Interplay between decoupling and non-decoupling effective field theories in electroweak phase transitions

Abstract

Gravitational-wave (GW) observations offer a promising probe of new physics associated with a strong first-order electroweak phase transition. Null results from direct searches and constraints from precision measurements, together with the comparatively weak constraints on Higgs self-interactions, motivate scenarios in which non-decoupling effects in the Higgs potential coexist with additional decoupling new physics. Previous Fisher matrix studies within the Standard Model effective field theory (SMEFT) have explored the sensitivity of future GW observations to new physics, focusing on transitions driven by the dimension-six operator $(H^\dagger H)^3$. However, the validity of the truncated EFT expansion can become questionable in the parameter regions relevant to such transitions. We instead consider transitions driven by non-decoupling effects described by the nearly aligned Higgs effective field theory (naHEFT). We investigate whether GW observations can probe small corrections to the Higgs effective potential induced by decoupling effects in interactions other than Higgs self-interactions. As a representative benchmark for additional decoupling effects, we consider the dimension-six SMEFT operator $(H^\dagger H)(\overline{q}_3 t_R\widetilde{H})$ with Wilson coefficient $C_{uH}$. Although we focus on this benchmark, the same framework can be applied to other dimension-six SMEFT operators. We perform two-parameter Fisher matrix analyses for DECIGO and BBO to quantify their expected sensitivity to $C_{uH}$ and the naHEFT mass scale $Λ$. For the benchmark configurations considered, the non-decoupling dynamics generates a detectable GW signal. We find that these small corrections can produce potentially measurable changes in the GW spectrum, even after accounting for the correlation between $C_{uH}$ and $Λ$.