We present a comprehensive bottom-up analysis of lepton mass and mixing based on the non-holomorphic $A_{4}$ modular symmetry. Neutrinos are assumed to be Majorana particles, and the light neutrino masses are generated through the Weinberg operator. In this framework, we construct all phenomenologically viable models with minimal number of free parameters, with the Yukawa couplings expressed in terms of polyharmonic Maaß forms of weights $\pm4$ , $\pm2$ , and 0 at level $N=3$ . Without imposing generalized CP (gCP) symmetry, we identify 147 (six) viable models with eight real free parameters that successfully reproduce the current experimental data of the lepton sector for the normal (inverted) mass ordering. When gCP symmetry consistent with $A_{4}$ modular symmetry is included, the number of free parameters is reduced by one, yielding 47 (five) phenomenologically viable models in the normal (inverted) mass ordering. Finally, we present detailed numerical analyses of a representative model for both mass orderings to illustrate these results.

China

Xiang-Yan Gao

Cai-Chang Li

Minimal lepton models with non-holomorphic modular $\textit{A}$ $_{4}$ symmetry * Supported by Natural Science Basic Research Program of Shaanxi (2024JC-YBQN-0004) and the National Natural Science Foundation of China (12547106, 12247103)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

We analyze the gauge dependence of the effective action in an interacting quantum theory of gravitational and matter fields. An explicit off-shell result is obtained in a general background gauge at one-loop order, which reduces in a particular gauge to the effective action found by ’t Hooft and Veltman [Ann. Inst. Henri Poincare Phys. Theor. A 20, 9 (1974)]. We confirm the validity of DeWitt-Kallosh theorem, which implies that the on-shell effective action should be independent of the gauge-fixing parameter. We employ this theorem to expose the nonrenormalizability of the theory in a general background gauge.

J. Frenkel

S. Martins-Filho

Quantum gravity and matter fields in a general background gauge

We develop a unified framework for analyzing black hole thermodynamics and spacetime structure in Einstein gravity coupled to causal nonlinear electrodynamics in asymptotically anti–de Sitter (AdS) backgrounds. The electromagnetic sector is governed by a generalized nonlinear electrodynamics Lagrangian obtained from a root-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math> deformation constructed via the Courant-Hilbert approach, ensuring both duality invariance and causal propagation. This theory contains modified Maxwell (ModMax), generalized Born-Infeld, and self-dual logarithmic electrodynamics as continuous limits. Within this framework we obtain exact charged AdS black hole solutions and perform a detailed study of their thermodynamic properties, including mass, temperature, entropy, and free energy. The resulting phase structure exhibits van der Waals–type transitions between small and large black holes and features a characteristic swallowtail in the free energy at the critical point. We further investigate the internal geometry, showing that the nature of the central singularity is determined by the matter fields that source the spacetime. An analysis of the Kretschmann scalar reveals how mass and electric charge jointly govern curvature divergence in ModMax black holes. We derive an explicit charge-to-mass bound within a causal logarithmic electrodynamic theory. This extends the finite self-energy property of the point charge beyond the standard Born-Infeld model. This bound cleanly distinguishes black holes from naked singularities, showing that naked singularities occur precisely when the mass parameter is smaller than the electromagnetic self-energy of the point charge. This provides a clear energetic criterion for horizon formation in the absence of a Cauchy horizon.

H. Babaei-Aghbolagh

Komeil Babaei Velni

Song He

Fateme Isapour

Unified causal framework for a nonlinear electrodynamics black hole from the Courant-Hilbert approach: Thermodynamics and singularity

Higgs boson pair production in the massless quark-antiquark channel proceeds at leading order (LO) via electroweak boson loops. We calculate the next-to-leading order QCD corrections to this process. For the corresponding two-loop amplitudes, an analytic representation has been achieved. Even though the size of this contribution at the level of total cross sections is below 1% compared to the LO gluon channel, the effect on differential observables can be in the 10% range and therefore this contribution should be taken into account when comparing to LHC data.

Germany

Marco Bonetti

Gudrun Heinrich

Philipp Rendler

United Kingdom

William Torres Bobadilla

NLO QCD corrections to the electroweak production of a Higgs boson pair in the quark-antiquark channel

We investigate the QCD phase diagram and the associated Lee–Yang edge singularities using the two-flavor nonlocal Nambu–Jona-Lasinio model extended to complex chemical potential. We show explicitly there exists a strong correlation between the chiral phase transition and the patterns in the effective potential in the complex plane of order parameter, serving as a criterion to differentiate crossover from first-order transitions. Typically, the Lee–Yang edge singularities can be understood as a generalization of the critical end point (CEP) separating the crossover and the first-order transition, where the positive Nambu phase and the Wigner phase coalesce. We further analyze the scaling behavior near the CEP by extracting the critical exponent associated with the Lee–Yang singularities. Additionally, we confirm that the extrapolation of the Lee–Yang edge singularity trajectories provides an efficient method of determining the CEP location, even at a small real chemical potential. This provides a viable method for exploring regions of the QCD phase diagram that remain inaccessible to lattice QCD.

Zong-shuai Zhang

Yi Lu

Yu-xin Liu

Lee-Yang edge singularities in a nonlocal Nambu–Jona-Lasinio model

We discuss spontaneous Leptogenesis in the Type II Seesaw model of neutrino masses featuring an electroweak triplet scalar $\textit{T}$ in a coherent pseudo Nambu-Goldstone boson (pNGB) background. In the “wash-in” scenario the inverse decays of Higgs bosons to $\textit{T}$ generate a chemical potential for the triplet, that is then transmitted to the lepton sector via the leptonic decays of $\textit{T}$. Our mechanism works with a single triplet, that can be as light as 1 TeV, and has a vacuum expectation value $\textit{v}$ in the window $$ \mathcal{O}\left(1\ \textrm{keV}\right) $$ < $\textit{v}$ < $$ \mathcal{O}\left(1\ \textrm{MeV}\right) $$ . This range of $\textit{v}$ can lead to appreciable decays of the triplet’s doubly charged component into both same sign di-leptons and same sign pairs of $\textit{W}$-bosons, which could potentially allow for an experimental distinction from a recently proposed inflationary Type II Seesaw Affleck-Dine scenario preferring the leptonic mode. In the “singlet-doublet-triplet Majoron” UV-completion of the Type II Seesaw model, the required pNGB is automatically included in the form of the Majoron, that originates from the phase of the lepton number breaking singlet scalar. The coherent motion of the Majoron can furthermore explain the dark matter relic abundance via the kinetic misalignment mechanism. Cogenesis of dark matter and the baryon asymmetry can work for a lepton number breaking scale of $$ \mathcal{O}\left({10}^5\ \textrm{GeV}\right) $$ < $\textit{v}$ < $$ \mathcal{O}\left({10}^8\ \textrm{GeV}\right) $$ and a Majoron mass of $$ \mathcal{O}\left(1\ \textrm{eV}\right) $$ > $\textit{m}$ > $$ \mathcal{O}\left(1\ \upmu \textrm{eV}\right) $$ .

Spain

Maximilian Berbig

Type II Seesaw Leptogenesis in a Majoron background

We investigate gravitational wave signals in a nonsupersymmetric grand unified model where the group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> is broken in two steps to the Standard Model gauge group. We calculate the analytical form of the one-loop effective potential responsible for the first step of symmetry breaking and show that it can lead to a first-order phase transition with gravitational wave production. We also determine the gravitational wave background produced by the primordial plasma of relativistic particles. The present experimental sensitivity is still far from the expected signals but could be in reach of novel detector concepts.

Injun Jeong

Jörn Kersten

Stefano Scopel

Liliana Velasco-Sevilla

Gravitational wave signals in a promising realization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> unification

We establish a no-go theorem in the context of string and M-theory flux compactifications on Riemann-Flat manifolds with Casimir energy. Specifically, we show that no dS minimum exists in this setup in dimension $\textit{d}$ > 3. The case of dS minima is not excluded, but their actual fate can only be ascertained via an explicit construction. We also point out that the problem of finding dS minima on RFM’s and more general flux compactifications is mathematically equivalent to a semidefinite programming problem, identical to those studied in CFT bootstrap, and hence the search for dS can benefit from the existing vast literature and numerical tools. We illustrate this in a toy model.

Bruno Bento

Miguel Montero

de Sitter no-go’s for Riemann-flat manifolds and a link to semidefinite optimisation

The future circular $\textit{e}$ $\textit{e}$ collider (FCC-ee or CEPC) will provide unprecedented sensitivity to indirect new physics signals emerging as small deviations from the Standard Model predictions in electroweak precision tests. Assuming new physics scenarios containing a dark matter candidate and a $\textit{t}$-channel mediator, we analyse the synergy and interplay of future Tera-$\textit{Z}$ factories and non-collider tests conducted through direct and indirect searches of dark matter. Our results highlight the excellent prospect for a Tera-$\textit{Z}$ run to indirectly probe the presence and nature of dark matter.

Italy

Pablo Olgoso

Paride Paradisi

Nudžeim Selimović

The dark side of a Tera-$\textit{Z}$ factory