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

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