Scattering of an Ultrasoft Pion and the X(3872)

TL;DR

This paper extends an effective field theory for the X(3872) to include pion scattering, enabling precise calculations of low-energy pion-X(3872) interactions and breakup cross sections based on known meson properties.

Contribution

It introduces an extension of XEFT to include pion interactions, allowing for model-independent calculations of pion scattering and breakup cross sections of the X(3872).

Findings

Cross sections are fully calculable at leading order for low-energy pions.

Explicit calculation of the X(3872) breakup cross section into D*+ Dbar*0.

The approach depends only on known meson masses, widths, and binding energy.

Abstract

The identification of the X(3872) as a loosely-bound charm-meson molecule allows it to be described by an effective field theory, called XEFT, for the D^* Dbar, D Dbar^* and D Dbar pi sector of QCD at energies small compared to the pion mass. We point out that this effective field theory can be extended to the sector that includes an additional pion and used to calculate cross sections for the scattering of a pion and the X(3872). If the collision energy is much smaller than the pion mass, the cross sections are completely calculable at leading order in terms of the masses and widths of the charm mesons, pion masses, and the binding energy of the X(3872). We carry out an explicit calculation of the cross section for the breakup of the X(3872) into D^{*+} Dbar^{*0} by the scattering of a very low energy pi^+.