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.
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Jansen et al. (2015) studied this question.
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