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

Abstract

We study $D{\bar{D}}^{\ast }$ ($D^{\ast }\bar{D}$) scattering in the framework of unitarized heavy meson chiral perturbation theory with pion exchange and a contact interaction. ${}^3{S}_1-$${}^3{D}_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 $D{\bar{D}}^{\ast }$ ($D^{\ast }\bar{D}$) 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.

5 pages, 4 figures