Searching for the $X(3872)$ and $Z_c^{+}(3900)$ on HISQ lattices

Abstract

We present preliminary simulation results for the I = 0 charmonium state $X(3872)(1^{++})$ and the I = 1 charmonium state $Z_c^{+}(3900)(1^{+-})$. The study is performed on gauge field configurations with 2+1+1 flavors of highly improved staggered sea quarks (HISQ) with clover (Fermilab interpretation) charm quarks and HISQ light valence quarks. Since the $X(3872)$ lies very close to the open charm $D{\bar{D}}^{\ast }$ threshold, we use a combination of $\bar{c}c$ and $D{\bar{D}}^{\ast }+\bar{D}{D}^{\ast }$ interpolating operators. For the $Z_c^{+}(3900)$ we use a combination of $J/\psi \pi$ and $D{\bar{D}}^{\ast }+\bar{D}{D}^{\ast }$ channels. This is the first such study with HISQ sea quarks and light valence quarks. To this end, we describe a variational method for treating staggered quarks that incorporates both oscillating and non-oscillating components.

Comments: Lattice 2014, 7 pages, 3 figures