Exploring loop-induced first-order electroweak phase transition in the Higgs effective field theory

The nearly aligned Higgs Effective Field Theory (naHEFT) is based on the general assumption: all deviations in the Higgs boson couplings are originated from quantum one-loop effects of new particles that are integrated out. If the new particles integrated out have the same non-decoupling property, physics of the electroweak symmetry breaking can be then described by several parameters in the naHEFT, so that there is a correlation among the Higgs boson couplings such as $h \gamma \gamma$, $hWW$ and $hhh$ couplings. In this paper, we analyze the strongly first-order electroweak phase transition (EWPT) with the condition of sphaleron decoupling and the completion condition of the phase transition, and investigate the relation among the deviations in the Higgs boson couplings and the dynamics of the EWPTs. We also take into account the gravitational wave spectrum as well as the primordial black hole predicted at the EWPT. We show that if the new particles integrated out include charged scalar states future precision measurements of the $h \gamma \gamma$ coupling can give a useful prediction on the $hhh$ coupling to realize the strongly first-order EWPT. We can explore the nature of EWPT and the new physics behind it by the combination of precision measurements of various Higgs boson couplings at future collider experiments, gravitational wave observations at future space-based interferometers and searches for primordial black holes.