Quenched charmonium spectrum

TL;DR

This study calculates the charmonium hyperfine splitting using lattice QCD in the quenched approximation, finding a value about 30% below experimental results, with detailed analysis of lattice spacing effects.

Contribution

It provides a controlled continuum extrapolation of the hyperfine splitting in quenched lattice QCD using improved operators and analyzes the effects of lattice spacing and operator choices.

Findings

Hyperfine splitting is about 77 MeV, below experimental value.

Non-perturbatively improved operators show minimal lattice spacing dependence.

Results suggest quenched approximation and omitted diagrams account for the discrepancy.

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 eta_c and J/psi, 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 $a \leq 0.1$ fm. The dependence is much stronger for Wilson and tree-level improved clover operators, but they still yield consistent extrapolations if sufficiently fine lattices, $a \leq 0.07$ fm ($a M(\eta_c) \leq 1$), 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 eta_c and J/psi wave functions are also presented.