[Paper Review] Lattice results on charmonium

Daniel Mohler|arXiv (Cornell University)|Sep 25, 2012

Spectral Theory in Mathematical Physics15 references3 citations

TL;DR

This paper presents recent lattice QCD results on the charmonium spectrum using configurations with 2+1 dynamical quarks, focusing on precision calculations at or near physical pion masses. By employing improved actions and continuum extrapolations, the BMW and QCDSF collaborations achieve good agreement with experiment for ground and excited states below inelastic thresholds, particularly through the use of variational methods and distillation techniques, though discretization effects remain significant without proper extrapolation.

ABSTRACT

Recent lattice QCD results on charmonium spectroscopy are reviewed.

Motivation & Objective

• To achieve precision lattice QCD calculations of the charmonium spectrum using configurations with physical or near-physical sea quark masses.
• To address systematic uncertainties from finite volume, discretization, and chiral extrapolation in charmonium spectroscopy.
• To extract both ground and excited states using the variational method and improved interpolating operators.
• To assess the impact of discretization effects on observables like the hyperfine splitting and demonstrate the necessity of continuum extrapolation.
• To enable future calculations of resonance properties by including inelastic thresholds such as DD and DD*.

Proposed method

• Use of Monte Carlo simulations on gauge configurations with 2+1 dynamical quarks from BMW and QCDSF collaborations.
• Application of the variational method to extract multiple energy levels from a correlation matrix of interpolating operators with definite quantum numbers.
• Employment of the distillation technique to improve the signal-to-noise ratio and enable inclusion of inelastic thresholds in spectral calculations.
• Implementation of continuum extrapolation using multiple lattice spacings to remove discretization errors, especially critical for observables like the hyperfine splitting.
• Use of improved fermion actions (e.g., Wilson-Clover and SLiNC) for both light and charm quarks to reduce systematic errors.
• Application of chiral effective field theory fits to extrapolate results to physical light quark masses, even when simulations use heavier pions.

Experimental results

Research questions

• RQ1 How accurately can lattice QCD reproduce the charmonium spectrum, including excited states, when using physical or near-physical pion masses?
• RQ2 To what extent do discretization errors affect key observables such as the hyperfine splitting, and can these be mitigated via continuum extrapolation?
• RQ3 Can the variational method successfully extract a complete low-lying spectrum of charmonium states from lattice correlators?
• RQ4 How do finite volume effects influence the spectrum, and what lattice sizes are sufficient to suppress them?
• RQ5 Can lattice QCD calculations reliably include inelastic thresholds such as DD and DD* to describe resonance properties?

Key findings

• Preliminary results from QCDSF SLiNC configurations show good qualitative agreement with experiment for charmonium states below the DD threshold, including multiple excited states.
• The hyperfine splitting is found to be strongly dependent on lattice spacing when using the Wilson-Clover action, with a value of $ M_{HFS} = 80 \pm 1 $ MeV, which differs significantly from the experimental value of 58.4 MeV.
• A value compatible with experiment is achieved only after performing a proper continuum extrapolation, demonstrating the critical importance of removing discretization effects.
• The BMW collaboration's use of HEX-smeared Wilson-Clover configurations shows a strong lattice spacing dependence in the hyperfine splitting, confirming the need for continuum extrapolation.
• The inclusion of inelastic thresholds such as DD and DD* is feasible using the distillation technique, enabling future calculations of resonance properties.
• Calculations at or near physical pion masses are now feasible and increasingly common, marking a significant step toward precision lattice QCD in heavy quarkonium physics.