[Paper Review] The heavy quarkonium spectrum from quenched lattice QCD

Peter Boyle|ArXiv.org|Mar 10, 1999

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper presents a lattice QCD study of the heavy quarkonium spectrum using the quenched approximation and the tadpole-improved clover action at two lattice spacings. It achieves the first relativistic calculation of the triplet fine structure in quarkonium, providing precise masses for the lowest S- and P-wave states, including spin-splitting splittings consistent with experimental expectations.

ABSTRACT

We present results of simulations of the quenched quarkonium spectrum at two values of the lattice spacing and for quark masses around $m_c$ using the tadpole improved clover action. Attention is focussed on the lowest lying S and P states, and the triplet fine structure is obtained for the first time using a relativistic action.

Motivation & Objective

• To compute the spectrum of heavy quarkonium states, including S- and P-wave levels, using lattice QCD with a relativistic action.
• To determine the triplet fine structure splitting in quarkonium for the first time using a relativistic formulation.
• To assess the impact of lattice spacing and quark mass variation on the computed spectrum.
• To provide a benchmark for quarkonium spectroscopy in the quenched approximation using improved gauge and fermion actions.

Proposed method

• Simulations are performed using the quenched approximation of QCD with the tadpole-improved clover fermion action to reduce discretization errors.
• Two different lattice spacings are employed to enable continuum extrapolation and control systematic uncertainties.
• Spectroscopic states are extracted from correlation functions using variational methods to improve state identification.
• The relativistic nature of the clover action allows for accurate description of spin-dependent interactions, crucial for fine structure.
• Masses of the lowest-lying S- and P-wave states are extracted via fitting to time-correlation functions.
• Spin splittings (fine structure) are computed directly from the energy differences between triplet and singlet states.

Experimental results

Research questions

• RQ1 What are the masses of the lowest-lying S- and P-wave quarkonium states in quenched lattice QCD?
• RQ2 Can the triplet fine structure splitting in quarkonium be reliably computed using a relativistic fermion action on the lattice?
• RQ3 How do the results depend on lattice spacing and quark mass, and what is the convergence behavior toward the continuum limit?
• RQ4 How do the computed masses compare with experimental values and non-relativistic QCD predictions?

Key findings

• The ground state charmonium (1S) mass is computed with high precision, showing good agreement with experimental values.
• The first lattice QCD calculation of the spin-triplet fine structure splitting in quarkonium is achieved, yielding consistent splittings for the 1P and 2P states.
• The hyperfine splitting for the 1S state is found to be in good agreement with experimental data, validating the relativistic action's accuracy.
• The P-wave states (1P) are resolved into their spin multiplets, with the fine structure splitting clearly resolved in the spectrum.
• Systematic errors from discretization are reduced by using two lattice spacings, enabling reliable continuum extrapolation.
• The results demonstrate the viability of the tadpole-improved clover action for studying heavy quarkonium with relativistic accuracy.