Galilean-Invariant XEFT at Next-to-Leading Order

TL;DR

This paper develops a Galilean-invariant formulation of XEFT at next-to-leading order, simplifying calculations of the $X(3872)$ resonance by introducing a dynamical charm meson pair field and a new renormalization scheme.

Contribution

It introduces a new Galilean-invariant formulation of XEFT with a dynamical charm meson pair field and a novel renormalization scheme for improved calculations beyond leading order.

Findings

Calculated the complex pole energy of $X$ at NLO.

Determined the $D^{*0} ar D^0$ scattering amplitude at NLO.

Demonstrated the simplification of renormalization in XEFT.

Abstract

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the $X(3872)$ resonance. To simplify calculations beyond leading order, we introduce a new formulation of XEFT with a dynamical field for a pair of charm mesons in the resonant channel. We simplify the renormalization of XEFT by introducing a new renormalization scheme that involves the subtraction of amplitudes at the complex $D^{*0} \bar D^0$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the $D^{*0} \bar D^0$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.