The variational method is used widely for determining eigenstates of the QCD hamiltonian for actions with a conventional transfer matrix, e.g., actions with improved Wilson fermions. An alternative lattice fermion formalism, staggered fermions, does
not have a conventional single-time-step transfer matrix. Nonetheless, with a simple modification, the variational method can also be applied to that formalism. In some cases the method also provides a mechanism for separating the commonly paired parity-partner states. We discuss the extension to staggered fermions and illustrate it by applying it to the calculation of the spectrum of charmed-antistrange mesons consisting of a clover charm quark and a staggered strange antiquark.
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.
We present results from an ongoing study of mass splittings of the lowest lying states in the charmonium system. We use clover valence charm quarks in the Fermilab interpretation, an improved staggered (asqtad) action for sea quarks, and the one-loop
, tadpole-improved gauge action for gluons. This study includes five lattice spacings, 0.15, 0.12, 0.09, 0.06, and 0.045 fm, with two sets of degenerate up- and down-quark masses for most spacings. We use an enlarged set of interpolation operators and a variational analysis that permits study of various low-lying excited states. The masses of the sea quarks and charm valence quark are adjusted to their physical values. This large set of gauge configurations allows us to extrapolate results to the continuum physical point and test the methodology.
