Galilean-invariant effective field theory for the X(3872)

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 D*(0) -> D-0 pi(0). The transitions D*(0) -> D-0 pi(0) and X -> D-0(D) over bar (0)pi(0) are described explicitly in XEFT. The effects of the decay D*(0) -> D-0 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 D*(0) propagator and for the D*(0)(D) over bar (0) propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*(0)(D) over bar (0) 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.