arXiv subjects

Fabio Bernardo

Publications and source records attributed to Fabio Bernardo.

3 recordsLinked to original sources

arXiv2026

Matching higher-dimensional operators at finite temperature for general models

High-temperature dimensional reduction provides a systematic effective field theory framework for studying finite-temperature thermodynamics and cosmological phase transitions. While the matching of super-renormalizable operators in the resulting three-dimensional effective theories is well established, the matching of higher-dimensional operators has recently been reinvigorated. These operators become phenomenologically relevant in strong first-order phase transitions where they quantify the convergence of the high-temperature expansion. This work automates the matching of generic three-dimensional dimension-five and -six operators for arbitrary models containing scalars, fermions, and gauge fields, implemented as an extension of the Mathematica package DRalgo. We present the operator basis, the matching procedure, and explicit examples including a scalar-Yukawa model, hot QCD, and the full Standard Model up to dimension six, covering operators mixing the strong and electroweak sectors as well as parity-violating contributions. Redundant operators, gauge dependence, and the corresponding field redefinitions are discussed in detail. The code and example model files are publicly available at https://github.com/DR-algo/DRalgo.

hep-ph↗

arXiv2026

Hard thermal contributions to phase transition observables at NNLO

To construct the high-temperature effective field theory of gauge-Higgs models up to $\mathcal{O}(g^6)$ in the gauge coupling, we integrate out hard modes to three-loop level and use the next-to-next-to-leading order effective potential. For the Abelian Higgs model, we quantify the impact of both higher-dimensional operators and higher-loop corrections on thermodynamic parameters relevant for gravitational-wave observables, finding that one-loop dimension-six effects typically dominate over two- and three-loop corrections to super-renormalizable parameters for the strongest transitions. We derive the three-loop scalar and Debye masses for the ${\rm U(1)}$ and ${\rm SU}(N)$ gauge-Higgs models, as well as the two-loop quartic couplings for the Abelian case, show gauge independence of physical parameters, and demonstrate that no new master integrals are required for the matching, while consistency of 4d and 3d renormalizability points to previously missing contributions in these master integrals. As a byproduct, we report a previously missing contribution to the three-loop QCD Debye mass.

hep-ph↗

arXiv2025

Higher-dimensional operators at finite-temperature affect gravitational-wave predictions

We investigate the effect of higher-dimensional marginal operators on the thermodynamics of cosmological phase transitions. Using the Abelian Higgs model as a representative for radiatively-generated one-step transitions, we systematically match these operators, which arise at higher orders in the underlying high-temperature expansion of thermal effective field theory, and use field redefinitions to construct a complete, minimal, and gauge-invariant operator basis. The Abelian Higgs model shares the essential infrared structure of more realistic gauge-Higgs theories at high temperatures, allowing us to test the validity of dimensional reduction in a simplified setting. We argue that for strong transitions, temporal gauge modes, which enhance the transition strength, should be treated on equal footing with spatial ones. Marginal operators are found to weaken the transition and introduce significant uncertainties for strong transitions. For transitions strong enough to produce gravitational waves detectable by LISA, our findings suggest that the high-temperature expansion may break down entirely. This would limit the applicability of effective theory techniques, including their use in non-perturbative lattice studies.

hep-ph↗