Quenched charmonium spectrum

Abstract

We study charmonium using the standard relativistic formalism in the quenched approximation, on a set of lattices with isotropic lattice spacings ranging from 0.1 to 0.04 fm. We concentrate on the calculation of the hyperfine splitting between η c and J/ψ, aiming for a controlled continuum extrapolation of this quantity. The splitting extracted from the non-perturbatively improved clover Dirac operator shows very little dependence on the lattice spacing for a ≤ 0.1fm. The dependence is much stronger for Wilson and tree-level improved clover operators, but they still yield consistent extrapolations if sufficiently fine lattices, a ≤ 0.07 fm (aM(η c ) ≤ 1), are used. Our result for the hyperfine splitting is 77(2)(6) MeV (where Sommer's parameter, r 0 , is used to fix the scale). This value remains about 30% below experiment. Dynamical fermions and OZI-forbidden diagrams both contribute to the remainder. Results for the η c and J/ψ wave functions are also presented.

Improved lattice fermion action for heavy quarks

“…Also we observe that our value of the continuum limit is consistent with that of Ref. [30] in which the charmonium spectra are simulated on quenched lattices with some different valence quark formalisms.…”

Mass of theηbandαsfrom the Nonrelativistic Renormalization Group

“…We should emphasize the crucial role of the resummation to bring the perturbative prediction closer to the experimental figure. Note also that the recent lattice estimates undershoot the experimental value by 20 -30% [25]. For an estimate, we attribute the whole difference of 14 MeV to the nonperturbative effects.…”

Contribution of disconnected diagrams to the hyperfine splitting of charmonium

“…This is the approach taken in Ref. [2] by the QCD-TARO Collaboration, using the nonperturbatively O(a)-improved Wilson quark action on quenched isotropic lattices [2]. Numerical simulations with lattice cutoffs ranging from 2 to 5 GeV found ∆M = 77(2)(6)MeV in the continuum limit.…”

“…1 [2]. Such diagrams must be included in the evaluation of correlators of unflavoured mesons, such as η c and J/ψ.…”