Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

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} $ .

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)

We investigate the information paradox in the four-dimensional Kerr–Newman black hole by employing the recently proposed island paradigm. To accurately capture the behavior of entanglement entropy in Kerr–Newman spacetime, we analyze the form of quantum fields in the near-horizon limit. We demonstrate the field can be effectively described by a reduced two-dimensional field theory. Under the framework of this reduced two-dimensional theory, the entanglement entropy of radiation satisfies the Page curve. We also examine the impact of angular momentum and charges on the Page time and the scrambling time. A step further, we concentrate on analyzing the near extremal case. Resort to the Kerr/CFT correspondence, the near-horizon geometry of near extremal Kerr–Newman black holes can be taken account for a warped AdS geometry. In this scenario, the low-energy effective degrees of freedom are dominated by the Schwarzian zero mode, resulting in a one-loop correction to the partition function. The entanglement entropy is subsequently recalculated under the thermodynamic with corrections. Through explicit calculations, we finally find that the Page time and the scrambling time exhibits quantum delays. This strongly suggests that the near extremal geometry is governed by the Schwarzian dynamics, in which quantum fluctuations result in a reduced rate of information leakage. Moreover, we provide a rigorous discussion on the validity of the island formula and compute the entanglement entropy in Kerr–Newman AdS spacetime as a supplementary example. Our findings further substantiate information conservation and extend the island paradigm to the most general class of stationary spacetime.

Ming-Hui Yu

Xian-Hui Ge

Islands in Kerr–Newman black holes

We extend a top-down holographic model of a Weyl semimetal to finite charge density and compute the fermionic spectral function by introducing two probe fermions of opposite chirality. The model is controlled by the boundary fermion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>M</mi></mrow></math> and the chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>. In the zero density, small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> limit, we recover four energy bands, two Weyl points, and linear dispersion in their vicinity, the hallmarks of a Weyl semimetal. As <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> increases, the bands between the Weyl points become progressively compressed and the spectral weight associated with those bands is smeared out. At finite charge density, we map the Fermi surface in momentum space and identify a Lifshitz transition: two distinct Fermi pockets, each enclosing a different Weyl point, merge into a single large Fermi surface that encloses both. This transition can be induced by either control parameter. Varying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> alters the band structure and thus the band shape, which drives the Lifshitz transition, whereas changing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> shifts the bands relative to the Fermi level without qualitatively changing the band structure, producing the Lifshitz transition by moving the band positions.

Cheng-Yuan Lu

South Korea

Sang-Jin Sin

Lifshitz transition in a holographic finite density flavor brane Weyl semimetal

We investigate the connection between thermodynamic phase transitions and quasinormal modes (QNMs) in charged black holes with a positive curvature constant, within the framework of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math>-Euler-Heisenberg gravity. Nonlinear electromagnetic fields lead to rich thermodynamic phase structures and significantly affect the QNMs of massless scalar fields. By analyzing the QNM spectrum, we find that the transition point marking the disappearance of the divergence in the QNM slope parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> aligns with the change of the thermodynamic phase structure described by the heat capacity, within the bounds of computational uncertainty. This precise matching holds under variations of the curvature parameter and charge. Furthermore, we show that a larger angular quantum number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>l</mi></math> diminishes this correspondence, while a higher overtone number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> restores it beyond a threshold. These findings demonstrate that thermodynamic phase transitions of black holes carry embedded dynamical information, uncovering a fundamental link between black hole thermodynamic and dynamical properties.

Zi-Yu Hou

Yu-Qi Lei

Quasinormal modes and nonlinear electrodynamics in black hole phase transitions

We unify the dynamics of massive vector (Proca) fields in Schwarzschild spacetime with supersymmetric gauge theories through the Seiberg-Witten/quasinormal mode (SW/QNM) duality. By mapping Proca perturbations—specifically monopole and odd-parity modes governed by confluent Heun equations—to the quantum Seiberg-Witten curve, we establish a gauge-gravity correspondence. Leveraging instanton counting, we analytically compute QNM and quasibound state frequencies to high precision, resolving spectral properties nonperturbatively. Our results align with numerical benchmarks while extending the SW framework beyond scalar fields.

Japan

Masataka Matsumoto

Kilar Zhang

Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory

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 beta decay of $$^{77}$$ Ge and $$^{77\textrm{m}}$$ Ge, both produced by neutron capture on $$^{76}$$ Ge, is a potential background for Germanium based neutrinoless double-beta decay search experiments such as GERDA or the LEGEND experiment. In this work we present a search for $$^{77}$$ Ge decays in the full GERDA Phase II data set. A delayed coincidence method was employed to identify the decay of $$^{77}$$ Ge via the isomeric state of $$^{77}$$ As ( $$9/2^+$$ , $${475}\,\hbox {keV}$$ , $${T_{1/2} = {114}\,{\upmu }\hbox {s}}$$ , $$^{77\textrm{m}}$$ As). New digital signal processing methods were employed to select and analyze pile-up signals. No signal was observed, and an upper limit on the production rate of $$^{77}$$ Ge was set at $$<0.216$$ nuc/(kg $$\cdot $$ yr) (90% CL). This corresponds to a total production rate of $$^{77}$$ Ge and $$^{77\textrm{m}}$$ Ge of $$<{0.38}$$ nuc/(kg $$\cdot $$ yr) (90% CL), assuming equal production rates. A previous Monte Carlo study predicted a value for in-situ $$^{77}$$ Ge and $$^{77\textrm{m}}$$ Ge production of (0.21 ± 0.07) nuc/(kg.yr), a prediction that is now further corroborated by our experimental limit. Moreover, tagging the isomeric state of $$^{77\textrm{m}}$$ As can be utilised to further suppress the $$^{77}$$ Ge background. Considering the similar experimental configurations of LEGEND-1000 and GERDA, the cosmogenic background in LEGEND-1000 at LNGS is estimated to remain at a sub-dominant level.

United Kingdom

M. Agostini

A. Alexander

Switzerland

G. Araujo

Russia

A. Bakalyarov

Italy

M. Balata

I. Barabanov

L. Baudis

Germany

C. Bauer

S. Belogurov

A. Bettini

L. Bezrukov

V. Biancacci

E. Bossio

V. Bothe

R. Brugnera

A. Caldwell

S. Calgaro

C. Cattadori

A. Chernogorov

P.J. Chiu

T. Comellato

V. D’Andrea

E. Demidova

N. Marco

E. Doroshkevich

M. Fomina

A. Gangapshev

A. Garfagnini

C. Gooch

P. Grabmayr

V. Gurentsov

K. Gusev

J. Hakenmüller

S. Hemmer

W. Hofmann

J. Huang

Belgium

M. Hult

L. Inzhechik

Hungary

J. Janicskó Csáthy

J. Jochum

M. Junker

V. Kazalov

Y. Kermaïdic

H. Khushbakht

T. Kihm

K. Kilgus

I. Kirpichnikov

A. Klimenko

K. Knöpfle

O. Kochetov

V. Kornoukhov

P. Krause

V. Kuzminov

M. Laubenstein

M. Lindner

I. Lippi

A. Lubashevskiy

B. Lubsandorzhiev

G. Lutter

C. Macolino

B. Majorovits

W. Maneschg

G. Marshall

Poland

M. Misiaszek

M. Morella

Y. Müller

I. Nemchenok

M. Neuberger

L. Pandola

K. Pelczar

L. Pertoldi

P. Piseri

A. Pullia

C. Ransom

L. Rauscher

M. Redchuk

S. Riboldi

N. Rumyantseva

C. Sada

S. Sailer

F. Salamida

S. Schönert

J. Schreiner

A.K. Schütz

O. Schulz

M. Schwarz

B. Schwingenheuer

O. Selivanenko

E. Shevchik

M. Shirchenko

L. Shtembari

H. Simgen

A. Smolnikov

D. Stukov

S. Sullivan

A. Vasenko

A. Veresnikova

C. Vignoli

K. Sturm

T. Wester

Search for the in-situ production of $$^{77}$$ Ge in the GERDA neutrinoless double-beta decay experiment

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo>=</mo><mi>i</mi><mn>2</mn><mi>π</mi><msub><mi>T</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>s</mi><mo stretchy="false">)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mi>π</mi><mi>L</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> denotes spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>=</mo><mi>L</mi></math> for the scalar field of spin 0 and the fermionic field of spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> correspond one to one with those in the classical limit as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mo stretchy="false">→</mo><mn>0</mn></math> in double-scaled Sachdev-Ye-Kitaev model when the temperature is infinite (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>DSSYK</mi></mrow><mi>∞</mi></msub></math>). This provides a numerical correspondence between quantum gravity in the static patch of two-dimensional dS spacetime and a one-dimensional quantum system, which we consider as a realization of the DS/dS correspondence.

Haiming Yuan

Keun-Young Kim

Pole skipping in two-dimensional de Sitter spacetime and double-scaled SYK model

We investigate the fermionic properties of a dyonic Gubser-Rocha model in the context of gauge/gravity duality. This model incorporates both a magnetic field and momentum relaxation. We have derived this model’s scaling exponent, revealing the influence of the magnetic field and momentum relaxation on low-energy physics. As the magnetic field strength and momentum relaxation increase, the spectral function of the dual field changes significantly. Specifically, we observe variations in the scaling exponent, Fermi momentum, and dispersion relations as the magnetic field increases, highlighting the system’s transition from a Fermi liquid to a non-Fermi liquid, and eventually to an insulating state. Our analysis of the magneto-scattering rate reveals that it is nearly zero in the Fermi liquid region, increases significantly in the non-Fermi liquid region, and ultimately arrives at a maximum value in the insulating state.

Holographic fermions in the dyonic Gubser-Rocha black hole