Investigating the Electroweak Phase Transition with a Real Scalar Singlet at a Muon Collider

A strong first-order electroweak phase transition (SFOEWPT) is essential for explaining baryogenesis and for potentially generating observable gravitational waves. This study investigates the potential of a high-energy muon collider to examine the occurrence of SFOEWPT within the context of a Standard Model extended by a real scalar singlet (xSM). We analyzed all possible decay modes of the singlet to constrain the valid parameter space of SFOEWPT, which was extracted numerically at different renormalization scales to account for theoretical uncertainties, thereby determining the sensitivity of a muon collider to the production and decay channels of novel heavy scalar particles that emerge in the xSM. The findings demonstrate that a 3 TeV muon collider can directly examine the nature of electroweak symmetry breaking by efficiently detecting novel scalar particles associated with a first-order electroweak phase transition through jet-rich final states, thus complementing the indirect constraints from gravitational wave experiments.