The S Wave Pion Deuteron Scattering Length in Effective Field Theory

TL;DR

This paper calculates the S wave pion deuteron scattering length at NLO using Effective Field Theory with perturbative pions, highlighting the role of unknown parameters and the potential for future experimental refinement.

Contribution

It provides a perturbative EFT calculation of the scattering length, incorporating counter terms and comparing with non-perturbative approaches.

Findings

The scattering length depends on the iso-scalar pion-nucleon scattering length and counter terms.

Current data can be fitted by natural-sized parameters within EFT.

Future experiments will improve the determination of counter terms.

Abstract

The S wave pion deuteron scattering length is presented at NLO in the Effective Field Theory formulation of the two nucleon system with perturbative pions. At this order, this observable is determined by the iso-scalar S wave pion nucleon scattering length a^+, by pion re-scattering contributions inside the deuteron and by two nucleon two pion contact interactions that involve two unknown parameters which renormalise the appearing divergences. By choosing their values accordingly and in agreement with their natural sizes predicted by the power counting, we are able to accommodate the available experimental data. However, a^+ cannot be determined from pion deuteron scattering directly. An ongoing experiment at PSI aiming to reduce the error bars by an order of magnitude will make it possible to pin down the size of these counter terms more accurately. We compare our findings to an approach in which pions are treated non-perturbatively.