More on scattering processes of dressed particles with a time-dependent mass

We discuss the scattering process of a scalar field having a time-dependent mass with another scalar field having a constant mass as a toy model of the scattering problems during preheating after inflation. Despite a general difficulty of analytically solving such models, in our previous work [QFT approach to dressed particle processes in preheating and non-perturbative mechanism in kinematically-forbidden regime, ], we considered an exactly calculable model of such scattering processes with a time-dependent mass of the form m2(t)⊃μ4t2 and the time-dependence never disappears formally. In this work, we discuss another exactly calculable model with a time-dependent mass that has a spike/peak but asymptotes to a constant, which effectively appears in the preheating model of Higgs inflation with a nonminimal coupling. Thanks to the localized time-dependence of the mass, the daughter particle number density behaves in a physically reasonable way contrary to the one in our previous model due to the infinite time-dependent mass in the asymptotic future. On the other hand, we find that the daughter particle experiences the kinematically forbidden process, which is a nonperturbative phenomenon found in our previous work. As in the previous model, the kinematically forbidden process produces daughter particles exponentially more than the parent particle having the time-dependent mass, which never happens for particle decay processes without time-dependent backgrounds. This result supports the existence of such a nonperturbative particle production process in general time-dependent backgrounds. Published by the American Physical Society 2025