We investigate a scalar–vector–tensor theory in which matter is minimally coupled to a Jordan-frame metric $$\tilde{g}_{\mu \nu }=(1+\Xi )g_{\mu \nu }$$ , while a massive vector sector interacts with the baryonic current. We show that the conformal scalar coupling modifies the physical expansion rate measured by matter observers, leading to an enhancement of the Hubble constant inferred at low redshift. We stress, however, that the Hubble rate is not a conformal invariant, whereas the acoustic angular scale $$\theta _s$$ is, and we derive the exact integral condition that the scalar field evolution must satisfy. We show that a single-signed scalar velocity cannot satisfy it, and we construct instead a two-epoch phenomenological evolution which matches $$\theta _s$$ exactly while retaining the late-time enhancement, at the cost of a small pre-recombination shift of the effective gravitational coupling. We stress that the scalar is not separately conserved, and that retaining the scalar–matter energy exchange in its continuity equation supplies a further restriction: positivity of the scalar energy density bounds the early component to $$z_E\lesssim 13$$ . Notably, the recombination $\textit{temperature}$ is unmodified, since particle masses are constant in the Jordan frame, only the expansion rate at that epoch being altered. The scalar potential naturally acts as a dynamical dark-energy sector, while the vector sector provides two distinct contributions. The temporal component, determined algebraically by the baryon current, yields an apparent matter-like term in the background expansion that is not a true fluid but rather a manifestation of the interaction energy. The propagating spatial modes, on the other hand, form a vector condensate that behaves as a collisionless pressureless component and can play the cosmological role of cold dark matter. Hence, the framework connects scalar dynamics, effective dark-energy evolution, and the $$H_0$$ tension within a single setup. Finally, local gravitational constraints require a chameleon-type screening mechanism, whose efficiency we discuss critically.

North Macedonia

Kimet Jusufi

Iran

Amir Khodahami

Ahmad Sheykhi

Malta

Jackson Said

Chile

China

Greece

Emmanuel Saridakis

Unified dark sector and Hubble-tension alleviation in scalar–vector–tensor gravity

We investigate the thermodynamics and thermodynamic geometry of three classes of Anti-de Sitter (AdS) black holes arising from nonlinear electrodynamics, namely ModMax, nonlinear electrodynamics (NED), and Euler–Heisenberg black holes, together with their holographically dual conformal field theory (CFT) descriptions. The analysis is performed using the standard Bekenstein–Hawking entropy as well as the generalized R’enyi and Kaniadakis entropy formalisms. The phase structure is characterized through the temperature, specific heat, and the Legendre-invariant scalar curvature of geometrothermodynamics (GTD). We show that thermodynamic critical points coincide with extrema of the temperature–entropy curve, divergences of the specific heat, and singularities of the GTD curvature, establishing a consistent geometric characterization of phase transitions. A comparison between the bulk black holes and their dual CFTs further demonstrates that the number, ordering, and structure of the critical points are preserved under the holographic correspondence, providing a nontrivial consistency check of bulk-boundary thermodynamics rather than a proof of the AdS/CFT correspondence. The Euler–Heisenberg AdS black hole exhibits the richest phase structure among the models considered, while the Kaniadakis entropy consistently introduces an additional critical point absent in the Bekenstein–Hawking and R’enyi descriptions. These results illustrate how nonlinear electromagnetic interactions and generalized entropy formalisms jointly influence the thermodynamic behavior of AdS black holes and their holographic duals.

India

Abhishek Baruah

Amijit Bhattacharjee

Prabwal Phukon

Testing the AdS/CFT correspondence through thermodynamic geometry of nonlinear electrodynamics AdS black holes with generalized entropies

Recently the CMS and ATLAS Collaborations have found evidence for an unexpectedly large $${\textrm{t}}{\bar{\textrm{t}}}$$ cross section in the threshold region, with an excess of the order of 5–10 pb relative to continuum perturbative calculations. A convenient approach to the theoretical study of this region, unifying the above- and below-threshold behaviour, is the non-relativistic Green’s function formalism. It was first applied to top production more than 35 years ago, well before the discovery of the top. We therefore revive and dissect the old formalism, and put it back together in a more consistent form, suited for Monte Carlo event generation. Combined with some practical prescriptions, it can be applied to current conditions. As an example, the below-threshold cross section comes out to be of the order of 6.5 pb, $\textit{i.e.}$ comparable with the CMS and ATLAS numbers. The new code is publicly available in the event generator so can be used for more detailed comparisons.

Sweden

Torbjörn Sjöstrand

United Kingdom

Valery Khoze

Germany

Christian Preuss

Top pair threshold revisited

Experimental limits on neutrino magnetic moments remain several orders of magnitude above the predictions of the Standard Model; therefore, any future detection would provide unambiguous evidence for new physics. In models with Dirac neutrinos, however, mechanisms that enhance the magnetic moment typically generate excessively large neutrino masses. Recently, it has been argued that in frameworks where neutrinos mix with weak-triplet Dirac fermions, the magnetic moment can be decoupled from the neutrino mass. In this work, we revisit this possibility and show that sizable enhancements remain highly nontrivial to realize naturally. We demonstrate that, although the minimal realization allows the magnetic moment to be decoupled from the neutrino mass, obtaining an observable enhancement requires a delicate adjustment of the model parameters. Moreover, in extended scenarios, the decoupling no longer persists: the magnetic moment and neutrino mass become intrinsically linked, such that attempts to enhance the former inevitably induce large contributions to the latter.

Slovenia

Svjetlana Fajfer

Shaikh Saad

Weak triplet models of neutrino magnetic moments

We point out several algebraic and dimensional inconsistencies in the derivation of the teleparallel double-wall dynamics and of the axial torsion coupling bound published in this Journal [Eur. Phys. J. C (2026) 86: 785]. Recomputing the torsion two-forms from the tetrads with vanishing spin connection, we obtain expressions that differ from those used in the paper. Consequently, the equations for the wall separation function do not lead to the reported solution, and the approximation $$h^2\ll z^2$$ does not restore the polynomial form adopted there. We also show that the proposed wave equation for the wall separation and the corresponding gravitational-wave interpretation require rederivation. In the fermionic sector, the zero-mode solutions and the scalar Dirac bilinear must be distinguished from the positive density $$\varPsi ^\dagger \varPsi $$ . With the corrected solutions, the effective coefficient $$A=eB+g_T S$$ determines a localization length $$\ell _{\textrm{loc}}\sim |A|^{-1/2}$$ , so that estimating $$g_T$$ requires specifying an additional physical scale rather than imposing $$A=0$$ . Hence the claimed constant condensate and the bound $$g_T\sim 10^{-4}$$ are not established by the calculations presented.

Brazil

Luis Castro

Comment on “Einstein–Cartan fermion condensates trapped in double walls induce axial torsion coupling bounds [Eur. Phys. J. C (2026) 86: 785]”

We investigate the supercritical thermodynamics of Euler–Heisenberg AdS black holes within the framework of Lee–Yang phase transition theory. We show that the system admits two distinct critical points associated with a four-phase thermodynamic structure and identify a degenerate higher-order critical point where the two criticalities merge. Extending the thermodynamic description into the complex domain, we determine the distribution of Lee–Yang singularities and construct the corresponding complex phase diagrams. At the degenerate critical point, we find that a well-defined Widom line emerges despite the absence of a conventional coexistence curve, acting as an effective stability boundary in the supercritical regime. In the two-critical-point regime, the complex phase diagram exhibits two distinct Widom lines, one associated with a coexistence curve and the other arising solely from the complex singularity structure. We further show that the Lee–Yang formalism consistently reproduces the expected phase structure for systems with a single critical point and in the absence of criticality. Our results reveal a rich supercritical phase structure and provide new insights into the origin and physical interpretation of Widom lines.

Mozib Awal

Complex phase structure and Widom line for Euler–Heisenberg black holes

A right-handed neutrino is a promising candidate for dark matter (DM) which has no interaction with nuclei. Since two right-handed neutrinos explain neutrino oscillation data and baryon number asymmetry through both the seesaw mechanism and leptogenesis based on the out-of-equilibrium decay of the lighter one, the lightest third right-handed neutrino could be free from them and stable to be DM. It suggests a possibility that the right-handed neutrinos could be common key particles for the explanation of three problems in the standard model (SM). We study this possibility by analyzing the structure of a neutrino mass matrix in the scotogenic model for neutrino mass.

Japan

Daijiro Suematsu

Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry

Recent time-domain analyses suggest that black hole stability may be sensitive to localized near-horizon geometric deformations, while the underlying spectral mechanism remain unclear. In this work, after verifying the instability of the model in the time domain, we systematically investigate quasi-normal mode spectra under static localized non-positive perturbations within a frequency-domain framework. We find that such deformations generically induce a new purely imaginary mode. As the deformation approaches the horizon, the imaginary part of this mode increases and eventually enters the upper half complex-frequency plane, signaling the onset of black hole instability. Numerical results reveal clear scaling relations between the critical distance for instability and the deformation strength. We further derive rigorous proofs for our discoveries in frequency domain. These results demonstrate that black hole stability under long scale is conditionally sensitive to localized deformation of metric near the horizon and establish a unified spectral framework for understanding their induced instabilities.

Shi-Jie Ma

Zhan-Feng Mai

Run-Qiu Yang

Near-horizon deformation of metric and the black hole instability

<p>In the three-flavor neutrino oscillation framework, we investigate the transition probabilities of an initial muon neutrino flavor state in the presence of nonstandard interactions (NSIs) characterized by complex off-diagonal (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>ε</mi><mrow><mi>α</mi><mi>β</mi></mrow></msub><mo stretchy="false">|</mo><msup><mi>e</mi><mrow><mi>i</mi><msub><mi>ϕ</mi><mrow><mi>α</mi><mi>β</mi></mrow></msub></mrow></msup></math>) and diagonal parameters (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>ε</mi><mrow><mi>α</mi><mi>α</mi></mrow></msub><mo>−</mo><msub><mi>ε</mi><mrow><mi>β</mi><mi>β</mi></mrow></msub><mo stretchy="false">|</mo></math>), including a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase and a constant matter potential, under both normal (NO) and inverted mass ordering (IO) scenarios. Within these scenarios and through the lens of mode entanglement, bipartite entanglement measures such as entanglement entropy and capacity of entanglement are quantified in terms of the transition probabilities, which can be measured in neutrino oscillation experiments. Using these two bipartite entanglement measures, we further explore the quantum speed limit (QSL) time, which describes how rapidly bipartite entanglement evolves during neutrino oscillations. We illustrate our results using the baseline lengths and energies corresponding to ongoing long-baseline accelerator neutrino experiments, such as T2K, NOvA, and the upcoming DUNE experiment. In the presence of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase and a constant matter potential, both with and without NSI effects, we compare the QSL time behavior for bipartite entanglement in neutrino oscillations for NO and IO. The most pronounced discrepancies in the QSL time for bipartite entanglement arise from the off-diagonal NSI parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ε</mi><mrow><mi>μ</mi><mi>τ</mi></mrow></msub></math> across both the NO and IO scenarios. We emphasize that among all the experiments considered, NOvA and DUNE exhibit a rapid suppression of bipartite entanglement in neutrino oscillations in the standard oscillation scenario with NO at the end of their baseline lengths for the corresponding best-fit value of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase. Our results hint at a possible imprint of new physics in neutrino oscillations.</p>

Abhishek Kumar Jha

Lekhashri Konwar

Rukmani Mohanta

Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions

<p>There are two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factors frequently used in the phenomenology of exclusive processes at small values of the Bjorken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> variable. One <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factor takes into account the effects of nonzero longitudinal momentum transfer, which is assumed to be zero in the dipole scattering amplitude. Another <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factor accounts for the real part of the elastic scattering amplitude which is often neglected, with the standard dipole scattering amplitude giving only the imaginary part of the elastic amplitude. In this work we present two new theoretical developments aimed at eliminating the need for the two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factors. We argue that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factors can be replaced by (i) modifying the argument of the dipole scattering amplitude and by (ii) augmenting the initial conditions for its nonlinear small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> evolution. Specifically, we show that to account for the effects of nonzero skewness <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math>, one has to replace the rapidity argument <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo>=</mo><mi>ln</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo stretchy="false">)</mo></math> of the eikonal dipole amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> and the odderon dipole amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Y</mi><mo>=</mo><mi>ln</mi><mtext> </mtext><mi>min</mi><mrow><mo stretchy="false">{</mo><mn>1</mn><mo>/</mo><mo stretchy="false">|</mo><mi>x</mi><mo stretchy="false">|</mo><mo>,</mo><mn>1</mn><mo>/</mo><mo stretchy="false">|</mo><mi>ξ</mi><mo stretchy="false">|</mo><mo stretchy="false">}</mo></mrow></mrow></math>. The prescription applies to the elastic scattering cross sections, as well as for calculations of the generalized parton distributions and generalized transverse momentum dependent parton distributions at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and at small but nonzero skewness <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math>. We also show that the real part of the scattering amplitude, proportional to Im <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, which is intimately connected to the signature factor of the amplitude, can be accounted for by a more careful evaluation of the initial condition for the evolution and by writing the nonlinear evolution equation in an integral form. One can similarly construct Im <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi></math> for the odd-signature odderon amplitude. We hope that future implementation of our prescriptions presented here will eliminate the need for both phenomenological <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-factors.</p>

United States

Yuri V. Kovchegov

M. Gabriel Santiago

Huachen Sun

Two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> factors in the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math> shockwave formalism