We investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

China

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

Within the framework of the next-to-minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $ \tau\rightarrow e M^+ M^- $ decays: $ \tau \rightarrow e \pi^+\pi^- $ , $ \tau \rightarrow e \pi^+K^- $ , and $ \tau \rightarrow e K^+K^- $ . Based on the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensitive parameters and LFV sources are non-diagonal elements corresponding to the initial and final leptons. This work can provide a basis for discovering the existence of new physics (NP).

Rong-Zhi Sun

Shu-Min Zhao

Shuang Di

Portugal

Xing-Xing Dong

Study of ${\boldsymbol\tau\rightarrow {\boldsymbol e M^+ M^-}}$ decays in N-B-LSSM * Supported by National Natural Science Foundation of China (NNSFC) (12075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), the Project of the China Scholarship Council (CSC) (202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit (UIDB/00777/2020, UIDP/00777/2020)

In this study, we investigated the neutrino transition magnetic moment in $ U(1)_X $ SSM. $ U(1)_X $ SSM is the $ U(1) $ extension of the Minimal Supersymmetric Standard Model (MSSM), and its local gauge group is extended to $S U(3)_C\times S U(2)_L \times U(1)_Y\times U(1)_X$ . To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to the MSSM, which can explain the results of neutrino oscillation experiments. The neutrino transition magnetic moment is induced by electroweak radiative corrections. By applying the effective Lagrangian method and on-shell scheme, we studied the associated Feynman diagrams and transition magnetic moment of neutrinos in the model. We fit experimental data for neutrino mass variances and mixing angles. Based on the range of data selection, the influences of different sensitive parameters on the results were analyzed. The numerical analysis shows that many parameters, such as $ g_X $ , $ M_2 $ , $ \mu $ , $ \lambda_H $ , and $ g_{YX} $ , have an effect on the neutrino transition magnetic moment. In our numerical results, the order of magnitude of $ \mu_{ij}^M/\mu_B $ is approximately $ 10^{-20} $ $ \sim $ $ 10^{-19} $ .

Long Ruan

Ming-Yue Liu

Xing-Yu Han

Xi Wang

Neutrino transition magnetic moment in $\textit{U}$(1) $\textit{X }$ SSM * Supported by National Natural Science Foundation of China (NNSFC, 12075074), Natural Science Foundation of Hebei Province (A2020201002, A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), Scholarship Council (CSC, 202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit UIDB/00777/2020 and UIDP/00777/2020

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region $\textit{a}$ possesses an associated generalized entanglement wedge $\textit{E}$($\textit{a}$) ⊃ $\textit{a}$ on a static Cauchy surface $\textit{M}$ in general gravitational spacetimes, where $\textit{E}$($\textit{a}$) may contain an entanglement island $\textit{I}$($\textit{a}$). It suggests that the fine-grained entropy for bulk region $\textit{a}$ is given by the generalized entropy $\textit{S}$ ($\textit{E}$($\textit{a}$)). Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy $\textit{S}$ ($\textit{E}$($\textit{a}$)) of a bulk gravitational region $\textit{a}$ is established on the static Cauchy surface $\textit{M}$, such that $\textit{S}$ ($\textit{E}$($\textit{a}$)) is equal to the maximum flux of any flow that starts from the boundary $\textit{∂M}$ and ends at bulk region $\textit{a}$, or equivalently, the maximum number of bit threads that connect the boundary $\textit{∂M}$ to the bulk region $\textit{a}$. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region $\textit{E}$($\textit{a}$) \ $\textit{a}$, particularly on an entanglement island region $\textit{I}$($\textit{a}$) ⊂ ($\textit{E}$($\textit{a}$) \ $\textit{a}$), as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.

Dong-Hui Du

Jia-Rui Sun

Towards bit threads in general gravitational spacetimes

We study the information paradox of Reissner-Nordström anti–de Sitter black holes in the large dimension limit by using the island formula. The entanglement entropy of Hawking radiation is calculated both for the nonextremal and the extremal cases, in which the boundary of the radiation region is close to the outer horizon. For the nonextremal case, the entanglement entropy of Hawking radiation obeys the Page curve, i.e., the entanglement entropy of Hawking radiation increases with time and reaches saturation about twice Bekenstein-Hawking entropy at the Page time. For the extremal case, the entanglement entropy of Hawking radiation becomes ill defined in the absence of the island due to the appearance of the singularity at the origin of the radial coordinate, while when the island exists, the entanglement entropy is found to be equal to the Bekenstein-Hawking entropy. In addition, for the case where the boundary of the radiation region is close to the horizon, there are some obvious constraints required by the existence of the island solution for both nonextremal and extremal cases, which can be utilized to put constraints on the size of the black hole. These results reveal new features of the semiclassical large <math><mi>D</mi></math> black holes from the island perspective.

Chen-Wei Tong

Island of Reissner-Nordström anti–de Sitter black holes in the large <math><mi>D</mi></math> limit

We reconsider <math><mi>D</mi><mo>≥</mo><mn>4</mn></math> dimensional asymptotically flat eternal Schwarzschild black hole and focus on the situation where the inner boundary of the radiation region is chosen to be near the horizon (i.e., <math><mrow><mi>β</mi><mo>≪</mo><mn>1</mn></mrow></math>). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in [K. Hashimoto, N. Iizuka, and Y. Matsuo, J. High Energy Phys. 06 (2020) 085]. We remove this tension by introducing a more proper near horizon condition; thus, the resulting island solution is well-behaved in any <math><mi>D</mi><mo>≥</mo><mn>4</mn></math> dimensional spacetime. Interestingly, a novel constraint is obtained in this situation as required by the existence of the island solution, which directly leads to the constraints on the size of the Schwarzschild black hole, the position of the inner boundary for the radiation region, or the value of <math><mrow><mi>c</mi><mo>·</mo><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> in any <math><mi>D</mi><mo>≥</mo><mn>4</mn></math> dimension. When considering the large <math><mi>D</mi></math> limit, the constraint on the size of the Schwarzschild black hole obtained in this situation is in agreement with the result given in [F. Holdt-Sordrensen, D. A. McGady, and N. Wintergerst, Phys. Rev. D 102, 026016 (2020)]. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity.

Wen-Cong Gan

Fu-Wen Shu

Unitary constraints on semiclassical Schwarzschild black holes in the presence of island

Great breakthrough in solving black hole information paradox took place when semiclassical island rule for entanglement entropy of Hawking radiation was proposed in recent years. Up to now, most papers which discussed island rule of asymptotic flat black hole with D ≥ 4 focus on eternal black hole. In this paper, we take one more step further by discussing island of “in” vacuum state which describes one-sided asymptotically flat black hole formed by gravitational collapse in D ≥ 4. We find that island I emerges at late time and saves entropy bound. And boundary of island ∂I depends on the position of cutoff surface. When cutoff surface is far from horizon, ∂I is inside and near horizon. When cutoff surface is set to be near horizon, ∂I is outside and near horizon. This is different from the case of eternal black hole in which ∂I is always outside horizon no matter cutoff surface is far from or near horizon. We will see that different states will manifestly affect S ent in island formula when cutoff surface is far from horizon and thus have different result for Page time.

Island and Page curve for one-sided asymptotically flat black hole

The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map f, which is very difficult to construct especially for more-region (n ≥ 4) cases. In this work, we develop a general and effective rule to rule out most of the cases such that f can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states.

Nan Li

Chuan-Shi Dong

Improved proof-by-contraction method and relative homologous entropy inequalities

In this work we focus on a toy model: ( $$3+1$$  <math> <mrow> <mn>3</mn> <mo>+</mo> <mn>1</mn> </mrow> </math>  )-dimensional Hořava–Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a ( $$4+1$$  <math> <mrow> <mn>4</mn> <mo>+</mo> <mn>1</mn> </mrow> </math>  )-dimensional Hořava–Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter  $$\beta $$  <math> <mi>β</mi> </math>   in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives  $$|1-\sqrt{\beta }|&lt;(10^{-19}-10^{-18})$$  <math> <mrow> <mrow> <mo>|</mo> <mn>1</mn> <mo>-</mo> </mrow> <msqrt> <mi>β</mi> </msqrt> <mrow> <mo>|</mo> <mo>&lt;</mo> </mrow> <mrow> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </msup> <mo>-</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>18</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </math>  .