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

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 ${(m_π^3 / Λ_χ^2)}\times (m_π^{1/2}m_N^{3/2}/8πf_π^2)^n$ 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.

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