Potential description of the charmonium from lattice QCD

TL;DR

This paper computes interquark potentials for charmonium using lattice QCD with relativistic heavy quarks, and solves the Schrödinger equation to predict the spectrum, showing good agreement with experimental data.

Contribution

It introduces a method to derive spin-independent and spin-spin potentials for charmonium directly from lattice QCD with physical quark masses.

Findings

Charmonium spectrum matches experimental data below open charm threshold.

Finite quark mass potentials are obtained via Bethe-Salpeter amplitudes.

Relativistic heavy quark action improves potential calculations.

Abstract

We present spin-independent and spin-spin interquark potentials for charmonium states, that are calculated using a relativistic heavy quark action for charm quarks on the PACS-CS gauge configurations generated with the Iwasaki gauge action and 2+1 flavors of Wilson clover quark. The interquark potential with finite quark masses is defined through the equal-time Bethe-Salpeter amplitude. The light and strange quark masses are close to the physical point where the pion mass corresponds to $M_\pi \approx 156(7)$ MeV, and charm quark mass is tuned to reproduce the experimental values of $\eta_c$ and $J/\psi$ states. Our simulations are performed with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3 {\rm fm})^3$. We solve the nonrelativistic Schr\"odinger equation with resulting charmonium potentials as theoretical inputs. The resultant charmonium spectrum below the open charm threshold shows a fairly good agreement with experimental data of well-established charmonium states.