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Hard thermal contributions to phase transition observables at NNLO
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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.
Forward citations
Cited by 7 Pith papers
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Matching higher-dimensional operators at finite temperature for general models
The authors automate matching of generic 3D dimension-five and -six operators for arbitrary models, implemented in an extension of DRalgo with public code and examples for scalar-Yukawa, hot QCD, and the full Standard Model.
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Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT
The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
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SIRENA -- Sum-Integral REductioN Algorithm
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Polyakov Loops Tame Phase Transitions
Polyakov loop contributions to the thermal effective potential soften electroweak phase transitions, disfavoring first-order transitions and suppressing gravitational-wave signals.
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Matchotter: An Automated Tool for Dimensional Reduction at Finite Temperature
Matchotter automates one-loop finite-temperature dimensional reduction and supersoft matching for generic Lagrangians using functional techniques.
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A critical look at low-scale cosmological phase transitions in the PTA era
Precision study of dark sector phase transitions finds PTA-favored parameters near EFT breakdown with disfavored GW signals after higher-order corrections.
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Higher-dimensional operators and Polyakov loop in hot Scalar QED from the heat kernel
Computes dimension-six operators in finite-temperature massive scalar QED via heat kernel methods and evaluates their combined effect with the Polyakov loop on first-order phase transition thermodynamics.
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