2023 Vol. 47, No. 6

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2023-6 Contents
2023, 47(6): 1-2.
Lepton mass correction in partial wave analyses of charmed meson semi-leptonic decays
Han Zhang, Bai-Cian Ke, Yao Yu, En Wang
2023, 47(6): 063101. doi: 10.1088/1674-1137/acc642
We derive a parameterization formula for the partial wave analyses of charmed meson semi-leptonic decays while considering the effects of lepton mass. Because the proposed super-tau-charm factory will reach a significantly enhanced luminosity and BESIII is collecting new \begin{document}$ \psi(3770)\to D\bar{D} $\end{document} data, our results will help improve the measurement precision of future partial wave analyses of charmed meson semi-muonic decays.
Light meson emissions of selected charmonium-like states within compact tetraquark configurations
Ning Li, Hui-Zhen He, Wei Liang, Qi-Fang Lü, Dian-Yong Chen, Yu-Bing Dong
2023, 47(6): 063102. doi: 10.1088/1674-1137/acc648
We adopt the quark pair creation model to investigate the light meson emissions of several charmonium-like states. The quark pair creation model is applied to four-body systems, and we calculate the pion/kaon emissions of \begin{document}$ X(4700) $\end{document}, \begin{document}$ Z_c(4430) $\end{document}, \begin{document}$ Y(4230) $\end{document}, \begin{document}$ Y(4360) $\end{document}, \begin{document}$ Y(4390) $\end{document}, and \begin{document}$ Y(4660) $\end{document} within compact tetraquark configurations. We find that the pion/kaon decay widths of \begin{document}$ X(4700) $\end{document} and \begin{document}$ Z_c(4430) $\end{document} are relatively small, whereas the partial decay widths of the resonances \begin{document}$ Y(4230) $\end{document}, \begin{document}$ Y(4360) $\end{document}, \begin{document}$ Y(4390) $\end{document}, and \begin{document}$ Y(4660) $\end{document} are significant. We expect that our exploration of these decay behaviors will provide useful information for future experimental searches and theoretical interpretations.
W-boson mass anomaly from a general SU(2)L scalar multiplet
Jiajun Wu, Da Huang, Chao-Qiang Geng
2023, 47(6): 063103. doi: 10.1088/1674-1137/acc8bf
We explain the W-boson mass anomaly by introducing an \begin{document}$S U(2)_L$\end{document} scalar multiplet with general isospin and hypercharge {in the case without its vacuum expectation value}. It is shown that the dominant contribution from the scalar multiplet to the W-boson mass arises at the one-loop level, which can be expressed in terms of the electroweak (EW) oblique parameters T and S at leading order. We first rederive the general formulae of T and S induced by a scalar multiplet of EW charges, confirming the results in literature. We then study several specific examples of great phenomenological interest by applying these general expressions. As a result, it is found that the model with a scalar multiplet in an \begin{document}$S U(2)_L$\end{document} real representation with \begin{document}$Y=0$\end{document} cannot generate the required \begin{document}$M_W$\end{document} correction because it leads to vanishing values of T and S. However, the cases with scalars in a complex representation under \begin{document}$S U(2)_L$\end{document} with a general hypercharge can explain the \begin{document}$M_W$\end{document} excess observed by CDF-II owing to nonzero T and S. We further consider the strong constraints from the perturbativity and EW global fit of the precision data and vary the isospin representation and hypercharge of the additional scalar multiplet to assess the extent of the model to solve the W-boson mass anomaly. It turns out that these constraints play important roles in setting limits on the model parameter space. We also briefly describe the collider signatures of the extra scalar multiplet, especially when it contains long-lived, heavy, highly charged states.
Further study of ${{\boldsymbol{\Omega^*}} \boldsymbol{|1P_{\bf 3/2^-}\rangle} }$ within a chiral quark model
Hui-Hua Zhong, Ru-Hui Ni, Mu-Yang Chen, Xian-Hui Zhong, Ju-Jun Xie
2023, 47(6): 063104. doi: 10.1088/1674-1137/acc9a2
In our previous studies, we analyzed the two-body strong decays of the low-lying Ω baryon states within a chiral quark model. The results showed that the mass, total width, and two body decay \begin{document}$ \Omega(2012) \to \bar{K}\Xi $\end{document} could be well reproduced with the spin-parity \begin{document}$ J^P=3/2^- $\end{document} state \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} classified in the quark model. Stimulated by the new observations of the three-body decay process \begin{document}$ \Omega(2012)^-\to \Xi^*(1530)^0K^-\to \Xi^-\pi^+K^- $\end{document} at Belle, in the present study, we further investigate the three-body strong decay \begin{document}$ \Omega^*|1P_{3/2^-}\rangle \to \Xi^*(1530)\bar{K} \to \Xi\pi\bar{K} $\end{document} within the chiral quark model. It is found that the \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} has a sizeable decay rate into the three-body final states \begin{document}$ \Xi\pi\bar{K} $\end{document}. When considering \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} as the \begin{document}$ \Omega(2012) $\end{document} resonance, the predicted ratio \begin{document}$R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}=\mathcal{B}[\Omega^*|1P_{3/2^-}\rangle\to \Xi^*(1530)\bar{K}\to \Xi\pi\bar{K}]/ $\end{document}\begin{document}$ \mathcal{B}[\Omega^*|1P_{3/2^-}\rangle \to \Xi\bar{K}]\simeq 12{\text%}$\end{document} is close to the upper limit \begin{document}$ 11{\text%} $\end{document} measured by the Belle Collaboration in 2019; however, it is too small to be comparable to the recent measurement \begin{document}$ 0.97 \pm 0.24\pm 0.07 $\end{document}. In addition, the coupled-channel effects on the bare three-quark state \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} from nearby channels \begin{document}$ \Xi \bar{K} $\end{document}, \begin{document}$ \Omega\eta $\end{document}, and \begin{document}$ \Xi^*(1530)\bar{K} $\end{document} are studied. Our theoretical results show that the coupled-channel effects on \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} are not very large, and the molecular component is no more than \begin{document}$ 30\% $\end{document}. To clarify the nature of \begin{document}$ \Omega(2012) $\end{document} resonance, precise measurements on the ratio \begin{document}$ R_{\Xi\bar{K}}^{\Xi\pi\bar{K}} $\end{document} are needed, and further investigation on the effects of coupled channels is recommended.
Doubly charmed dibaryon states
Zhe Liu, Hong-Tao An, Zhan-Wei Liu, Xiang Liu
2023, 47(6): 063105. doi: 10.1088/1674-1137/acc792
In this work, we study the doubly charmed dibaryon states with the \begin{document}$ qqqqcc $\end{document} (\begin{document}$ q =u, d, s $\end{document}) configuration. The mass spectra of doubly charmed dibaryon states are obtained systematically within the chromomagnetic interaction model. In addition to the mass spectrum analysis, we illustrate their two-body strong decay behaviours. Our results suggest that there may be narrow states or even stable states that cannot decay through the strong interaction. We hope that our results will provide valuable information for further experimental searches for doubly charmed dibaryon states.
Hadron spectra and pion form factor in dynamical holographic QCD model with anomalous 5D mass of scalar field
Ruixiang Chen, Danning Li, Kazem Bitaghsir Fadafan, Mei Huang
2023, 47(6): 063106. doi: 10.1088/1674-1137/acc92d
The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS\begin{document}$ _5 $\end{document} metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized. The light-flavor hadron spectra and the pion form factor were investigated, but it was difficult to reconcile the light-flavor hadron spectra and pion form factor. By considering the anomalous 5-dimension mass correction of the scalar field from QCD running coupling, it is found that the light flavor hadron spectra and pion form factor can be described well simultaneously. In particular, the ground state and lower excitation states of the scalar, pseudo scalar, and axial vector meson spectra are improved. However, the vector meson spectra are not sensitive to the anomalous 5-dimension mass correction of the scalar field.
Investigation of the tetraquark states ${\boldsymbol Qq\bar{\boldsymbol Q} \bar{\boldsymbol q}} $ in the improved chromomagnetic interaction model
Tao Guo, Jianing Li, Jiaxing Zhao, Lianyi He
2023, 47(6): 063107. doi: 10.1088/1674-1137/accb87
In the framework of the improved chromomagnetic interaction model, we complete a systematic study of the S-wave tetraquark states \begin{document}$ Qq\bar{Q}\bar{q} $\end{document} (\begin{document}$ Q=c,b $\end{document}, and \begin{document}$ q=u,d,s $\end{document}) with different quantum numbers: \begin{document}$ J^{PC}=0^{+(+)} $\end{document}, \begin{document}$ 1^{+(\pm)} $\end{document}, and \begin{document}$ 2^{+(+)} $\end{document}. The mass spectra of tetraquark states are predicted, and the possible decay channels are analyzed by considering both the angular momentum and \begin{document}$ \mathcal{C} $\end{document}-parity conservation. The recently observed hidden-charm tetraquark states with strangeness, such as \begin{document}$ Z_{cs}(3985)^- $\end{document}, \begin{document}$ X(3960) $\end{document}, and \begin{document}$ Z_{cs}(4220)^+ $\end{document}, can be well explained in our model. Additionally, according to the wave function of each tetraquark state, we find that the low-lying states of each \begin{document}$ Qq\bar{Q}\bar{q} $\end{document} configuration have a large overlap to the \begin{document}$ Q\bar Q $\end{document} and \begin{document}$ q\bar q $\end{document} meson basis, instead of the \begin{document}$ Q\bar q $\end{document} and \begin{document}$ q\bar Q $\end{document} meson basis. This indicates that one can search these tetraquark states in future experiments via the channel of \begin{document}$ Q\bar Q $\end{document} and \begin{document}$ q\bar q $\end{document} mesons.
Glueballs at physical pion mass
Feiyu Chen, Xiangyu Jiang, Ying Chen, Keh-Fei Liu, Wei Sun, Yi-Bo Yang
2023, 47(6): 063108. doi: 10.1088/1674-1137/accc1c
Glueballs are investigated through gluonic operators on two \begin{document}$ N_f=2+1 $\end{document} RBC/UKQCD gauge ensembles at the physical pion mass. The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor, and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential \begin{document}$ A_\mu(x) $\end{document} in the Coulomb gauge. These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions, where the ground state masses are extracted. These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point. The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.
Single inclusive hadron production at the LHC with an improved impact parameter dependent saturation model
Xiaofeng Gong, Yanbing Cai, Daicui Zhou, Wenchang Xiang
2023, 47(6): 064101. doi: 10.1088/1674-1137/acc23b
To obtain a reasonable description of the hadron production at the LHC energies, the impact parameter dependent saturation model is modified by inclusion of an anomalous dimension γ, which controls the slope of the scattering amplitude in the transition from the dilute region to the saturation region. We calculate the transverse momentum distribution and nuclear modification factor of the \begin{document}$ \pi^0 $\end{document} and charged hadrons with the improved model, and the results are consistent with measurements performed at the LHC. Moreover, we use the original impact parameter dependent model to study the aforementioned measurements performed at the LHC by adjusting its parameters. We find that the improved model is more consistent with the experimental data than the original one, as the anomalous dimension plays a significant role in the suppression of the evolution of the scattering amplitude.
Robustness of pair structures for nuclear yrast states
Yi-Fei Pan, Yi-Yuan Cheng, Yi Lu, Hui Jiang, Xian-Rong Zhou, Yu-Min Zhao
2023, 47(6): 064102. doi: 10.1088/1674-1137/acc1cc
In this study, we investigate the robustness of pair structures for nuclear yrast states, that is, whether the structures of relevant collective pairs as building blocks of different yrast states are the same. We focus on deformed and transitional nuclei and study the yrast states of \begin{document}$ ^{28} $\end{document}Si, \begin{document}$ ^{50} $\end{document}Cr, and \begin{document}$ ^{132} $\end{document}Xe, whose experimental \begin{document}$ R_{4/2} $\end{document} values are 2.60, 2.40, and 2.16, respectively, using the nucleon-pair approximation (NPA) and shell-model effective interactions. For each yrast state, we consider optimized pair structures to be those providing the energy minimum for this state. To find the minimum, many full NPA calculations are performed with varying pair structures, and the numerical optimization procedure of the conjugate gradient method is implemented. Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus. Our results also suggest that after backbending, that is, changing of the intrinsic state, the structure of the S pair, which is essential to build the monopole pairing correlation, remains approximately unchanged, whereas the structures of the non-S pairs, which are essential to build the quadrupole correlation, change significantly.
Restriction on the form of the quark anomalous magnetic moment from lattice QCD results
Mamiya Kawaguchi, Mei Huang
2023, 47(6): 064103. doi: 10.1088/1674-1137/acc641
The quark anomalous magnetic moment (AMM) is dynamically generated through spontaneous chiral symmetry breaking. It has been revealed that, even though its exact form is still unknown, the quark AMM is essential to exploring quark matter properties and QCD phase structure under external magnetic fields. In this study, we take three different forms of the quark AMM and investigate its influence on the chiral phase transition under a magnetic field. In general, a negative (positive) quark AMM acts as a magnetic-catalyzer (magnetic-inhibitor) for chiral symmetry breaking. It is found that a constant quark AMM drives an unexpected 1st order chiral phase transition, a quark AMM proportional to the chiral condensate flips the sign on the chiral condensate, and a quark AMM proportional to the square of the chiral condensate suppresses the magnetic enhancement in the chiral condensate at finite temperatures while retaining the chiral crossover phase transition. We also evaluate the intrinsic temperature dependence of the effective AMM form by fitting the effective model result of the chiral condensate to lattice QCD data, which may have a nontrivial correlation with the chiral phase transition.
Elastic scattering based on energy-dependent relativistic Love-Franey model at energies between 20 and 800 MeV
Si-Na Wei, Zhao-Qing Feng
2023, 47(6): 064104. doi: 10.1088/1674-1137/accb88
In order to investigate the elastic scattering, we fit scattering observables of the weighted fits (WF16) with the relativistic Love-Franey (RLF) model. The masses, cutoff parameters, and initial coupling strengths of RLF are assumed to be independent of energy. Because the energy boundary between low energy and high energy is around 200 MeV, the masses, cutoff parameters, and initial coupling strengths of RLF are obtained by fitting scattering observables of WF16 at an incident energy of 200 MeV. With the masses, cutoff parameters, and initial coupling strengths as the input, the energy-dependent RLF model is constructed over the laboratory energy range of 20 to 800 MeV within a unified fit. To examine the validity of this fit, we investigate p+\begin{document}$ ^{208}\rm{Pb} $\end{document} elastic scattering for various energies. Although the scattering observables of pp and pn of 200 MeV best fit the values of WF16, the RLF model of 200 MeV without the Pauli blocking (PB) corrections fails to describe the experimental differential cross sections, analyzing powers, and spinrotation functions. When the PB corrections are taken into account for various energies, the RLF model can well describe the experimental data of p+\begin{document}$ ^{208}\rm{Pb} $\end{document} elastic scattering.
Simple scenario of integrated neutron-proton interaction
Xin Yin, Yumin Zhao
2023, 47(6): 064105. doi: 10.1088/1674-1137/acc5dd
In this study, we investigate the patterns exhibited by integrated neutron-proton interactions (denoted as \begin{document}$V_{\rm NP}$\end{document}) that exhibit systematic differences among particle-particle, hole-hole, hole-particle, and particle-hole cases. A simple formula of \begin{document}$V_{\rm NP}$\end{document} is proposed to be in approximate linearity with \begin{document}$N_{n} N_{p}$\end{document}. This formula yields regular patterns of \begin{document}$ V_{\rm NP} $\end{document} that are highly consistent with those previously extracted according to binding energies. The observed ordering of \begin{document}$ V_{\rm NP} $\end{document}, i.e., \begin{document}$ V_{\rm NP} $\end{document} of the particle-particle case is the largest, \begin{document}$ V_{\rm NP} $\end{document} of the hole-hole case is in-between, and \begin{document}$ V_{\rm NP} $\end{document} of the particle-hole and hole-particle cases is the smallest, is explained in terms of the dominant part of \begin{document}$ V_{\rm NP} $\end{document} originating from symmetry energy and refinement involving the shell correction in the mass formulas.
Three-dimensional potential energy surface for fission of 236U within covariant density functional theory
Ming-Hui Zhou, Ze-Yu Li, Sheng-Yuan Chen, Yong-Jing Chen, Zhi-Pan Li
2023, 47(6): 064106. doi: 10.1088/1674-1137/acc4ac
We calculate the three-dimensional potential energy surface (PES) for the fission of the compound nucleus \begin{document}$ ^{236} $\end{document}U using covariant density functional theory with constraints on the axial quadrupole and octupole deformations \begin{document}$ (\beta_2, \beta_3) $\end{document} as well as the nucleon number in the neck \begin{document}$ q_N $\end{document}. By considering the additional degree of freedom \begin{document}$ q_N $\end{document}, the coexistence of the elongated and compact fission modes is predicted for \begin{document}$ 0.9\lesssim \beta_3 \lesssim 1.3 $\end{document}. Remarkably, the PES becomes shallow across a large range of quadrupole and octupole deformations for small \begin{document}$ q_N $\end{document}, and consequently, the scission line in the \begin{document}$ (\beta_2, \beta_3) $\end{document}plane extends to a shallow band, leading to fluctuations of several to ten MeV in the estimated total kinetic energies and of several to approximately ten nucleons in the fragment masses.
New Geiger-Nuttall law for cluster radioactivity half-lives
Lin-Jing Qi, Dong-Meng Zhang, Song Luo, Biao He, Xi-Jun Wu, Xun Chen, Xiao-Hua Li
2023, 47(6): 064107. doi: 10.1088/1674-1137/accc78
In this study, derived from Balasubramaniam's formula [Phys. Rev. C 70, 017301 (2004)] and further considering the effect of the parent nucleus mass, blocking effect, and effect of reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the half-lives of this process for 16 even-even nuclei and 10 odd-A nuclei. For comparison, a single universal curve for cluster radioactivity and α decay proposed by Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)], an extension of the Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives, with the least rms being 0.606, and are better than the compared values. Moreover, we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.
Pulsars as candidates of LHAASO sources J2226+6057, J1908+0621, and J1825-1326: The leptonic origin
Zhe Chang, Yu-Ting Kuang, Xukun Zhang, Jing-Zhi Zhou
2023, 47(6): 065101. doi: 10.1088/1674-1137/acc571
Recently, from 12 γ-ray Galactic sources, the LHAASO has detected ultrahigh-energy photons up to 1.4 PeV. The γ-ray spectra of the sources J2226+6057, J1908+0621, and J1825-1326 and the suggested origin pulsars near the sources have been published. In our previous work, we studied the hadronic γ-ray spectra of the sources J2226+6057, J1908+0621, and J1825-1326 in terms of the Hertzian dipole model of pulsars. In this paper, we investigate the possibility of the leptonic origin of the γ-ray. We use the Hertzian dipole model to describe the pulsars around the sources. The electrons around the pulsars can be accelerated to PeV by the electromagnetic fields of pulsars. Under the assumption that the initial electrons are uniformly distributed in a spherical shell between\begin{document}$ 10^{7} $\end{document} and \begin{document}$ 10^{9} $\end{document}m around the pulsar, we obtain the energy distribution of electrons. The leptonic γ-ray spectra can be calculated through inverse Compton scattering processes. The leptonic γ-ray can roughly conform to the observation of LHAASO.
Shadow thermodynamics of the Hayward-AdS black hole
Zhi Luo, Hao Yu, Shuo Cao, Jin Li
2023, 47(6): 065102. doi: 10.1088/1674-1137/acc570
In this paper, the phase structure of the Hayward-anti-de Sitter (AdS) black hole (BH) is studied using shadow formalism. It has been found that the shadow radius is a monotonic function of the horizon radius and can therefore play an equivalent role to the horizon radius in characterizing the thermodynamics of the Hayward-AdS BH. The thermodynamic phase transition (PT) of the Hayward-AdS BH is investigated with the shadow radius. It is shown that as the magnetic charge increases, the shadow radius becomes larger, while the coexistence temperature becomes lower. The thermal profile of the Hayward-AdS BH is established by combining the temperature diagram and the shadow cast diagram, which shows that for a fixed magnetic charge, the temperature of the Hayward-AdS BH increases with the pressure whereas the region of the thermal profile decreases with the pressure. In particular, the temperature of the Hayward-AdS BH follows an N-type change trend when it is smaller than the critical temperature. It implies that the BH shadow may be used to investigate the thermodynamics of the Hayward-AdS BH.
Extended phase space thermodynamics of black hole with non-linear electrodynamic field
G. Abbas, R. H. Ali
2023, 47(6): 065103. doi: 10.1088/1674-1137/acc56f
This paper deals with the thermodynamical properties of the black hole formulated in Einstein's theory of relativity associated with a nonlinear electromagnetic field. The transition of the black hole is analyzed using the mass, electric charge, coupling constant, and cosmological constant. We examine the thermodynamical aspects of exact black hole solutions to compute the black hole mass, temperature, entropy, Gibbs free energy, specific heat, and critical exponents in the phase space. Further, we study the stability of the black hole solution using the specific heat and Gibbs free energy. We examine the first and second phase changes and show a P-V criticality, which is similar to the van der Waals phase change. We also examine the equation of the state and the critical exponents.
Joint constraints on cosmological parameters using future multi-band gravitational wave standard siren observations
Shang-Jie Jin, Shuang-Shuang Xing, Yue Shao, Jing-Fei Zhang, Xin Zhang
2023, 47(6): 065104. doi: 10.1088/1674-1137/acc8be
Gravitational waves (GWs) from compact binary coalescences can be used as standard sirens to explore the cosmic expansion history. In the next decades, it is anticipated that we could obtain the multi-band GW standard siren data (from nanohertz to a few hundred hertz), which are expected to play an important role in cosmological parameter estimation. In this work, we provide, for the first time to the best of our knowledge, joint constraints on cosmological parameters using the future multi-band GW standard siren observations. We simulate the multi-band GW standard sirens based on the SKA-era pulsar timing array (PTA), Taiji observatory, and Cosmic Explorer (CE) to perform cosmological analysis. In the ΛCDM model, we find that the joint PTA+Taiji+CE data could provide a tight constraint on the Hubble constant with a \begin{document}$ 0.5\% $\end{document} precision. Moreover, PTA+Taiji+CE could break the cosmological parameter degeneracies generated by CMB, especially in the dynamical dark energy models. When combining the PTA+Taiji+CE data with the CMB data, the constraint precisions of \begin{document}$\Omega_\rm{m}$\end{document} and \begin{document}$ H_0 $\end{document} are \begin{document}$ 1.0\% $\end{document} and \begin{document}$ 0.3\% $\end{document}, respectively, meeting the standard of precision cosmology. The joint CMB+PTA+Taiji+CE data give \begin{document}$ \sigma(w)=0.028 $\end{document} in the wCDM model and \begin{document}$ \sigma(w_0)=0.11 $\end{document} and \begin{document}$ \sigma(w_a)=0.32 $\end{document} in the \begin{document}$ w_0w_a $\end{document}CDM model, which are comparable with or close to the latest constraint results by CMB+BAO+SN. In conclusion, the future multi-band GW observations are expected to be used for exploring the nature of dark energy and measuring the Hubble constant.
Optical appearance of the Schwarzschild black hole in the string cloud context
Sen Guo, Yu-Xiang Huang, Guo-Ping Li
2023, 47(6): 065105. doi: 10.1088/1674-1137/accad5
The image of a black hole (BH) consists of direct and secondary images that depend on the observer position. We investigate the optical appearance of a Schwarzschild BH in the context of a string cloud to reveal how the BH's observable characteristics are influenced by the inclination angle, string cloud parameter, and impact parameter. Following Luminet's work [Astron. Astrophys. 75, 228 (1979)], we adopt a semi-analytic method to calculate the total bending angle of the light ray and derive the direct and secondary images of the Schwarzschild string cloud BH. Our results show that an increase in the inclination angle leads to a more pronounced separation of the images. We consider the gravitational redshift and present the redshift distribution of the direct image while illustrating the flux distribution. We observe that the direct image exhibits blueshift and redshift simultaneously, and the asymmetry of the flux distribution increases with the inclination angle. Finally, we obtain the Schwarzschild string cloud BH image via a numerical simulation, which provides an approximate illustration of the EHT resolution.