Non-relativistic and potential non-relativistic effective field theories for scalar mediators

TL;DR

This paper develops a rigorous, model-independent framework using effective field theory to analyze non-relativistic limits of scalar Yukawa interactions, with implications for dark matter models.

Contribution

It constructs non-relativistic and potential non-relativistic EFTs for scalar Yukawa interactions, filling a gap in the theoretical understanding of these models.

Findings

Established non-relativistic EFTs for scalar Yukawa interactions.

Provided a systematic approach for dark matter interactions via scalar mediators.

Enhanced the theoretical tools for cosmological and particle physics applications.

Abstract

Yukawa-type interactions between heavy Dirac fermions and a scalar field are a common ingredient in various extensions of the Standard Model. Despite of that, the non-relativistic limit of the scalar Yukawa theory has not yet been studied in full generality in a rigorous and model-independent way. In this paper we intend to fill this gap by initiating a series of investigations that make use of modern effective field theory (EFT) techniques. In particular, we aim at constructing suitable non-relativistic and potential non-relativistic EFTs of Yukawa interactions (denoted as NRY and pNRY respectively) in close analogy to the well known and phenomenologically successful non-relativistic QCD (NRQCD) and potential non-relativistic QCD (pNRQCD). The phenomenological motivation for our study lies in the possibility to explain the existing cosmological observations by introducing heavy fermionic dark matter particles that interact with each other by exchanging a light scalar mediator. A systematic study of this compelling scenario in the framework of non-relativistic EFTs (NREFTs) constitutes the main novelty of our approach as compared to the existing studies.