Study on X(3872) from effective field theory with pion exchange interaction

TL;DR

This paper investigates the nature of the X(3872) particle using unitarized heavy meson chiral perturbation theory with pion exchange, confirming its molecular structure and analyzing its quark mass dependence.

Contribution

It provides a theoretical confirmation of the X(3872) as a $D\bar{D}^*$ molecular state using effective field theory with pion exchange and explores its quark mass sensitivity.

Findings

X(3872) is a loosely bound $D\bar{D}^*$ molecular state.

The pole position is insensitive to contact interaction strength.

The state disappears at pion masses above 142 MeV.

Abstract

We study $D\bar{D}^*$ ($D^*\bar{D}$) scattering in the framework of unitarized heavy meson chiral perturbation theory with pion exchange and a contact interaction. $^3S_1-$$^3D_1$ mixing effects are taken into account. A loosely bound state X(3872), with the pole position being $M_{pole}=(3871.70-i0.39)\mathrm{MeV}$, is found. The result is not sensitive to the strength of the contact interaction. Our calculation provides a theoretical confirmation of the existence of the $1^{++}$ state X(3872). The light quark mass dependence of the pole position indicates it has a predominately $D\bar{D}^*$ ($D^*\bar{D}$) molecular nature. When the $\pi$ mass is larger than 142 MeV, the pole disappears which makes impossible the lattice simulation of this state at large quark mass.