Galilean-Invariant XEFT

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D0 --> D0 pi0. The transitions D0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D0 propagator and for the D0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.