Charmonium potentials: Matching perturbative and lattice QCD

TL;DR

This paper combines lattice QCD and perturbative QCD to accurately determine charmonium potentials, enabling precise predictions of mass splittings that align well with experimental data.

Contribution

It introduces a method to match lattice and perturbative QCD potentials for charmonium, improving the understanding of spin-dependent interactions at various distances.

Findings

The matched potentials agree with lattice results at intermediate distances.

Predicted charmonium mass splittings match experimental values.

A controlled extension of the spin-spin potential to short distances is achieved.

Abstract

Central and spin-spin potentials for charmonium, constructed from Nambu-Bethe-Salpeter amplitudes in lattice simulations of full QCD, are matched with results from perturbative QCD at an appropriate distance scale. This matching is made possible by defining the perturbative potentials through Fourier transforms with a low-momentum cutoff. The central (spin-independent) potential is compared with potentials derived from an expansion in powers of the inverse quark mass. A well-controlled continuation of the charmonium spin-spin potential from lattice QCD to short distances is performed. The mass splittings of the charmonium singlet and triplet states below the open charm threshold, obtained from the matched spin-spin potential, are in good agreement with the experimental values.