In this paper, we construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch–Xing (FX) parametrization, which is obtained by trivializing arguments of the matrix elements in the third row and third column. We further analyze rephasing invariant structure of the FX phase <italic>&#948;</italic> <inf>FX</inf> under an approximation <math altimg='si1.svg'><mrow><msubsup><mi>U</mi><mrow><mn>13</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, where the 1&#8211;3 element of the diagonalization matrix of charged leptons <italic>U<sup>e</sup></italic> is neglected. With an additional approximation <math altimg='si2.svg'><mrow><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase <math altimg='si3.svg'><msubsup><mi>&#948;</mi><mrow><mrow><mi mathvariant='normal'>F</mi></mrow><mi>X</mi></mrow><mi>&#957;</mi></msubsup></math> and the contribution from the relative phase <math altimg='si4.svg'><mrow><msubsup><mi>&#961;</mi><mn>1</mn><mo>&#8242;</mo></msubsup><mo linebreak='goodbreak'>&#8722;</mo><msubsup><mi>&#961;</mi><mn>2</mn><mo>&#8242;</mo></msubsup></mrow></math> between the lighter 1-2 generations. The phase <italic>&#948;</italic> <inf>FX</inf> for finite <math altimg='si5.svg'><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup></math> is understood as a generalization of the compact expression. This result covers almost all perturbative calculations of CP phases for the CKM and MNS matrices with hierarchical charged fermions.

Japan

Masaki J.S. Yang

Rephasing invariant structure of CP phase in Fritzsch–Xing parametrization for simplified mixing matrices

We investigate the cosmological viability of Kaniadakis Holographic Dark Energy (KHDE) within an anisotropic Bianchi-I spacetime, adopting a hyperbolic expansion law to parameterize the cosmic expansion history. To constrain the model’s free parameters, we employ a dual inferential strategy, comparing the results from a rigorous Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods with those from a computationally efficient deep learning approach utilizing Artificial Neural Networks (ANNs) for likelihood-free inference. Both techniques are applied to a comprehensive dataset comprising cosmic chronometer measurements of the Hubble parameter <italic>H</italic>( <italic>z</italic>), Baryon Acoustic Oscillation (BAO) data, and the Pantheon+ compilation of Type Ia Supernovae. Our analysis demonstrates the comparative efficacy of the neural network approach in capturing parameter constraints consistent with standard Bayesian methods, highlighting its potential for rapid cosmological inference in complex anisotropic models.

India

 Kapil

Lokesh Kumar Sharma

A comparative analysis of Bayesian and deep learning methods for constraining Kaniadakis holographic dark energy

Employing holographic duality, we evaluate the running coupling of a heavy quark-antiquark ( <math altimg='si4.svg'><mrow><mi>Q</mi><mover accent='true'><mi>Q</mi><mo>&#175;</mo></mover></mrow></math>) pair in the STU black hole background by computing the Nambu-Goto action for a fundamental string, whose worldsheet is anchored to a rectangular Wilson loop. It is shown that an increase in the black hole charge leads to a reduction in both the free energy and the running coupling of the <math altimg='si4.svg'><mrow><mi>Q</mi><mover accent='true'><mi>Q</mi><mo>&#175;</mo></mover></mrow></math>. This reduction implies a lowering of the free energy of <math altimg='si4.svg'><mrow><mi>Q</mi><mover accent='true'><mi>Q</mi><mo>&#175;</mo></mover></mrow></math>, thereby enhancing their thermodynamic stability and strengthening the quark-antiquark attractive interaction, while also weakening the intrinsic short-range strong interaction between quarks by reducing the running coupling of <math altimg='si4.svg'><mrow><mi>Q</mi><mover accent='true'><mi>Q</mi><mo>&#175;</mo></mover></mrow></math>.

China

Wenxing Cheng

Zi-qiang Zhang

The running coupling of a heavy quark-antiquark pair in the STU background

Recent studies have shown that the interplay between nonlinear electrodynamics (NLED) and a cloud of strings can significantly alter particle dynamics, motivating our investigation into whether the long-term dynamical evolution of such systems exhibits chaotic behavior. To test this hypothesis, we examine the Ayón-Beato-García black hole coupled to a cloud of strings (ABG NLED-CS). First, we construct a fourth-order explicit symplectic algorithm to ensure the accuracy and stability of long-term numerical integration. Then, by computing Poincaré sections and the fast Lyapunov indicator (FLI), we systematically analyze the influence of various parameters on particle orbital dynamics. The key parameters considered are the energy <italic>E</italic>, angular momentum <italic>L</italic>, magnetic field parameter <italic>&#946;</italic>, magnetic monopole charge <italic>g</italic>, and the cloud of strings parameter <italic>&#945;</italic>. The results indicate that in the absence of string-cloud coupling ( <math altimg='si14.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>), the parameters <italic>E, L, &#946;</italic>, and <italic>g</italic> barely induce any chaotic behavior. In other words, the string-cloud coupling effect is the key factor driving chaos. When string-cloud coupling is present ( <italic>&#945;</italic>&#8239;&#8800;&#8239;0), the chaotic region expands with increasing <italic>E, &#946;</italic>, and <italic>&#945;</italic>, but shrinks with increasing <italic>g</italic> or <italic>L</italic>. When multiple parameters are varied simultaneously, <italic>&#946;</italic> and <italic>g</italic> are found to play dominant roles.

Bai-Hua Liu

Da-Zhu Ma

Zhen-Meng Xu

Chaos in Ayón-Beato-García black hole coupled with cloud of strings

We compare the spectrum of the elliptic Ruijsenaars–Schneider model with the finite-size spectrum of the sine-Gordon model, highlighting both their similarities and differences. Our analysis focuses on the two-particle sector in the center-of-mass frame. At the free point, we carry out an analytic comparison, while at generic couplings we employ non-perturbative numerical calculations based on the truncated Hilbert space method adapted to difference operators. To benchmark this numerical approach, we first study the trigonometric limit, where analytic results are available. We then compare the Bethe–Yang momentum quantization conditions, derived from infinite-volume scattering phases, with the exact finite-volume solutions. We find that these conditions hold exactly in the rational and trigonometric cases, but acquire finite-size corrections in the hyperbolic and elliptic cases, however, these corrections are different in quantum field theories and in many body systems.

Hungary

Poland

Zoltan Bajnok

Apor Roth

Comparing the elliptic Ruijsenaars–Schneider model to the finite volume sine-Gordon theory

In this paper, we investigate for the first time the quasi-periodic oscillations (QPOs) that arise as a result of halting the Bondi-Hoyle-Lyttleton (BHL) accretion mechanism around a Kerr black hole. Unlike previous studies, which focused on shock cones or perturbed tori, we show that stopping BHL accretion leads to the formation of a new plasma structure. On this plasma structure, spiral shock waves are observed to develop. These shock waves are found to excite both low-frequency (LFQPOs) and high-frequency QPOs (HFQPOs). Two key results emerge from our numerical simulations. First, LFQPOs arise only when the halted flow is supersonic, identifying for the first time the velocity dependence of their formation. Second, nonlinear couplings that produce 3: 2, 2: 1, and 1: 2: 3 resonances appear exclusively for rapidly rotating black holes ( <math altimg='si1.svg'><mrow><mi>a</mi><mo linebreak='goodbreak'>/</mo><mi>M</mi><mo linebreak='goodbreak'>=</mo><mn>0.9</mn></mrow></math>), directly linking spin to resonance states. In addition, it is demonstrated that HFQPOs are strongly influenced by the black hole spin. The generated QPOs are observed to be excited through the modes induced by the black hole spacetime curvature. The frequencies obtained from the numerical simulations align with observations of <math altimg='si16.svg'><mrow><mi>G</mi><mi>R</mi><mi>S</mi><mn>1915</mn><mo linebreak='goodbreak'>+</mo><mn>105</mn></mrow></math>, <math altimg='si18.svg'><mrow><mi>X</mi><mi>T</mi><mi>E</mi><mi>J</mi><mn>1550</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>564</mn></mrow></math>, and <math altimg='si20.svg'><mrow><mi>R</mi><mi>E</mi><mi>J</mi><mn>1034</mn><mo linebreak='goodbreak'>+</mo><mn>396</mn></mrow></math>, thereby bridging stellar-mass and supermassive black hole systems within a unified framework. Thus, the newly uncovered physical mechanism associated with halted BHL accretion is capable of explaining both the persistence and the intermittency of QPOs across diverse astrophysical environments.

Kuwait

Orhan Donmez

Evolution of shock structures and QPOs after halting BHL accretion onto Kerr black hole

Positive and negative flows of the Chen-Lee-Liu model and its various reductions, including Burgers hierarchy, are formulated within the framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator. Two classes of vacua, namely zero vacuum and constant non-zero vacuum can be realized within a centerless Heisenberg algebra. The tau functions for soliton solutions are obtained by a dressing method and vertex operators are constructed for both types of vacua. We are able to select and classify the soliton solutions in terms of the type of vertices involved. A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method by letting them interact with various integrable defects.

Brazil

Ireland

Y.F. Adans

United States

H. Aratyn

C.P. Constantinidis

J.F. Gomes

G.V. Lobo

T.C. Santiago

New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations

In the canonical type-I seesaw mechanism for neutrino masses, a residual symmetry known as lepton parity: <math altimg='si21.svg'><msup><mrow><mo>(</mo><mo>&#8722;</mo><mn>1</mn><mo>)</mo></mrow><mi>L</mi></msup></math>, remains preserved. Introducing a Majorana fermion <italic>S</italic> with even lepton parity renders it naturally stable, making it a viable dark matter (DM) candidate. The addition of a lepton parity odd singlet scalar <italic>&#963;</italic> allows for the coupling <italic>NS&#963;</italic>, where <italic>N</italic> is the right-handed neutrino. If <italic>S</italic> is not thermalized, then DM relic can be produced in two distinct ways: (i) for reheating temperature, <italic>T</italic> <inf>rh</inf>&#8239;&gt;&#8239; <italic>m<inf>N</inf></italic>, dominantly through the decay of <italic>N</italic> ( <italic>N</italic>&#8239;&#8594;&#8239; <italic>S&#963;</italic>), and (ii) for <italic>T</italic> <inf>EW</inf>&#8239;&lt;&#8239; <italic>T</italic> <inf>rh</inf>&#8239;&#8810;&#8239; <italic>m<inf>N</inf></italic>, via standard model Higgs ( <italic>h</italic>) decay ( <italic>h</italic>&#8239;&#8594;&#8239; <italic>SS</italic> at one loop). If the <math altimg='si22.svg'><mrow><mi>&#963;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>h</mi></mrow></math> quartic coupling is large, then it can lead to a strong first-order electroweak phase transition even if <math altimg='si23.svg'><mrow><mo>&#9001;</mo><mi>&#963;</mi><mo>&#9002;</mo><mo>=</mo><mn>0</mn></mrow></math>. Alternatively, if <math altimg='si22.svg'><mrow><mi>&#963;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>h</mi></mrow></math> coupling is small, then <italic>&#963;</italic> can freeze out with a larger abundance, and hence its decay ( <italic>&#963;</italic>&#8239;&#8594;&#8239; <italic>S&#957;</italic>) at late epochs can give rise to additional relativistic degrees of freedom (&#916; <italic>N</italic> <inf>eff</inf>). Thus, the framework gives a viable DM with mass range varying from MeV to TeV and leaves observable imprints, via gravitational waves and &#916; <italic>N</italic> <inf>eff</inf>, which offer complementary probes, potentially detectable in future gravitational wave and CMB experiments.

Ernest Ma

Partha Kumar Paul

Narendra Sahu

Cosmological probes of lepton parity freeze-in dark matter: Δ <italic>N</italic> <inf>eff</inf> &amp; gravitational waves

William Allan Bardeen (September 15, 1941 − November 18, 2025) was an American theoretical physicist who worked at the Fermi National Accelerator Laboratory. He is renowned for his foundational work on the chiral anomaly, the Adler-Bardeen theorem, the non-Abelian anomaly and gravitational anomalies. He was instrumental in the development of quantum chromodynamics and its applications, such as semileptonic decays and the <math altimg='si1.svg'><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mover accent='true'><mrow><mi>M</mi><mi>S</mi></mrow><mo>&#175;</mo></mover></msub></math> scheme frequently used in perturbative analysis of high energy processes involving strong interactions. Bardeen also played a major role in developing a theory of dynamical breaking of electroweak symmetry via top quark condensates, leading to one of the first composite Brout-Englert-Higgs boson models. His work on the chiral symmetry dynamics of heavy-light quark bound states correctly predicted abnormally long-lived resonances which are chiral symmetry partners of the ground state.

Christopher T. Hill

William A. Bardeen: A life in physics and the legacy of the chiral anomaly <cross-ref id='crf0001' refid='bib0001'>[1]</cross-ref>

We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory. For reasons that will become clear, we call this quotient the mixed doubles category, <math altimg='si2.svg'><mi mathvariant='sans-serif'>MD</mi></math>. Then our main result is a theorem classifying all mixed doubles representations in rank-2.