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

TL;DR

This paper analyzes how finite volume effects influence the binding energy of the X(3872) meson in lattice QCD simulations, highlighting the importance of volume corrections and quark mass dependence in effective field theory.

Contribution

It provides a next-to-leading order effective field theory calculation of finite volume corrections to the X(3872) binding energy, including quark mass dependence and perturbative pions.

Findings

Finite volume effects are significant at box sizes as large as 20 fm.

The quark mass dependence of the binding energy is moderate up to twice the physical quark mass.

Finite volume corrections must be considered in lattice calculations 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 (XEFT). 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 box length as large as 20 fm.