An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the Standard Model where the dark sector consists of dark matter particles charged under a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>x</mi></msub></math> gauge symmetry, while a subset of dark fields also carry lepton number but no <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>x</mi></msub></math> charge. We demonstrate that, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves the lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Furthermore, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>p</mi></msub><mo>/</mo><msub><mi>m</mi><msub><mi>A</mi><mi>x</mi></msub></msub><mo>≪</mo><mn>1</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>p</mi></msub></math> is the percolation temperature and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msub><mi>A</mi><mi>x</mi></msub></msub></math> is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, and PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.

China

Wan-Zhe Feng

United States

Jinzheng Li

Pran Nath

Zong-Huan Ye

Gauge-independent gravitational waves from cogenesis in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> conserving universe

In this study, we investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting from a post-Maxwellian version of electromagnetism that includes LQG effects, we derive and discuss the influence of LQG parameters on classical quantities such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and examine the optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect of the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves by considering issues such as group velocities and refractive indices of the QED vacuum, in detail. Finally, with the aid of the previously analyzed LQG-extended photonic dispersion relations, we re-discuss the kinematics of the Compton effect and conclude that an interesting nonlinear profile emerges in the wavelengths of the incoming and deflected photons.

Brazil

P.A.L. Mourão

G.L.L.W. Levy

J.A. Helayël-Neto

Reassessing aspects of LQG-modified dispersion relations of photons * P. A. L. Mourão is support by CAPES. G. L. L. W. L. Levy is support by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No. E-26/202.437/2024.

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

Pursuing our analysis of the companion Letter, [Celestial symmetries of black hole horizons, <a href="http://dx.doi.org/10.1103/gx7p-8k34">Phys. Rev. D 113, L041504 (2026)</a>.], we study the gravitational solution space around a null hypersurface in the bulk of spacetime, such as a black hole or a cosmological horizon. We discuss the corresponding characteristic initial value problem both in the metric and Newman-Penrose formalisms and establish an explicit dictionary between the two. This allows us to identify Weyl-covariant structures in the solution space, including hierarchies of recursion relations encoding the flux-balance laws. We then establish a correspondence between the gravitational phase space at null infinity and the subleading phase space around the null hypersurface at finite distance. This connection is naturally formulated within the Newman-Penrose formalism by performing a partially off-shell conformal compactification and identifying the analog of the Ashtekar-Streubel symplectic structure in the radial expansion near the null hypersurface. Using this framework, we identify the celestial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><msub><mi>w</mi><mrow><mn>1</mn><mo>+</mo><mi>∞</mi></mrow></msub></math> symmetries in the subleading phase space at finite distance by constructing their canonical generators and imposing self-duality conditions. This allows us to define a notion of covariant radiation, whose absence gives rise to an infinite tower of conserved charges, revealing physical quantities relevant to observers near black hole or cosmological horizons. As a concrete illustration, we consider the case of the self-dual Taub-Newman-Unti-Tamburino black hole.

Romain Ruzziconi

Canada

Belgium

France

Céline Zwikel

Celestial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><msub><mi>w</mi><mrow><mn>1</mn><mo>+</mo><mi>∞</mi></mrow></msub></math> symmetries and subleading phase space of null hypersurfaces

We advance “latent entropy” (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>L</mi></mrow></math> entropy) as a novel measure to characterize genuine multipartite entanglement in pure states, applicable to quantum systems with both finite and infinite degrees of freedom. This measure, derived from an upper bound on reflected entropy, attains its maximum for three-party Greenberger-Horne-Zeilinger states and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></math>, 5-party 2-uniform states. We establish that it satisfies all essential properties of a genuine multipartite entanglement measure, including being a pure-state entanglement monotone. We further obtain an analog of the Page curve by analyzing the behavior of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> entropy in multiboundary wormholes, emphasizing their connection to multipartite entanglement in random states. Specifically, for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>5</mn></math>, we show that random states approximate 2-uniform states, exhibiting maximal multipartite entanglement. Extending these ideas to finite temperatures, we introduce the multipartite thermal pure quantum state, a generalization of the thermal pure quantum state to multipartite systems, and demonstrate that the entanglement structure in states of the multicopy Sachdev-Ye-Kitaev model exhibits finite-temperature 2-uniform behavior.

South Korea

Jaydeep Kumar Basak

Vinay Malvimat

Junggi Yoon

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>L</mi></mrow></math> Entropy: A New Genuine Multipartite Entanglement Measure

We propose a new extension of the Standard Model that incorporates a gauged $$ U(1)_{\mathrm{B-L}} $$ symmetry and the type-III seesaw mechanism to explain neutrino mass generation and provide a viable dark matter (DM) candidate. Unlike the type-I seesaw, the type-III seesaw extension under $$ U(1)_{\mathrm{B-L}} $$ is not automatically anomaly-free. We show that these anomalies can be canceled by introducing additional chiral fermions, which naturally emerge as DM candidates in the model. We thoroughly analyze the DM phenomenology, including relic density, direct and indirect detection prospects, and constraints from current experimental data. Furthermore, we explore the collider signatures of the model, highlighting the enhanced production cross-section of the triplet fermions mediated by the $$ \mathrm B-L $$ gauge boson, as well as the potential disappearing track signatures. Additionally, we investigate the gravitational wave signals arising from the first-order phase transition during $$ \mathrm B-L $$ symmetry breaking, offering a complementary cosmological probe of the framework.

India

Satyabrata Mahapatra

Partha Paul

Narendra Sahu

Prashant Shukla

Verifiable type-III seesaw and dark matter in a gauged $$U(1)_{\mathrm{B-L}}$$ symmetric model

The extension of the Standard Model Higgs doublet with three nonzero hypercharge triplets is examineled in this article. The triplets are charged under additional <inline-formula><tex-math id='TM0002' notation='LaTeX'>$U(1)_{L_{\mu }-L_{\tau }}$</tex-math></inline-formula> symmetry. We investigate the stability of the electroweak vacuum at both the tree level and the two-loop level. It is observed that the vacuum stability can be satisfied up to the Planck scale using two-loop <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\beta$</tex-math></inline-formula>-functions. In contrast, due to the increase in the positive effect from triplet degrees of freedom, the perturbative unitarity can be satisfied only up to <inline-formula><tex-math id='TM0004' notation='LaTeX'>$10^{12}$</tex-math></inline-formula> GeV. The parameter space allowed from the Planck scale stability is checked for the strongly electroweak first-order phase transition. The model satisfies the strongly first-order phase transition for the triplet bare mass parameters up to the TeV scale due to the sufficient contribution to the cubic term from the triplet degrees of freedom. It is observed that this model foresees a strongly first-order phase transition for all mass ranges until the degrees of freedom become heavy enough to decouple from the thermal bath. The benchmark points satisfying the strongly first-order phase transition are tested for gravitational-wave signatures. The benchmark points that are allowed from the Planck scale stability, strongly first-order phase transition also comes out to lie in the detectable frequency range of the LISA and BBO experiments.

Seong Chan Park

Anirban Biswas

Shilpa Jangid

Strongly Electroweak Phase Transition with <italic>U</italic>(1) <italic>L</italic>&#956;&#8211;<italic>L</italic>&#964; Gauged Nonzero Hypercharge Triplet

In this work, we derive a new class of analytic black hole solutions within the framework of <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math>, enabling a detailed exploration of how anisotropic pressures and different <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters ( <italic>&#946;</italic> <inf>1</inf>, <italic>&#946;</italic> <inf>2</inf>, <italic>&#946;</italic> <inf>3</inf>) under which the energy condition is satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian <math altimg='si9.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> and the trace <italic>T</italic> of the energy-momentum tensor.

Aniruddha Ghosh

Ujjal Debnath

The new black hole solution with anisotropic fluid in <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity: Thermodynamics

The observed matter–antimatter asymmetry of the Universe remains a fundamental challenge in modern physics. In this work, we explore gravitational baryogenesis within the framework of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity, where the gravitational Lagrangian depends on both the torsion scalar <italic>T</italic> and the matter Lagrangian <italic>L<inf>m</inf></italic>. We consider three representative models and examine their ability to generate the observed baryon-to-entropy ratio. Our analysis shows that couplings involving both torsion and the matter Lagrangian, <math altimg='si35.svg'><mrow><msub><mi>&#8706;</mi><mi>&#956;</mi></msub><mrow><mo>(</mo><mo>&#8722;</mo><mi>T</mi><mo linebreak='badbreak'>&#8722;</mo><mfrac><msub><mi>L</mi><mi>m</mi></msub><msub><mi>L</mi><mn>0</mn></msub></mfrac><mo>)</mo></mrow></mrow></math>, can successfully account for the baryon asymmetry for decoupling temperatures in the range 10 12&#8211;10 14&#8201;GeV, while remaining consistent with small deviations from General Relativity. These results highlight the capacity of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity to provide novel mechanisms for baryogenesis, demonstrating that the interplay between torsion and matter-sector contributions can naturally generate the observed asymmetry. The framework also remains compatible with late-time cosmological evolution, offering a unified setting for early- and late-time dynamics.

Portugal

Daniel F P Cruz

David S. Pereira

Francisco S N Lobo

Gravitational baryogenesis in <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity

We formulate a general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of $$\mathfrak{g}\mathfrak{l}(N)$$ . We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of $$\mathfrak{s}\mathfrak{u}(4)$$ .

Nan Bai

A general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains: application to the ABJM spin chain