Chinese Physics C

Neutrino masses, leptonic flavor mixing, and muon (g−2) in the seesaw model with the $ {\boldsymbol U(1)^{}_{\boldsymbol L^{}_\mu - \boldsymbol L^{}_\tau} } $ gauge symmetry

Shun Zhou

2022, 46(1): 011001. doi: 10.1088/1674-1137/ac2a25

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Abstract:
The latest measurements of the anomalous muon magnetic moment

\begin{document}$a^{}_\mu \equiv (g^{}_\mu - 2)/2$\end{document}

show a

\begin{document}$4.2\sigma$\end{document}

discrepancy between the theoretical prediction of the Standard Model and the experimental observations. To account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged

\begin{document}$L^{}_\mu - L^{}_\tau$\end{document}

symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry

\begin{document}${U}(1)^{}_{L^{}_\mu - L^{}_\tau}$\end{document}

and its spontaneous breaking are crucial not only for explaining the muon

\begin{document}$(g - 2)$\end{document}

result but also for generating the neutrino masses and leptonic flavor mixing. Various phenomenological implications and experimental constraints on the model parameters are also discussed.

First lattice QCD calculation of semileptonic decays of charmed-strange baryons Ξ_c

Qi-An Zhang, Jun Hua, Fei Huang, Renbo Li, Yuanyuan Li, Caidian Lü, Peng Sun, Wei Sun, Wei Wang, Yibo Yang

2022, 46(1): 011002. doi: 10.1088/1674-1137/ac2b12

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Abstract:
While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics, it has been constantly scrutinized for over four decades. Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation. As the lowest charm-strange baryons with three different flavors,

\begin{document}$\Xi_c$\end{document}

baryons (composed of

\begin{document}$csu$\end{document}

or

\begin{document}$csd$\end{document}

) have been extensively studied in experiments. In this study, we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings,

\begin{document}$a=(0.108,\; 0.080\;{\rm{fm}})$\end{document}

. Then, we present the first ab-initio lattice QCD calculation of the

\begin{document}$\Xi_c\to \Xi$\end{document}

form factors. Our theoretical results for the

\begin{document}$\Xi_{c}\to \Xi \ell^+\nu_{\ell}$\end{document}

decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations. Based on the latest experimental measurements, we independently obtain the quark-mixing matrix element

\begin{document}$|V_{cs}|$\end{document}

, which is in good agreement with results from other theoretical approaches.

Same-sign tetralepton signature in type-II seesaw at lepton colliders

Xu-Hong Bai, Zhi-Long Han, Yi Jin, Hong-Lei Li, Zhao-Xia Meng

2022, 46(1): 012001. doi: 10.1088/1674-1137/ac2ed1

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Abstract:
The same-sign tetralepton signature via the mixing of neutral Higgs bosons and their cascade decays to charged Higgs bosons is a unique signal in the type-II seesaw model with the mass spectrum

\begin{document}$M_{A^0}\simeq M_{H^0}>M_{H^\pm}>M_{H^{\pm\pm}}$\end{document}

. In this study, we investigate this signature at future lepton colliders, such as the ILC, CLIC, and MuC. Direct searches for doubly charged scalar

\begin{document}$H^{\pm\pm}$\end{document}

at the LHC have excluded

\begin{document}$M_{H^{\pm\pm}}<350(870)$\end{document}

GeV in the

\begin{document}$H^{\pm\pm}\to W^\pm W^\pm (\ell^\pm\ell^\pm)$\end{document}

decay mode. Therefore, we choose

\begin{document}$M_{A^0}=400,600,1000,1500$\end{document}

GeV as our benchmark scenarios. Constrained by direct search,

\begin{document}$H^{\pm\pm}\to W^\pm W^\pm$\end{document}

is the only viable decay mode for

\begin{document}$M_{A^0}=400$\end{document}

GeV at the

\begin{document}$\sqrt{s}=1$\end{document}

TeV ILC. With an integrated luminosity

\begin{document}$\mathcal{L}=8~ \mathrm{ab}^{-1}$\end{document}

, the promising region, with approximately 150 signal events, corresponds to a narrow band in the range of

\begin{document}$10^{-4}~\text{GeV}\lesssim v_\Delta \lesssim10^{-2}$\end{document}

GeV. Meanwhile, for

\begin{document}$M_{A^0}=600$\end{document}

GeV at the

\begin{document}$\sqrt{s}=1.5$\end{document}

TeV CLIC, approximately 10 signal events can be produced with

\begin{document}$\mathcal{L}=2.5~\text{ab}^{-1}$\end{document}

. For heavier triplet scalars

\begin{document}$M_{A^0}\gtrsim 870$\end{document}

GeV, although the

\begin{document}$H^{\pm\pm}\to \ell^\pm \ell^\pm$\end{document}

decay mode is allowed, the cascade decays are suppressed. A maximum event number

\begin{document}$\sim 16$\end{document}

can be obtained at approximately

\begin{document}$v_\Delta\sim4\times10^{-4}$\end{document}

GeV and

\begin{document}$\lambda_4\sim0.26$\end{document}

for

\begin{document}$M_{A^0}=1000$\end{document}

GeV with

\begin{document}$\mathcal{L}=5~ \mathrm{ab}^{-1}$\end{document}

at the

\begin{document}$\sqrt{s}=3$\end{document}

TeV CLIC. Finally, we find that this signature is not promising for

\begin{document}$M_{A^0}=1500$\end{document}

GeV at the

\begin{document}$\sqrt{s}=6$\end{document}

TeV MuC. Based on the benchmark scenarios, we also study the observability of this signature. In the

\begin{document}$H^{\pm\pm}\to W^\pm W^\pm(\ell^\pm\ell^\pm)$\end{document}

mode, one can probe

\begin{document}$M_{A^0}\lesssim800(1160)$\end{document}

GeV at future lepton colliders.

Model-independent Veltman condition, naturalness and the little hierarchy problem

Fayez Abu-Ajamieh

2022, 46(1): 013101. doi: 10.1088/1674-1137/ac2ffa

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Abstract:
We adopt a bottom-up Effective Field Theory (EFT) approach to derive a model-independent Veltman condition to cancel out the quadratic divergences in the Higgs mass. We show using the equivalence theorem that all the deviations in the Higgs couplings to the

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

and

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

from the SM predictions should vanish. We argue based on tree-level unitarity that any new physics that naturally cancels out the quadratic divergences should be

\begin{document}$ \lesssim 19 $\end{document}

TeV. We show that the level of fine-tuning required is

\begin{document}$ O(0.1\%-1\%) $\end{document}

unless the UV sector has a symmetry that forces the satisfaction of the model-independent Veltman condition, in which case all fine-tuning is eliminated. We also conjecture that, if no new physics that couples to the Higgs is observed up to

\begin{document}$ \sim 19 $\end{document}

TeV, or if the Higgs couplings to the SM particles conform to the SM predictions, then the Higgs either does not couple to any UV sector or is fine-tuned.

Doubly heavy tetraquarks in an extended chromomagnetic model

Xin-Zhen Weng, Wei-Zhen Deng, Shi-Lin Zhu

2022, 46(1): 013102. doi: 10.1088/1674-1137/ac2ed0

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Using an extended chromomagnetic model, we perform a systematic study of the masses of doubly heavy tetraquarks. We find that the ground states of the doubly heavy tetraquarks are dominated by the color-triplet

\begin{document}$\left| {(qq)^{\bar{3}_{c}}(\bar{Q}\bar{Q})^{3_{c}}} \right\rangle $\end{document}

configuration, which is opposite to that of fully heavy tetraquarks. The combined results suggest that the color-triplet configuration becomes more important when the mass difference between the quarks and antiquarks increases. We find three stable states that lie below the thresholds of two pseudoscalar mesons. They are the

\begin{document}$IJ^{P}=01^{+}$\end{document}

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

tetraquark,

\begin{document}$IJ^{P}=00^{+}$\end{document}

\begin{document}$nn\bar{c}\bar{b}$\end{document}

tetraquark, and

\begin{document}$J^{P}=1^{+}$\end{document}

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

tetraquark.

Do we need to use regularization for the thermal part in the NJL model?

Kai Xue, Xiaozhu Yu, Xinyang Wang

2022, 46(1): 013103. doi: 10.1088/1674-1137/ac2ed3

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Abstract:
The Nambu–Jona-Lasinio (NJL) model is one of the most useful tools for studying non-perturbative strong interactions in matter. Because it is a nonrenormalizable model, the choice of regularization is a subtle issue. In this paper, we discuss one of the general issues regarding regularization in the NJL model, which is whether we need to use regularization for the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model. The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes. We found that, regardless of the regularization scheme we choose, it is necessary to use regularization for the thermal part when calculating physical quantities related to the chiral condensate and to not use regularization for the thermal part when calculating physical quantities related to the grand potential.

Prospects for chargino pair production at the CEPC

Jia-Rong Yuan, Hua-Jie Cheng, Xu-Ai Zhuang

2022, 46(1): 013104. doi: 10.1088/1674-1137/ac2f93

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The proposed Circular Electron Positron Collider (CEPC) with a center-of-mass energy

\begin{document}$ \sqrt{s} = 240$\end{document}

GeV will primarily serve as a Higgs factory. Additionally, it will offer good opportunities to search for new physics phenomena at low energies, which can be challenging with hadron colliders; however, these discoveries are highly motivated by theoretical models developed to explain, e.g., the relic abundance of dark matter. This paper presents sensitivity studies for chargino pair production by considering scenarios for both a Bino-like and a Higgsino-like neutralino as the lightest supersymmetric particle and using a full Monte Carlo (MC) simulation. By assuming systematic uncertainties at the level of 5%, the CEPC has the ability to discover chargino pair production up to the kinematic limit of

\begin{document}$ \sqrt{s}/2$\end{document}

for both scenarios. The results have a minor dependence on the reconstruction model and detector geometry. These results can also be considered as a reference and benchmark for similar searches at other proposed electron-positron colliders, such as the Future Circular Collider ee (FCC-ee) or the International Linear Collider (ILC), given the similar nature of the facilities, detectors, center-of-mass energies, and target luminosities.

Revealing pion and kaon structure via generalised parton distributions

K. Raya, Z.-F. Cui, L. Chang, J. M. Morgado, C. D. Roberts, J. Rodríguez-Quintero

2022, 46(1): 013105. doi: 10.1088/1674-1137/ac3071

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Abstract:
Clear windows onto emergent hadron mass (EHM) and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure, many of which are accessible via generalised parton distributions (GPDs). Beginning with algebraic GPD Ansätze, constrained entirely by hadron-scale

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

and K valence-parton distribution functions (DFs), in whose forms both EHM and Higgs boson influences are manifest, numerous illustrations are provided. They include the properties of electromagnetic form factors, impact parameter space GPDs, gravitational form factors and associated pressure profiles, and the character and consequences of all-orders evolution. The analyses predict that mass-squared gravitational form factors are stiffer than electromagnetic form factors; reveal that K pressure profiles are tighter than

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

profiles, with both mesons sustaining near-core pressures at magnitudes similar to that expected at the core of neutron stars; deliver parameter-free predictions for

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

and K valence, glue, and sea GPDs at the resolving scale

\begin{document}$\zeta=2\,$\end{document}

GeV; and predict that at this scale the fraction of meson mass-squared carried by glue and sea combined matches that lodged with the valence degrees-of-freedom, with a similar statement holding for mass-squared radii.

Isomeric ratio of the ¹⁸¹Ta(γ, 3n)^178m,gTa reaction products at energy E_γmax up to 95 MeV

O.S. Deiev, I.S. Timchenko, S.N. Olejnik, V.A. Kushnir, V.V. Mytrochenko, S.A. Perezhogin

2022, 46(1): 014001. doi: 10.1088/1674-1137/ac2a95

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Abstract:
The photoneutron reaction

\begin{document}$^{181}{\rm{Ta}}(\gamma,3{n})^{178{\rm{m,g}}}{\rm{Ta}}$\end{document}

was investigated with the beam from the NSC KIPT electron linear accelerator LUE-40. The measurements were performed using the residual γ-activity method. The bremsstrahlung flux-averaged cross-sections

\begin{document}$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$\end{document}

,

\begin{document}$\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{m}}$\end{document}

,

\begin{document}$\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{g}}$\end{document}

and the isomeric ratio of the reaction products

\begin{document}$d(E_{\rm{\gamma max}})$\end{document}

were measured. The theoretical values of the averaged cross-sections and isomeric ratio were calculated using the partial cross-sections from the TALYS1.95 code for different level density models

\begin{document}$LD$\end{document}

1-6. The obtained experimental

\begin{document}$d(E_{\rm{\gamma max}})$\end{document}

agree with the data in the literature, but differ from the theoretical values in absolute magnitude and the behavior of the energy dependence. A comparison of the determined averaged cross-sections with the calculated cross-sections showed the best agreement for the case of the

\begin{document}$LD$\end{document}

5 model.

Measurement of (n,α) and (n,2n) reaction cross sections at a neutron energy of 14.92 ± 0.02 MeV for potassium and copper with uncertainty propagation

A. Gandhi, Aman Sharma, Rebecca Pachuau, Namrata Singh, L. S. Danu, S. V. Suryanarayana, B. K. Nayak, A. Kumar

2022, 46(1): 014002. doi: 10.1088/1674-1137/ac2ed4

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Experimentally measured neutron activation cross sections are presented for the

\begin{document}$^{65}{\rm{Cu}}$\end{document}

(n,α)

\begin{document}$^{62m}{\rm{Cu}}$\end{document}

,

\begin{document}$^{41}{\rm{K}}$\end{document}

(n,α)

\begin{document}$^{38}{\rm{Cl}}$\end{document}

, and

\begin{document}$^{65}{\rm{Cu}}$\end{document}

(n,2n)

\begin{document}$^{64}{\rm{Cu}}$\end{document}

reactions with detailed uncertainty propagation. The neutron cross sections were measured at an incident energy of 14.92 ± 0.02 MeV, and the neutrons were based on the t(d,n)α fusion reaction. The

\begin{document}$^{27}{\rm{Al}}$\end{document}

(n,α)

\begin{document}$^{24}{\rm{Na}}$\end{document}

reaction was used as a reference reaction for the normalization of the neutron flux. The pre-calibrated lead-shielded HPGe detector was used to detect the residues' γ-ray spectra. The data from the measured cross sections are compared to the previously measured cross sections from the EXFOR database, theoretically calculated cross sections using the TALYS and EMPIRE codes, and evaluated nuclear data.

Fragmentation of stable and neutron-rich ^12-16C into boron fragments at approximately 240 MeV/nucleon

Shu-Ya Jin, Ya-Zhou Sun, Shi-Tao Wang, Zhi-Yu Sun, Xue-Heng Zhang, Zhi-Qiang Chen, Bo Mei, Yi-Xuan Zhao, Shu-Wen Tang, Yu-Hong Yu, Duo Yan, Fang Fang, Yong-Jie Zhang, Shao-bo Ma, Xiang-Man Liu, Rui Han

2022, 46(1): 014003. doi: 10.1088/1674-1137/ac2ed5

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Abstract:
The elemental fragmentation cross sections of boron fragments produced by stable and neutron-rich ^12-16C beams with a carbon target were systematically measured at an incident beam energy of approximately 240 MeV/nucleon. The measured cross sections were found to increase as the projectile mass number increases. The observed feature is explained qualitatively based on the abrasion-ablation two-stage reaction model and is compared quantitatively with predictions from various reaction models, including empirical and statistical models. All models agree with the measured cross sections within a factor of 2.

Universality test of short range nucleon-nucleon correlations in nuclei with strange and charmed probes

Yu. T. Kiselev

2022, 46(1): 014004. doi: 10.1088/1674-1137/ac2ff9

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Understanding the EMC effect and its relation to the short-range nucleon-nucleon correlations (SRC) in nuclei is a major challenge for modern nuclear physics. One of the key aspects of the connection between these phenomena is the universality. The universality states that the SRC is responsible for the EMC effect and that the modification of the partonic structure of the SRC is the same in different nuclei. The flavor dependence of the universality is one of the unanswered questions. The investigations conducted to date have demonstrated the existence and universality of the SRC for light

\begin{document}$ u $\end{document}

and

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

quarks. Recently, it was suggested that the universality for heavy flavors can be studied through their deep subthreshold production in

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

and eA collisions. In this paper, we discuss an alternative possibility to access the strange and gluon high-X structure of the SRC and to establish universality for heavy flavors using nuclear semi-inclusive deep inelastic scattering (nSIDIS), which probes different quark flavor combinations depending on the final state hadron. The specific reaction can be "tagged" by observation of a strange or charmed particle registered in coincidence with the scattering lepton. The universality of the SRC can be tested in the kinematic region, i.e.,

\begin{document}$ X>1 $\end{document}

, where the contribution to the cross section from SRC becomes dominant. Exploring the strangeness, charmonium, and open charm will shed light on the role of quarks and gluons in nuclei, thereby developing an understanding of how nuclei emerge within QCD.

Investigation of experimental observables in search of the chiral magnetic effect in heavy-ion collisions in the STAR experiment

Subikash Choudhury, Xin Dong, Jim Drachenberg, James Dunlop, ShinIchi Esumi, Yicheng Feng, Evan Finch, Yu Hu, Jiangyong Jia, Jerome Lauret, Wei Li, Jinfeng Liao, Yufu Lin, Mike Lisa, Takafumi Niida, Robert Lanny Ray, Masha Sergeeva, Diyu Shen, Shuzhe Shi, Paul Sorensen, Aihong Tang, Prithwish Tribedy, Gene Van Buren, Sergei Voloshin, Fuqiang Wang, Gang Wang, Haojie Xu, Zhiwan Xu, Nanxi Yao, Jie Zhao

2022, 46(1): 014101. doi: 10.1088/1674-1137/ac2a1f

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The chiral magnetic effect (CME) is a novel transport phenomenon, arising from the interplay between quantum anomalies and strong magnetic fields in chiral systems. In high-energy nuclear collisions, the CME may survive the expansion of the quark-gluon plasma fireball and be detected in experiments. Over the past two decades, experimental searches for the CME have attracted extensive interest at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The main goal of this study is to investigate three pertinent experimental approaches: the

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

correlator, the R correlator, and the signed balance functions. We exploit simple Monte Carlo simulations and a realistic event generator (EBE-AVFD) to verify the equivalence of the core components among these methods and to ascertain their sensitivities to the CME signal and the background contributions for the isobar collisions at the RHIC.

Fusion of spherical-octupole pairs of colliding nuclei for compact and elongated configurations

Shivani Jain, Manoj K. Sharma, Raj Kumar

2022, 46(1): 014102. doi: 10.1088/1674-1137/ac2ed2

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The deformation and associated optimum/uniquely fixed orientations play an important role in the synthesis of compound nuclei via cold and hot fusion reactions, respectively, at the lowest and highest barrier energies. The choice of optimum orientation (

\begin{document}$\theta_{\rm opt}$\end{document}

) for the ‘cold or elongated’ and ‘hot or compact’ fusion configurations of quadrupole (

\begin{document}$\beta_2$\end{document}

) deformed nuclei depends only on the +/- signs of

\begin{document}$\beta_2$\end{document}

-deformation [J. Phys. G: Nucl. Part. Phys. 31, 631-644 (2005)]. In our recent study [Phys. Rev. C 101, 051601(R) 2020], we proposed a new set of

\begin{document}$\theta_{\rm opt}$\end{document}

(different from the values reported for quadrupole deformed nuclei) after the inclusion of octupole deformation (up to

\begin{document}$\beta_3$\end{document}

) effects. Using the respective

\begin{document}$\theta_{\rm opt}$\end{document}

of

\begin{document}$\beta_3$\end{document}

-deformed nuclei for cold and hot optimum orientations, we analyzed the impact of the soft- and rigid-pear shapes of octupole deformed nuclei on the fusion barrier characteristics (barrier height

\begin{document}$V_B$\end{document}

and barrier position

\begin{document}$R_B$\end{document}

). This analysis is applied to approximately 200 spherical-plus-

\begin{document}$\beta_3$\end{document}

deformed nuclear partners, that is, ¹⁶O, ⁴⁸Ca+octupole deformed nuclei. Compared with the compact configuration, the elongated fusion configuration has a relatively larger impact on the fusion barrier and cross-sections owing to the inclusion of deformations up to

\begin{document}$\beta_3$\end{document}

. Its agreement with available experimental data for the ¹⁶O+¹⁵⁰Sm reaction (

\begin{document}$\beta_{22}$\end{document}

=0.205,

\begin{document}$\beta_{32}$\end{document}

=-0.055) also improves when the optimum orientation degree of freedom is fixed in view of octupole deformations. This reinforces the fact that nuclear structure effects play an important role in the nuclear fusion process. Thus, octupole deformed nuclei can be used for the synthesis of heavy and superheavy nuclei.

Coulomb and nuclear interactions in the dynamics of weakly-bound neutron-halo breakup on heavy target

B. Mukeru, Lauro Tomio

2022, 46(1): 014103. doi: 10.1088/1674-1137/ac2f2a

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Within our aim to clarify some aspects of the breakup dynamics of loosely-bound neutron-halo projectiles on a heavy target, we apply the continuum discretized coupled-channel formalism to investigate the beryllium ¹¹Be breakup on a lead ²⁰⁸Pb target at

\begin{document}$E_{\rm lab}$\end{document}

= 140 MeV incident energy. By evidencing that the continuum–continuum couplings are much stronger in the nuclear breakup than in the Coulomb breakup, we conclude that the strength of these couplings in the total breakup is dominated by the nuclear contribution, with the diagonal monopole nuclear potential in the projectile–target center-of-mass having negligible effect on the total and nuclear breakup cross-sections. For this kind of reaction, we show that the condition for the total breakup to approach its dominant component in the absorption region is strongly dependent on the continuum–continuum couplings and the diagonal monopole nuclear potential.

Comparative studies on nuclear elastic magnetic form factors between the relativistic and non-relativistic mean-field approaches

Xin Li, Yunsheng Wang, Xiaoyong Guo, Meina Chen, Jian Liu, Chang Xu

2022, 46(1): 014104. doi: 10.1088/1674-1137/ac2f94

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It is known that elastic magnetic electron scattering can be used to study the magnetic properties of nuclei and determine the outermost-shell single-particle orbitals. In this study, the magnetic form factors

\begin{document}$ |F_\mathrm{M}(q)|^{2} $\end{document}

of odd-A nuclei calculated with relativistic and non-relativistic models are systematically compared. We use the relativistic mean-field (RMF) and Skyrme Hartree-Fock (SHF) models to generate single-particle wave functions and calculate the

\begin{document}$ |F_\mathrm{M}(q)|^{2} $\end{document}

values of selected nuclei under relativistic and non-relativistic frameworks, respectively. Geometric factors are introduced through the spherical limit method to consider the influences of deformation, which improves the agreement between the theoretical results and experimental data. It is shown that both the models have the capability to describe the magnetic form factors in the spherical and deformed cases, and the discrepancies in

\begin{document}$ |F_\mathrm{M}(q)|^{2} $\end{document}

reflect the differences in the descriptions of the single-particle orbital between the two models.

Phase structures of neutral dense quark matter and applicationto strange stars

Shu-Sheng Xu

2022, 46(1): 014105. doi: 10.1088/1674-1137/ac2f95

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In the contact interaction model, the quark propagator has only one solution, namely, the chiral symmetry breaking solution, at vanishing temperature and density in the case of physical quark mass. We generalize the condensate feedback onto the coupling strength from the 2 flavor case to the 2+1 flavor case, and find the Wigner solution appears in some regions, which enables us to tackle chiral phase transition as two-phase coexistences. At finite chemical potential, we analyze the chiral phase transition in the conditions of electric charge neutrality and

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

equilibrium. The four chemical potentials,

\begin{document}$ \mu_u $\end{document}

,

\begin{document}$ \mu_d $\end{document}

,

\begin{document}$ \mu_s $\end{document}

and

\begin{document}$ \mu_e $\end{document}

, are constrained by three conditions, so that one independent variable remains: we choose the average quark chemical potential as the free variable. All quark masses and number densities suffer discontinuities at the phase transition point. The strange quarks appear after the phase transition since the system needs more energy to produce a

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

-quark than an

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

-quark. Taking the EOS as an input, the TOV equations are solved numerically, and we show that the mass–radius relation is sensitive to the EOS. The maximum mass of strange quark stars is not susceptible to the parameter

\begin{document}$ \Lambda_q $\end{document}

we introduced.

Shell evolution in neutron-rich nuclei: the single particle perspective

Wei-Qiang Ma, Yi-Bin Qian

2022, 46(1): 014106. doi: 10.1088/1674-1137/ac3072

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The isospin dependence of spin-orbit (SO) splitting becomes increasingly important as N/Z increases in neutron-rich nuclei. Following the initial independent-particle strategy toward explaining the occurrence of magic numbers, we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term. It is found that new magic numbers N = 14 and N =16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling, whereas the traditional magic number, N = 20, may disappear. The magic number N = 28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting, corresponding to the strength of the SO coupling term. Meanwhile, the N = 50 and 82 shells may persist within the single particle scheme, although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei. Besides, an appreciable energy gap appears at N = 32 and 34 in neutron-rich Ca isotopes. All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model. The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrè chart.

Effect of dark energy models on the energy content of charged and rotating black holes

Asia Liaqat, Ibrar Hussain

2022, 46(1): 015101. doi: 10.1088/1674-1137/ac2e66

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The energy content of the charged-Kerr (CK) spacetime surrounded by dark energy (DE) is investigated using approximate Lie symmetry methods for the differential equations. For this, we consider three different DE scenarios: cosmological constant with an equation of state parameter

\begin{document}$ {\omega}_{c}=-1$\end{document}

, quintessence DE with an equation of state parameter

\begin{document}$ {\omega}_{q}=-{2}/{3}$\end{document}

, and a frustrated network of cosmic strings with an equation of state parameter

\begin{document}$ {\omega}_{n}=- {1}/{3} $\end{document}

. To study the gravitational energy of the CK black hole surrounded by the DE, we explore the symmetries of the 2nd-order perturbed geodesic equations. It is noticed, for all the values of ω, the exact symmetries are recovered as 2nd-order approximate trivial symmetries. These trivial approximate symmetries give the rescaling of arc length parameter s in this spacetime which indicates that the energy in the underlying spacetime has to be rescaled by a factor that depends on the black hole parameters and the DE parameter. This rescaling factor is compared with the factor of the CK spacetime found in [Hussain et al. Gen. Relativ. Gravit. (2009)] and the effects of the DE on it are discussed. It is observed that for all the three values of the equation of state parameter ω, the effect of DE results in decreased energy content of the black hole spacetime, regardless of values of the charge Q, spin a and the DE parameter α. This reduction in the energy content due to the involvement of the DE favours the idea of mass reduction of black holes by accretion of DE given by [Babichev et al. Phys. Rev. Lett. (2004)].

2022 Vol. 46, No. 1