Charmonium spectrum from quenched anisotropic lattice QCD
Abstract
We present a detailed study of the charmonium spectrum using anisotropic lattice QCD. We first derive a treelevel improved clover quark action on the anisotropic lattice for arbitrary quark mass by matching the Hamiltonian on the lattice and in the continuum. The heavy quark mass dependence of the improvement coefficients, i.e., the ratio of the hopping parameters ζ=K_{t}/K_{s} and the clover coefficients c_{s,t}, is examined at the tree level, and effects of the choice of the spatial Wilson parameter r_{s} are discussed. We then compute the charmonium spectrum in the quenched approximation employing ξ=a_{s}/a_{t}=3 anisotropic lattices. Simulations are made with the standard anisotropic gauge action and the anisotropic clover quark action with r_{s}=1 at four lattice spacings in the range a_{s}=0.070.2 fm. The clover coefficients c_{s,t} are estimated from treelevel tadpole improvement. On the other hand, for the ratio of the hopping parameters ζ, we adopt both the treelevel tadpoleimproved value and a nonperturbative one. The latter employs the condition that the speed of light calculated from the meson energymomentum relation be unity. We calculate the spectrum of S and P states and their excitations using both the pole and kinetic masses. We find that the combination of the pole mass and the tadpoleimproved value of ζ to yield the smoothest approach to the continuum limit, which we then adopt for the continuum extrapolation of the spectrum. 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 1P1S splitting, the deviation from the experimental value is estimated to be ~30% for the Sstate hyperfine splitting and ~20% for the Pstate fine structure. Our 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. Making a leading order analysis based on potential models we show that a large hyperfine splitting ~95 MeV obtained by Klassen with a different choice of the clover coefficients is likely an overestimate.
 Publication:

Physical Review D
 Pub Date:
 May 2002
 DOI:
 10.1103/PhysRevD.65.094508
 arXiv:
 arXiv:heplat/0112020
 Bibcode:
 2002PhRvD..65i4508O
 Keywords:

 11.15.Ha;
 12.38.Gc;
 12.39.Hg;
 Lattice gauge theory;
 Lattice QCD calculations;
 Heavy quark effective theory;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 43 pages, 49 eps figures, revtex