stars and quark stars. Various conditions are employed for the hadron-quark phase transition with varying interface tension. We find that the expected behavior of the sound velocity can also be achieved by the nonperturbative properties of the quark phase, in addition to a deconfinement phase transition. Moreover, it leads to a more compact star with a similar mass. We then propose a new class of quark star equation of states, which can be tested by future high-precision radius measurements of pulsar-like objects.

Validity of thermodynamic laws and weak cosmic censorship for AdS black holes and black holes in a cavity

Peng Wang, Houwen Wu, Shuxuan Ying

2021, 45(5): 055105. doi: 10.1088/1674-1137/abeb5e

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By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and the weak cosmic censorship conjecture (WCCC) with two types of boundary conditions: the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in an asymptotically flat space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and near-extremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and the WCCC is satisfied/violated for the extremal/near-extremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.

Chinese Physics C

IF: 3.6

Monthly founded in 1977

Sponsored by:

ISSN 1674-1137 CN 11-5641/O4

Original research articles, Ietters and reviews Covering theory and experiments in the fieids of

Particle physics
Nuclear physics
Particle and nuclear astrophysics
Cosmology

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