Two and three point functions in real singlet and complex doublet scalar model

Abstract

We study dynamics of an interacting theory of a real singlet scalar and an $SU(2)$ symmetry preserving complex doublet scalar fields using lattice simulations over a broad region of the parameter space. The model contains all $SU(2)$-preserving quartic and a real singlet-$SU(2)$ invariant doublet field Yukawa interactions. The field propagators and the Yukawa vertex are the central structures for the study. We complement the study by implementing machine learning routines to the correlation functions in order to probe the underlying physics. The model reveals the role of nonperturbative effects in terms of infrared enhanced field propagators with a stable amputated Yukawa vertex, and a continuum-like scaling window in the parameter space with large regulator. The ultraviolet effects are visible in terms of an scaling structure appearing in a composite operator of mixed scalar interactions and the singlet expectation value.