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We present preliminary simulation results for the I = 0 charmonium state$X(3872)(1^{++})$ and the I = 1 charmonium state $Z_c^+(3900)(1^{+-})$. Thestudy is performed on gauge field configurations with 2+1+1 flavors of highlyimproved staggered sea quarks (HISQ) with clover (Fermilab interpretation)charm quarks and HISQ light valence quarks. Since the $X(3872)$ lies very closeto 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 $Z_c^+(3900)$ weuse a combination of $J/\psi \pi$ and $D \bar D^* + \bar D D^*$ channels. Thisis the first such study with HISQ sea quarks and light valence quarks. To thisend, we describe a variational method for treating staggered quarks thatincorporates both oscillating and non-oscillating components.

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