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

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 $D bar D^*$ threshold, we use a combination of $bar c c$ and $D bar D^* + bar D D^*$ interpolating operators. For the $Z_c^+(3900)$ we use a combination of $J/psi pi$ and $D bar D^* + bar D D^*$ 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.