Renormalization-group analysis of the SM: Loops, uncertainties, and vacuum stability
In the Standard Model (SM), renormalization group equations (RGEs) control the evolution of coupling constants from the electroweak scale up to the Planck scale. Of particular interest is the running of the Higgs self-coupling, which determines the stability of the electroweak vacuum.
A study of coupled SM RGEs was carried out in various orders of perturbation theory: from one-loop up to the state-of-the-art three- and partially four-loop orders. Main focus was on comparing the standard ("diagonal") approach, in which beta functions for gauge, Yukawa, and Higgs interactions are taken at the same loop order, with "nondiagonal" configurations motivated by Weyl consistency conditions. The dependence of parametric uncertainties (related to the precision of experimental data) and theoretical uncertainties (due to unknown higher-order contributions) on the employed loop orders was investigated. As an application, the electroweak vacuum decay probability was estimated. It was shown that the use of nondiagonal beta functions and the corresponding matching conditions leads to larger theoretical uncertainty compared to the diagonal approach.
A.V. Bednyakov, A.S. Fedoruk, D.I. Kazakov. Phys. Rev. D 113, 036018 (2026). DOI: 10.1103/lgnl-2nxv
Anisotropy of the electron mobility of two-dimensional biphenylene structures.
Phonon-limited electron mobility has been theoretically studied for a recently synthesized carbon allotrope, two-dimensional biphenylene. Quasi-one-dimensional structures corresponding to those obtained experimentally have been calculated. It has been found that the mobility increases linearly with the ribbon width. The strong anisotropy of the electron conductivity and mobility has been observed in two-dimensional biphenylene. Specifically, the mobility is 102 cm2/(V s) in the crystallographic direction corresponding to one-dimensional structures, while it is an order of magnitude higher in the perpendicular direction. The calculations have been performed using the nonorthogonal tight-binding method.
Katkov, V. L., Osipov, V. A. JETP Letters 123, 106 (2026). DOI: 10.1134/S0021364025609716
New minimal set of spherical bipolar harmonics
In many applications one has to deal with functions that depend on two directions. A convenient basis for function expansion is provided by bipolar harmonics that are given by an irreducible tensor product of the spherical functions with different arguments. The basis of biharmonic functions is overcomplete for a fixed total angular momentum and for arbitrary internal angular momenta. Bipolar harmonics with a small rank of total momentum often enter the final results while the ranks of the internal tensors can run over a wide (or infinite) range. But it is possible to decompose the bipolar harmonic using the smallest set of internal orbital momenta for a fixed total momentum. Here, the new method is applied for calculations of decomposition coefficients at low values of total angular momenta and arbitrary values of internal momenta. Basis functions from the minimal set are modified in two respects: 1. Expansion coefficients include total dependence on the angle between two directions and basis functions are independent from this angle. 2. New basis is orthogonal and normalized to the absolute value of unity. These tensors form the normalized orthogonal basis from the minimal set of bipolar harmonics.
S. N. Ershov. Phys. Rev. C 113, 014003 (2026). DOI: 10.1103/qzqx-h4hd
Representations of Hecke algebras and Markov dualities for interacting particle systems
Many continuous reaction-diffusion models on Z (annihilating or coalescing random walks, exclusion processes, voter models) admit a rich set of Markov duality functions which determine the single time distribution. A common feature of these models is that their generators are given by sums of two-site idempotent operators. In this paper, we classify all continuous time Markov processes on {0,1}Z whose generators have this property, although to simplify the calculations we only consider models with equal left and right jumping rates. The classification leads to six familiar models and three exceptional models. The generators of all but the exceptional models turn out to belong to an infinite dimensional Hecke algebra, and the duality functions appear as spanning vectors for small-dimensional irreducible representations of this Hecke algebra. A second classification explores generators built from two site operators satisfying the Hecke algebra relations. The duality functions are intertwiners between configuration and co-ordinate representations of Hecke algebras, which results in novel co-ordinate representations of the Hecke algebra. The standard Baxterisation procedure leads to new solutions of the Young-Baxter equation corresponding to particle systems which do not preserve the number of particles.
A. Povolotsky, P. Pyatov, R. Tribe, B. Westbury, and O. Zaboronski. Ann. Inst. H. Poincaré — Probab. Statist. 61, 967-1020 (2025). DOI: 10.1214/23-AIHP1449
Casimir effect for scalar field rotating on a disk
We compute the vacuum energy of a scalar field rotating with angular velocity Ω on a disk of radius R and with Dirichlet boundary conditions. The rotation is introduced by a metric obtained by coordinate transformation from a rest frame to rotation frame. The constraint ΩR < c must be obeyed to maintain causality. To compute the vacuum energy, we use an imaginary frequency representation and the well-known uniform asymptotic expansion of the Bessel function. We use the zeta-functional regularization and separate the divergent contributions, which we discuss in terms of the heat kernel coefficients. The divergences are found to be independent of rotation. The renormalized finite part of the vacuum energy is negative and becomes more negative with increasing rotation velocity.
M. Bordag, I.G. Pirozhenko. Eur. Phys. Lett. 150, 52001 (2025). DOI: 10.1209/0295-5075/add806