Phase transitions in dimensional reduction up to three loops*

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Abstract
We perform the first computation of phase-transition parameters to cubic order in , where m is the scalar mass and T is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalization-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings and largely surpass those from 3-loop thermal masses.
Funding Information
  • Agencia Estatal de Investigación (10.13039/501100011033)
  • Agencia Estatal de Investigación (CNS2022-136024)
  • European Regional Development Fund (PID2021-128396NB-I00)
  • European Regional Development Fund (PID2022-139466NB-C22)

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