A new study shows that in classically scale‑invariant extensions of the Standard Model the electroweak phase transition happens in a single, strongly supercooled step and completes at temperatures higher than the QCD scale. The authors compute the bubble‑nucleation path in two dimensions and then follow the fraction of space still in the false vacuum. They define the percolation temperature as the point where the integral of the nucleation rate equals 0.34.

The analysis keeps the wall velocity ultrarelativistic (vw = 1) and uses a temperature dependence g* = const. The benchmark points BP1 – BP3 illustrate how the transition strength parameter α falls from 546 to 3.30, while the inverse duration parameter β/H rises from 127 to 243. These values are obtained from a bootstrap fit to the Euclidean action, with quoted uncertainties reflecting numerical scatter and fitting errors.

The viable parts of parameter space are trimmed by experimental constraints: Higgs signal‑strength measurements rule out large scalar mixing or h → ηη decays; LEP bounds eliminate points with strong mixing at small βQ; and Landau‑pole or perturbativity checks exclude regions where the quartic couplings run too fast. The surviving one‑step band lies around 0.12 ≲ αQ/4π ≲ 0.2 and βQ/4π ≲ 0.03, within which the chosen benchmarks reside.

These results demonstrate that a strongly supercooled electroweak transition can be consistent with collider data, but the allowed parameter space remains narrow and is shaped by Higgs measurements and perturbativity limits.