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.