Charmonium spectrum from quenched anisotropic lattice QCD
Physical Review D, Particles and fields
We present a detailed study of the charmonium spectrum using anisotropic lattice QCD. We first derive a tree-level improved clover quark action on the anisotropic lattice for arbitrary quark mass. The heavy quark mass dependences of the improvement coefficients, i.e. the ratio of the hopping parameters ζ=K_t/K_s and the clover coefficients c_s,t, are examined at the tree level. We then compute the charmonium spectrum in the quenched approximation employing ξ = a_s/a_t = 3 anisotropic lattices.
... imulations are made with the standard anisotropic gauge action and the anisotropic clover quark action at four lattice spacings in the range a_s=0.07-0.2 fm. The clover coefficients c_s,t are estimated from tree-level tadpole improvement. On the other hand, for the ratio of the hopping parameters ζ, we adopt both the tree-level tadpole-improved value and a non-perturbative one. We calculate the spectrum of S- and P-states and their excitations. The results largely depend on the scale input even in the continuum limit, showing a quenching effect. When the lattice spacing is determined from the 1P-1S splitting, the deviation from the experimental value is estimated to be ∼30 S-state hyperfine splitting and ∼20 results are consistent with previous results at ξ = 2 obtained by Chen when the lattice spacing is determined from the Sommer scale r_0. We also address the problem with the hyperfine splitting that different choices of the clover coefficients lead to disagreeing results in the continuum limit.