Light quark mass dependence of theX(3872)in an effective field theory

Abstract

The quark mass dependence of hadrons is an important input for lattice calculations. We investigate the light quark mass dependence of the binding energy of the $X(3872)$ and the ${\overline{D}}^{0}{D}^{*0}$ scattering length in the $C=+1$ channel to next-to-leading order in an effective field theory for the $X$ (XEFT) where pion interactions are perturbative. At this order, the quark mass dependence is determined by a quark mass-dependent contact interaction in addition to the one-pion exchange. Using naturalness arguments to constrain unknown parameters, we find a moderate sensitivity of the binding energy for quark masses up to twice the physical value while the scattering length is more sensitive. The occurrence of infrared divergences due to on-shell pions in XEFT and their treatment is discussed in detail.