The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> is the baryon chemical potential, is investigated as well as the one with real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>. We calculate the scalar curvature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> and use the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo>=</mo><mn>0</mn></math> criterion to investigate the phase structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mn>2</mn></msup><mo>−</mo><mi>T</mi></math> plane where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> is the temperature. The curve on which <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo>=</mo><mn>0</mn></math> continues analytically from the imaginary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> region, where the lattice QCD is feasible, to the real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> one. In the presence of EVE, there are rich phase structures in the large real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> region as well as the Roberge-Weiss-like region where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> is imaginary and a singularity appears, while there is no phase structure in the large real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> region in the absence of EVE. The limiting temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limiting temperature we determined. A simple empiric sufficient condition, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi mathvariant="normal">B</mi></msub><mo>&gt;</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mn>2</mn><msub><mi>v</mi><mi mathvariant="normal">B</mi></msub><mo stretchy="false">)</mo></math>, is obtained for the quark deconfinement in the large real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> region, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi mathvariant="normal">B</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi mathvariant="normal">B</mi></msub></math> are the net baryon number density and the volume of a baryon, respectively.

Japan

Riki Oshima

Hiroaki Kouno

Azerbaijan

Motoi Tachibana

Kouji Kashiwa

Thermodynamic geometry in the hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement

Quantum tomography of tau lepton pairs produced at a Higgs factory collider will enable measurements of their spin correlations arising from quantum entanglement. Such measurements rely on the ability to measure the components of and correlations between the taus’ spins. We present a method to fully reconstruct the kinematics of tau pair events at an electron-positron Higgs factory collider, making use of measured particles’ momenta and impact parameters. This procedure results in several consistent solutions per event, which can be assigned weights according to various event properties. Full kinematic reconstruction allows the optimal extraction of the taus’ spin orientation via polarimeters. We estimate the precision with which polarimeters can be reconstructed in an ideal detector, and quantify the effects of more realistic detector performance. We conclude that for this analysis, achieving a photon angular resolution of around 0.1 mrad is the most crucial aspect of detector performance, while photon energy resolution and vertex detector performance are significantly less important.

Daniel Jeans

Experimental aspects of the quantum tomography of tau lepton pairs at a Higgs factory collider

We investigate the structural and physical properties of a strange star admixed with self-interacting bosonic dark matter within a unified thermodynamic framework. The total energy density is modelled as a weighted combination of quark matter and dark matter components regulated by a fixed local volume fraction, corresponding to the $\textit{coextensive limit}$ in which both the components share the same spacetime geometry and extend to a common radius ( $$R_D = R_Q=R$$ ). The quark component is described by a linear equation of state (EOS), while the dark matter follows a mean-field EOS with repulsive self-interactions. By combining these EOSs into a barotropic effective EOS derived from a unified thermodynamic potential, the two-fluid system is reformulated as a thermodynamically closed and mechanically equilibrated configuration. The construction preserves the dynamical distinction between the quark and dark sectors but treats them as a macroscopically unified mixture governed by a single hydrostatic equilibrium equation. This framework identifies the fully coextensive limit of two-fluid models as a physically meaningful and thermodynamically closed configuration and provides a coherent macroscopic closure linking dark matter-strange matter microphysics to stellar observables. Using the effective EOS, we solve the Tolman–Oppenheimer–Volkoff (TOV) equations to obtain the mass–radius relationship by varying the fixed local dark matter fraction, dark matter particle mass and self-coupling constant. Our results reveal distinct modifications to the $$M-R$$ profiles, suggesting observable signatures that could offer insights into the impacts of dark matter in extreme astrophysical environments. We note that even a modest dark matter admixture softens the equation of state, thereby shrinking the maximum mass limit and hence can explain a wide range of ultra-compact stars. In particular, our study provides a possible explanation and a radius estimate for ultra-compact stars with small radii, such as XTE J1814-338, as well as for heavier pulsars like PSR J0348+0432, PSR J0740+6620, and PSR J0952-0607.

India

Samstuti Chanda

Ranjan Sharma

A unified thermodynamic framework for coextensive dark matter admixed strange stars

A correction to this paper has been published: https://doi.org/10.1007/JHEP11(2012)010

Germany

Ioan Ghişoiu

Chile

York Schröder

Erratum to: A new method for taming tensor sum-integrals

We present a generalized phenomenological parameterization of the deceleration parameter $\textit{q}$($\textit{z}$) that incorporates an effective radiative component (ERC) in addition to a localized late-time contribution. The proposed framework extends previous two-parameter $\textit{q}$($\textit{z}$) reconstructions by explicitly regulating the high-redshift behavior while preserving the late-time transition dynamics. We constrain the free parameters $$(h, q_0, z_c, z_e)$$ using late-time observational data from cosmic chronometers (CC), Pantheon+ Type Ia supernovae (SNIa), H galaxies (HIIG), and intermediate-luminosity quasars (QSO). For the full data combination (CC+SNIa+HIIG+QSO), we obtain $$q_0 = -0.25^{+0.04}_{-0.04}$$ and a transition redshift $$z_T \simeq 0.80$$ , indicating a currently accelerating Universe with a transition occurring earlier than in the $$\Lambda $$ CDM model. Within the redshift range probed by the data, the reconstructed $\textit{q}$($\textit{z}$) deviates from the $$\Lambda $$ CDM trend, reduction of the late-time acceleration. Furthermore, the reconstruction favors a relatively high value of the Hubble parameter, $$h = 0.729 \pm 0.006$$ . The ERC remains weakly constrained by late-time data but ensures a smooth and monotonic evolution of $\textit{q}$($\textit{z}$), $\textit{j}$($\textit{z}$), and $$w_\textrm{eff}(z)$$ across a wide redshift range. Within the observed interval, the model effectively reproduces the late-time behavior of the previous parametrization, while providing a controlled extension toward early epochs. Our results show that current low- and intermediate-redshift data are compatible with a reduced late-time acceleration.

Mexico

Tomás Verdugo

Alberto Hernández-Almada

Miguel García-Aspeitia

Juan Magaña

Verónica Motta

Reconstructing the cosmic expansion with a generalized q(z) parameterization: a decelerating Universe from late-time constraints

We investigate quasi-periodic oscillations (QPOs) as a diagnostic tool for probing frame-dragging effects and accretion disk physics in the spacetime of a rotating regular magnetic black hole (BH). Specifically, we analyze the precession of bound orbits and the epicyclic oscillations of test-particles under small perturbations in the equatorial plane. We demonstrate how the BH’s nonminimal coupling parameter ( $$\lambda /M^4$$ ) and dimensionless magnetic charge ($\textit{Q}$/$\textit{M}$) significantly influence the three fundamental epicyclic frequencies. By applying the relativistic precession model and employing Markov Chain Monte Carlo simulations (MCMC), we constrain the BH’s characteristic parameters, including mass, spin, magnetic charge, and nonminimal coupling, with the use of observational QPO data from five X-ray binaries: $$GRO J1655-40$$ , $$XTE J1859+226$$ , $$H1743-322$$ , $$XTE J1550-564$$ , and $$GRS 1915+105$$ . Furthermore, we examine the Lense-Thirring, geodetic, and general spin precession frequencies of a test gyroscope attached to a stationary observer around the current BH. Our theoretical results indicate that the regular charged BH suppresses these precession frequencies compared with the Kerr BH case.

China

R. Ali

Meng-He Wu

South Korea

Hong Guo

Xiao-Mei Kuang

Precessions and parameter constraints from quasiperiodic oscillations in a rotating charged black hole

In gravitational theories containing matter fields and higher-derivative corrections, the standard Smarr formula often fails unless $\textit{all}$ dimensionful couplings are incorporated consistently. Traditionally, parameters such as the cosmological constant or the coefficients of higher-derivative terms are regarded as immutable features of the theory and therefore excluded from the thermodynamic phase space. In our recent work, we developed a fully general framework that promotes every such coupling to a dynamical, freely varying parameter of black hole solutions. This is accomplished by introducing, for each coupling, an auxiliary scalar and gauge field, through which the coupling appears as a conserved charge associated with the global sector of an emergent gauge symmetry. The corresponding conjugate variables naturally arise as electric potentials evaluated at the black hole horizon. As a result, the first law and the Smarr relation acquire additional, systematically determined contributions, yielding a consistent and universal extension of black hole thermodynamics. We illustrate the validity of this construction by revisiting several black hole examples in the literature where the Smarr formula remains inconsistent even after treating the cosmological constant as a thermodynamic variable. Our analysis shows that only by including $\textit{all}$ dimensionful couplings in this generalized manner can one obtain an internally consistent Smarr relation, thereby providing the foundation for a truly universal formulation of black hole thermodynamics.

Türkiye

Kamal Hajian

Bayram Tekin

Onur Uçanok

A universal Smarr formula via coupling constants

We study the gravitational form factors of the proton and some of its mechanical properties. We use a holographic model based on the AdS/CFT correspondence, in which a deformation in the anti–de Sitter background geometry is considered. By describing the proton as a Dirac field in this background, we numerically evaluate the gluon contribution of its gravitational form factors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> from its energy-momentum tensor. A comparison of our numerical results with respect to some lattice QCD results and previous results in holography is made. In general, a good agreement is found. We also evaluate the term <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> and make use of it to compute the pressure and shear distributions in the system, which result in a stable composed particle interpretation consistent with the von Laue stability condition. The energy distribution in the system is also obtained. Internal forces are investigated to support this picture. We are also able to compute the radii associated with these distributions in the proton.

Brazil

Ayrton Nascimento

Henrique Boschi-Filho

Mechanical properties of the proton from a deformed AdS holographic model

We propose a refinement of the Kontsevich-Soibelman operator for a class of four-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> superconformal field theories characterized by the following conditions: (1) Their Coulomb branch admits a source/sink chamber, i.e., a chamber in which the Bogomol’nyi-Prasad-Sommerfield (BPS) quiver consists of only source and sink nodes. (2) The nodes with valency greater than 2 of the BPS quiver in a source/sink chamber are either all sources or all sinks. We present strong evidence that the trace of this refined operator is related to the Macdonald index of the theory. In particular, we conjecture new closed form expressions for the Macdonald indices of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>,</mo><mi mathvariant="fraktur">g</mi><mo stretchy="false">)</mo></math> Argyres-Douglas theories for any simply laced Lie algebra <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="fraktur">g</mi></math>.

United States

George Andrews

Anindya Banerjee

Ranveer Kumar Singh

Runkai Tao

Macdonald index from a refined Kontsevich-Soibelman operator

In the Standard Model, partial unification of the non-Abelian running gauge couplings is achieved at the scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>μ</mi><mn>32</mn><mrow><mi>SM</mi></mrow></msubsup><mo>≈</mo><mn>2.8</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Elaborating on this fact, we discuss a simple general parametrization for the new physics corrections leading to full unification at some scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>X</mi></msub></math>. We show that for any new physics model such that the corrections to the non-Abelian couplings are equal (or nearly so), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>X</mi></msub></math> is equal (or close to) the partial unification scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>μ</mi><mn>32</mn><mrow><mi>SM</mi></mrow></msubsup></math>; the latter scales could be disentangled only if the corrections to the non-Abelian couplings are significantly different. We explore how the parametrization works for some relevant models with new physics below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>X</mi></msub></math>, as low-energy supersymmetry, split supersymmetry, etc. As for models with a desert up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>X</mi></msub></math>, we explore, in particular, how the parametrization works for string-inspired corrections; we find a phenomenologically remarkable possibility for unification at about 100 TeV, suggesting a low string scale, in addition to the more conservative possibility for unification at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>μ</mi><mn>32</mn><mrow><mi>SM</mi></mrow></msubsup></math>; for models with power-law running/threshold corrections, we also outline an interesting connection with the number of fermion families propagating in the bulk.

Italy

Isabella Masina

Spain

Mariano Quirós

Standard model partial unification scale as a guide to new physics model building