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.
Highlights
On top of being desirable from the phenomenological and observational points of views, the possibility of a richer dark sector, that comprises more than one particle, is fairly common in many DM models, cf. e.g. [21,22,23]
We shall employ the framework of nonrelativistic effective field theories [61, 62] (NREFTs) and potential non-relativistic effective field theories [63, 64], which are obtained by integrating out energy/momenta of order M and M v respectively
Our approach is based on the renowned non-relativistic EFTs (NREFTs) of this sort that have been obtained for QED and QCD, and served as precious and handy tools for rigorous and systematic analyses of e.g. hydrogen atom, positronium, heavy quarkonia, heavy-light hadrons or muonic hydrogen
Summary
We briefly introduce the DM model under consideration and discuss the relevant degrees of freedom. The interactions with quarks severely constrain the model via direct detection experiments [80, 85] These tensions can be removed in a number of different ways [83, 86]. Since a detailed phenomenological analysis is beyond the scope of this work, we do not specify Lportal further and merely focus on the complementary terms in eq (2.1) to derive the low-energy field theories relevant for the bound-state dynamics. This sets the stage for our NREFT and pNREFT formulations and paves the way for more thorough investigations ( with respect to the DM phenomenology) in future works
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