Recoil corrections in antikaon-deuteron scattering

TL;DR

This paper investigates recoil corrections in antikaon-deuteron scattering using effective field theory, demonstrating a systematic approach to include these effects despite the non-perturbative nature of low-energy scattering.

Contribution

It introduces a systematic perturbative expansion for recoil corrections in $K^-d$ scattering within an effective field theory framework, even with large scattering lengths.

Findings

Recoil corrections are small at physical mass ratios.

First order recoil correction is explicitly calculated.

Perturbative expansion remains valid despite non-perturbative scattering.

Abstract

The recoil retardation effect in the $K^-d$ scattering length is studied. Using the non-relativistic effective field theory approach, it is demonstrated that a systematic perturbative expansion of the recoil corrections in the parameter $\xi=M_K/m_N$ is possible in spite of the fact that $K^-d$ scattering at low energies is inherently non-perturbative due to the large values of the $\bar KN$ scattering lengths. The first order correction to the $K^-d$ scattering length due to single insertion of the retardation term in the multiple-scattering series is calculated. The recoil effect turns out to be reasonably small even at the physical value of $M_K/m_N\simeq 0.5$.