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

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 ${}^3{S}_1$ 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 ${}^1{S}_0$ channel. We apply our results to chiral extrapolations of current lattice data.

Comments: Journal version, one reference added; 16 pages, 9 figures