Quark-mass dependence of two-nucleon observables

Abstract

We study the potential implications of lattice QCD determinations of the $S$-wave nucleon-nucleon scattering lengths with unphysical light quark masses. If the light quark masses are small enough such that nuclear effective field theory (NEFT) can be used to perform quark-mass extrapolations, then the leading quark-mass dependence of not only the effective range and the two-body current, but also all the low-energy deuteron matrix elements up to next-to-leading-order in NEFT can be obtained. As a proof of principle, we compute the quark-mass dependence of the deuteron charge radius, magnetic moment, polarizability, and the deuteron photodisintegration cross section using the lattice calculation of the scattering lengths at 354 MeV pion mass by the ``Nuclear Physics with Lattice QCD'' (NPLQCD) collaboration and the NEFT power counting scheme of Beane, Kaplan, and Vuorinen (BKV), even though it is not yet established that the 354 MeV pion mass is within the radius of convergence of the BKV scheme. Once the lattice result with quark mass within the NEFT radius of convergence is obtained, our observation can be used to constrain the time variation of isoscalar combination of $u$ and $d$ quark mass ${m}_{q}$, to help the anthropic principle study to find the ${m}_{q}$ range that allows the existence of life, and to provide a weak test of the multiverse conjecture.