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

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.

Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators

“…We defer the scrutiny of the impact of thermal masses, and a thermal width, of the scalar propagator to future works on the subject. Since we included a fermion-pseudoscalar interaction, we denote the following towers of EFTs with NRY γ 5 and pNRY γ 5 in order to make clear that the corresponding low-energy theories differ from the ones obtained in the case of the sole scalar interaction [55].…”

“…To ensure the correctness of the results presented in the next sections we make use of computer tools that were already employed in our previous work on the subject [55]. Calculations within the fully relativistic DM model given in eq.…”

“…The matching coefficients, that generalize our result for the sole scalar interaction in ref. [55], read…”

“…Having obtained NRY γ 5 , the next natural step is to derive the corresponding EFT at the ultra-soft scale in order to calculate processes relevant to this work, namely the bound-state formation cross section, the bound-state dissociation width and the bound-state decays. To this aim, we work with the pNRY Lagrangian [55] where the degrees of freedom are heavy fermion-antifermion pairs and low-energetic scalars. In the following we briefly summarize its form and elucidate on the modifications that occur when the pseudo-scalar interaction is considered.…”

“…We shall attack this problem by using a recently proposed EFT for non-relativistic fermion-antifermion pairs interacting via a scalar mediator. Building upon the well-known NREFTs and potential NREFTs (pNREFTs) of QED and QCD [50][51][52][53][54] as well as scalar Yukawa theory [101,102], we developed potential non-relativistic Yukawa theory (pNRY) [55] that is well suited to address the questions at hand. The relevant degrees of freedom of pNRY are heavy fermion-antifermion pairs and ultra-soft scalars.…”