Searching for X(3872) using lattice QCD

In the past decade, many excited charmonium states have been discovered that cannot be explained within the conventional quark model. One of the those mesons, the narrow charmonium-like state $X(3872)$ has been examined using various phenomenological models. Since its mass is within 1~MeV of the $D\bar D^*$ threshold, one of the strong candidates is a $D\bar D^*$ molecular state. However, such a molecular state cannot be directly studied by perturbative QCD in such a low energy regime where the interaction of the colored quarks and gluons is very strong. Numerical simulation with lattice QCD is the method of choice. It provides a nonperturbative, {\it ab initio} method for studying this mysterious meson state. In this talk, I present preliminary simulation results for charmonium-like states with quantum numbers $J^{\rm PC} = 1^{++}$ in both the isospin 0 and 1 channels using lattice QCD. We use interpolating operators including both the conventional excited P-wave charmonium state($\chi_{c1}$) and the $D\bar D^*$ open charm state for the isospin 0 channel, but only $D\bar D^*$ for the isospin 1 channel. We find an $X(3872)$ candidate close to and below the $D\bar D^*$ threshold in the isospin 0 channel, but only scattering states in the isospin 1 channel.