An alternative scheme for effective range corrections in pionless EFT

M Ebert,A Rusetsky,H.-W Hammer

doi:10.1140/epja/s10050-021-00637-y

Abstract

We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T-matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T-matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence.

Highlights

Λχ [9,10]
We have provided some evidence for our choice τ1(k∗) and τ2(k∗) in the calculations at next-toleading order (NLO) and N2LO, respectively, based on the behavior of the slopes in Lepage and consistency plots
A novel procedure for removing the contribution from spurious poles in the three-body Faddeev equation for pionless Effective Field Theories (EFTs) has been proposed. These poles emerge in the two particle scattering amplitudes, which enter the threebody integral equation

Summary

Introduction

Λχ [9,10]. The pionless theory exploits the large scattering length but is independent of the mechanism responsible for it. At leading order (LO), one needs to resum a momentumindependent contact interaction in order to describe the large scattering length physics. This resummation is conveniently implemented using dibaryon or dimer fields [11]. The procedure of perturbative range insertions becomes tedious, and a direct calculation of the corrections requires fully off-shell LO amplitudes. In three- and higher-body systems it can limit the range of cutoffs that can be used in the numerical solution of the scattering equations. In the quartet S-wave, due to the Pauli principle, the solution is not sensitive to this deep pole and the cutoff can be made arbitrarily large

Objectives

Methods

Findings

Conclusion