Finite volume corrections to the binding energy of the X(3872)

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) in a finite box to next-to-leading order in an effective field theory for the X(3872) with perturbative pions. At this order, the quark mass dependence is determined by a quark-mass-dependent contact interaction in addition to the one-pion exchange. While there is only a moderate sensitivity to the light quark masses in the region up to twice their physical value, the finite-volume effects are significant already at a box length as large as 20 fm.