Charmonium Spectrum from Quenched Anisotropic Lattice QCD

TL;DR

This paper investigates the charmonium spectrum using anisotropic lattice QCD with improved actions, examining quark mass dependence, and comparing different scale settings and coefficient choices, revealing quenching effects and discrepancies in hyperfine splitting.

Contribution

It introduces a detailed study of the charmonium spectrum with anisotropic lattice QCD, including derivation of improved actions and analysis of quenching effects and coefficient choices.

Findings

Charmonium spectrum computed with anisotropic lattice QCD shows quenching effects.

Discrepancies in hyperfine splitting depend on coefficient choices and scale setting.

Results are consistent with previous studies at similar anisotropy ratios.

Abstract

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 $\zeta=K_t/K_s$ and the clover coefficients $c_{s,t}$, are examined at the tree level. We then compute the charmonium spectrum in the quenched approximation employing $\xi = a_s/a_t = 3$ anisotropic lattices. Simulations 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 $\zeta$, 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 $\sim$30% for the S-state hyperfine splitting and $\sim$20% for the P-state fine structure. Our results are consistent with previous results at $\xi = 2$ 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.