We study the two-particle approximation of the Ising field theory (IFT), formulated in terms of the Bethe-Salpeter (BS) equation. Derived by Fonseca and Zamolodchikov as a systematic realization of the McCoy-Wu approach, this equation captures confinement by modeling “mesons” as bound states of two Majorana fermions (“quarks”), in a way analogous to the integral equation in the ’t Hooft model. Despite its approximate nature, the BS equation provides remarkably accurate predictions for the mass spectrum of stable mesons across a wide range of parameters. Motivated by the striking structural similarity between the BS equation in IFT and the ’t Hooft equation in two-dimensional QCD, we develop a new nonperturbative analytical framework inspired by the method of Fateev, Lukyanov, and Zamolodchikov. Within this approach, we compute spectral sums and systematically derive the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> expansion for the Bethe-Salpeter equation, which governs the spectrum of an infinite tower of mesons. We further examine how our analytical results capture the known behavior of the spectrum in well-studied asymptotic regimes, such as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>8</mn></msub></math> limit and the free-fermion point, where exact solutions are available for comparison. Finally, we discuss how the obtained spectral data admit a natural analytic continuation to complex values of the parameters—an extension that was one of the primary motivations for this work.

Russia

Alexey Litvinov

Pavel Meshcheriakov

Egor Shestopalov

Meson mass spectrum in Ising field theory

Pion condensation in ultrarelativistic collisions presents a compelling theoretical phenomenon with significant implications for the dynamics of hadronic matter. Various theoretical frameworks offer insight into the nature of high-temperature Bose-Einstein condensation (BEC). The present study investigates the dissipative behavior of a relativistic pion gas undergoing BEC in ultrarelativistic heavy-ion collisions. Further, we obtain viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>), bulk viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math>), and speed of sound (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mi>s</mi></msub></math>) by employing the Boltzmann transport equation with the relaxation time approximation. Findings show a substantial drop in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi><mo>/</mo><mi>s</mi></math> with the fractional increase in condensation. This effect is becoming more evident in larger systems approaching the thermodynamic limit. Alongside the reduction in viscosities, the speed of sound also decreases with increasing condensation, indicating a softening of the equation of state. The analysis of finite-size effects reveals that larger systems exhibit more pronounced signatures of BEC. These results suggest that pion condensation can influence the hydrodynamic evolution of the hadronic phase in heavy-ion collisions, with consequential implications for interpreting collective flow observables and the underlying equation of state.

India

Kshitish Kumar Pradhan

Dushmanta Sahu

Captain R. Singh

Raghunath Sahoo

Bose-Einstein condensation and dissipative dynamics in a relativistic pion gas

We investigate the nucleon’s chiral-odd generalized parton distribution functions (GPDs) in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit of quantum chromodynamics (QCD). Extending previous work [<a href="http://dx.doi.org/10.1103/PhysRevD.111.074007">Phys. Rev. D 111, 074007 (2025)</a>] on the leading-order contribution in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion, we focus on the next-to-leading-order contributions and provide a complete set of flavor-singlet and flavor-non-singlet chiral-odd GPDs. This study includes the derivation of the spin-flavor structure of the baryon matrix element of the chiral-odd operator, the proof of the polynomiality property and associated sum rules, and numerical estimates based on the gradient expansion. The spin-flavor structure of the nucleon matrix element is interpreted through a multipole expansion in the transverse momentum transfer, leading to the definition of multipole mean-field GPDs. Using these GPDs as the basis of our analysis, we take their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math>th moments and demonstrate the polynomiality property within the mean-field framework, making use of discrete symmetries in the proof. In particular, the first moments (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>=</mo><mn>1</mn></math>) of the GPDs are related to the nucleon tensor form factors, as generally required. By performing a gradient expansion, we compute the chiral-odd GPDs and present numerical estimates. Our results show reasonable agreement with lattice QCD predictions.

France

June-Young Kim

Chiral-odd generalized parton distributions in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> limit of QCD: Next-to-leading-order contributions

Fast and accurate muon reconstruction is crucial for neutrino telescopes to improve experimental sensitivity and enable online triggering. This paper introduces a hybrid-graph neural network (GNN) method tailored for efficient muon track reconstruction, leveraging the robustness of GNNs, alongside traditional physics-based approaches. The “light GNN model” achieves a run-time of 0.19–0.29 ms per event on GPUs, offering a 3 orders of magnitude speedup compared to traditional likelihood-based methods, while maintaining a high reconstruction accuracy. For high-energy muons (10–100 TeV), the median angular error is approximately 0.1°, with errors in reconstructed Cherenkov photon emission positions being below 3–5 m, depending on the GNN model used. Furthermore, the semi-GNN method offers a mechanism to assess the quality of event reconstruction, enabling the identification and exclusion of poorly reconstructed events. These results establish the GNN-based approach as a promising solution for next-generation neutrino telescope data reconstruction.

China

Cen Mo

Liang Li

Hybrid-graph neural network method for muon fast reconstruction in neutrino telescopes

In this paper, we study chiral non-Abelian domain walls in a phase of unconventional vacua of the Ginzburg-Landau model for dense QCD by considering a wider range of parameters space not directly deduced from QCD. The phase is characterized by asymmetric vacuum expectation values (VEVs), for example with the left scalar field, corresponding to the left quark-quark condensate, having a nonvanishing VEV and the right field having a vanishing one. The domain wall soliton interpolates between this vacuum and another where the left and right scalar fields switch roles. We study this formal possibility, but not any mechanism to generate these vacua nonperturbatively at finite density or finite temperature. Using a strong-coupling, or sigma-model limit, we are able to reduce the full dynamical complex matrix valued equations of motion to the sine-Gordon, a generalization of the sine-Gordon, and a generalization of the double sine-Gordon equations. In this limit, we prove nonexistence of domain walls in one of the vacua studied here, and we find full numerical computations to converge to the sigma-model limit for many cases, with some exceptions that we discuss.

Sven Bjarke Gudnason

Japan

Muneto Nitta

Chiral non-Abelian domain walls in the Ginzburg-Landau theory

We present a tool to compute the sensitivity of the Future Circular Electron-Positron Collider (FCC-ee) to the interactions of new, heavy particles via publicly available extensions to the smelli and flavio computer programs. We parametrize new particles’ effects without any flavor assumptions and take into account the projected experimental and correlated theoretical uncertainties of various electroweak and Higgs observables at the proposed collider. We illustrate a use of the tool by estimating the sensitivity of the FCC-ee to a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> model with flavor-specific couplings, which explains anomalies inferred from present-day measurements and Standard Model predictions of observables that involve the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> transition.

United Kingdom

Ben Allanach

Eetu Loisa

Computation of FCC-ee sensitivity to heavy new physics with interactions of any flavor structure

Recently, it was observed that an aggressive cut on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> jets’ transverse momenta applied to Higgs boson production in weak-boson fusion followed by the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> leads to very large QCD corrections to the fiducial cross section. In this paper, we show that these corrections are caused by soft and collinear QCD radiation and, therefore, can be efficiently treated by a parton shower. We combine the parton-shower description of the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> with next-to-next-to-leading order QCD corrections to Higgs production in weak-boson fusion and its subsequent decay and demonstrate that the quality of the theoretical prediction is markedly improved even if <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> jets with rather high transverse momenta are selected. The remaining uncertainty of the theoretical prediction, mainly driven by imprecise modeling of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> decay, is estimated to be of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>5</mn><mi>–</mi><mn>7</mn><mo>%</mo><mo stretchy="false">)</mo></mrow></math>.

Germany

Arnd Behring

Kirill Melnikov

Ivan Novikov

Giulia Zanderighi

Parton-shower and fixed-order QCD effects in Higgs boson production in weak-boson fusion and its decays to bottom quarks

The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated <inline-formula><tex-math id='TM0001' notation='LaTeX'>$J_1$</tex-math></inline-formula>- <inline-formula><tex-math id='TM0002' notation='LaTeX'>$J_2$</tex-math></inline-formula> Ising model on the square lattice. Here <inline-formula><tex-math id='TM0003' notation='LaTeX'>$J_1 &lt; 0$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0004' notation='LaTeX'>$J_2 &gt; 0$</tex-math></inline-formula> are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of <inline-formula><tex-math id='TM0005' notation='LaTeX'>$g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7$</tex-math></inline-formula> and employ the resulting CNN to study the phase transition of <inline-formula><tex-math id='TM0006' notation='LaTeX'>$g = 0.8$</tex-math></inline-formula>. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature <inline-formula><tex-math id='TM0007' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0008' notation='LaTeX'>$g=0.7$</tex-math></inline-formula>, are needed to accurately determine the <inline-formula><tex-math id='TM0009' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0010' notation='LaTeX'>$g=0.8$</tex-math></inline-formula>. However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the <inline-formula><tex-math id='TM0011' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0012' notation='LaTeX'>$g=0.7$</tex-math></inline-formula>. Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the <inline-formula><tex-math id='TM0013' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0014' notation='LaTeX'>$g=0.8$</tex-math></inline-formula> accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.

Taiwan

Shang-Wei Li

Yuan-Heng Tseng

Ming-Che Hsieh

Fu-Jiun Jiang

Minimal Training Set for Training a Successful CNN: A Case Study of the Frustrated <italic>J</italic> 1- <italic>J</italic> 2 Ising Model on the Square Lattice

We propose a BRST extension of the higher-spin gauge theory in <italic>AdS</italic> <inf>4</inf> with the BRST operator associated with the local Lorentz symmetry. Our construction supports manifest local Lorentz covariance and is applicable both to any homotopy scheme of the perturbative analysis including the recently proposed differential homotopy and to the variety of further extended higher-spin models in <italic>AdS</italic> <inf>3</inf> and <italic>AdS</italic> <inf>4</inf> with higher differential forms and Coxeter higher-spin algebras.

O.A. Gelfond

M.A. Vasiliev

Lorentz covariance of the 4 <italic>d</italic> nonlinear higher-spin equations via BRST

In this work we introduce the rescaled <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected minimally coupled scalar field theory, a theory that contains minimal quantum corrections of the single scalar field Lagrangian. We develop the theoretical framework in the Jordan frame where the baryons geodesics are free fall geodesics and we do not treat the theory as a two scalar field theory in the Einstein frame. The theoretical framework can be reduced to a single scalar field theory framework by using a perturbative expansion at the level of the field equations, making the resulting theory easy to tackle analytically. The first two quantum corrections contain two terms, a linear <math altimg='si20.svg'><mrow><mo>&#8764;</mo><mi mathvariant='script'>R</mi></mrow></math> and a quadratic term <math altimg='si21.svg'><mrow><mo>&#8764;</mo><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></mrow></math>. The effect of the linear term alters the Einstein-Hilbert term, making the resulting theory a rescaled version of Einstein-Hilbert gravity. Due to the presence of the rescaled Einstein-Hilbert term <math altimg='si22.svg'><mrow><mo>&#8764;</mo><mi>&#955;</mi><mfrac><mi mathvariant='script'>R</mi><mrow><mn>16</mn><mi>&#960;</mi><mi>G</mi></mrow></mfrac></mrow></math>, the gravitational constant will no longer be that of Newton&#8217;s, but a rescaled one <math altimg='si23.svg'><mfrac><mi>G</mi><mi>&#955;</mi></mfrac></math> and hence gravity can be stronger primordially, or even weaker. The perspective of having stronger gravity primordially, is compatible with intuition, since one expects a stronger gravity primordially, but having a weaker gravity for some reason is not prohibited theoretically. The attribute of our theoretical framework is that it allows a stronger gravity primordially, which returns to ordinary gravity as the curvature of the Universe decreases. We examine the effects of the quantum terms on several mainstream scalar field inflationary potentials, such as hybrid inflation, monomial inflation and power-law inflation, and we demonstrate that the hybrid inflation and power-law inflation, which are 3-parameter models, are compatible with the Atacama Cosmology Telescope data in the strong gravity limit, while the monomial inflation, which is a 4-parameter model, can be compatible with the Atacama Cosmology Telescope data in the weak gravity limit, however the model suffers from perturbative expansion break down during inflation.

Greece

Kazakhstan

V.K. Oikonomou

Strong gravity effects on <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected single scalar field inflation and compatibility with the ACT data