Universal dimer–dimer scattering in lattice effective field theory

Serdar Elhatisari,Kris Katterjohn,Dean Lee,Ulf-G Meißner,Gautam Rupak

doi:10.1016/j.physletb.2017.03.011

Abstract

We consider two-component fermions with short-range interactions and large scattering length. This system has universal properties that are realized in several different fields of physics. In the limit of large fermion–fermion scattering length aff and zero-range interaction, all properties of the system scale proportionally with aff. For the case with shallow bound dimers, we calculate the dimer–dimer scattering phase shifts using lattice effective field theory. We extract the universal dimer–dimer scattering length add/aff=0.618(30) and effective range rdd/aff=−0.431(48). This result for the effective range is the first calculation with quantified and controlled systematic errors. We also benchmark our methods by computing the fermion–dimer scattering parameters and testing some predictions of conformal scaling of irrelevant operators near the unitarity limit.

Highlights

Two-component fermions at large scattering length are an important system with universal properties and relevance to several branches of physics
This universality is due to the existence of a conformal fixed point called the unitarity limit where the fermion– fermion scattering length is infinite and all other length scales are irrelevant at large particle separations or low energies
We will use Lüscher’s finite-volume method to calculate fermion–dimer scattering and dimer–dimer scattering. In these cases we consider the scattering of two bodies, where one or both bodies may be dimers

Summary

Introduction

Two-component fermions at large scattering length are an important system with universal properties and relevance to several branches of physics. In this letter we discuss the case where the scattering length is large and positive, and bound dimers composed of two fermions are formed with shallow binding energy. We compute dimer–dimer scattering and determine the dimer–dimer scattering length and effective range These results can be used to compute the energy density of a dimer gas in the dilute limit [5,6,7,8,9]. The effective range has been calculated as rdd/aff ≈ 0.12 in Ref. In this work we calculate the low-energy dimer–dimer phase shifts from lattice effective field theory and extract both the dimer–dimer scattering length add and effective range rdd.

Lattice formalism

Scattering phase shift

Results and analysis

Fermion–dimer scattering

Dimer–dimer scattering

Summary and conclusions