On the quark mass dependence of nucleon-nucleon S-wave scattering lengths

TL;DR

This paper investigates how the inverse scattering length in nucleon-nucleon S-wave channels depends on the pion mass using chiral effective theory, aiding lattice QCD extrapolations.

Contribution

It provides a detailed calculation of pion mass dependence of nucleon-nucleon scattering lengths in the $^3S_1$ channel at a specific order, including the analysis of higher order contributions.

Findings

Certain large higher order contributions vanish.

The method facilitates chiral extrapolations of lattice data.

Discussion of challenges in extending results to the $^1S_0$ channel.

Abstract

In the framework of a Chiral effective theory with dibaryon fields, we calculate the pion mass dependence of the inverse scattering length of the nucleon-nucleon system in the $^3S_1$ channel at order ${(m_\pi^3 / \Lambda_\chi^2)}\times (m_\pi^{1/2}m_N^{3/2}/8\pi f_\pi^2)^n$ for all $n\ge 0$. We show that certain sets of potentially large higher order contributions vanish. We discuss the difficulties of extending the proof to the $^1S_0$ channel. We apply our results to chiral extrapolations of current lattice data.