Galilean-invariant effective field theory for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> at next-to-leading order
Eric Braaten, Li-Ping He, Jun Jiang
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 ${D}^{*0}{\overline{D}}^{0}$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the ${D}^{*0}{\overline{D}}^{0}$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.