Cornell Model Calibration with NRQCD at N${}^3$LO

Abstract

The typical binding energy of heavy hadron spectroscopy makes the system accessible to perturbative calculations in terms of non-relativistic QCD. Within NRQCD the predictions of heavy quarkonium energy levels rely on the accurate description of the static QCD potential $V_{\mathrm{QCD}}(r)$. Historically, heavy quarkonium spectroscopy was studied using phenomenological approaches such as the Cornell model $V_{\mathrm{Cornell}}=-\kappa /r+\sigma r$, which assumes a short-distance dominant Coulomb potential plus a liner rising potential that emerges at long distances. Such model works reasonably well in describing the charmonium and bottomonium spectroscopy. However, even when there are physically-motivated arguments for the construction of the Cornell model, there is no conection a priori with QCD parameters. Based on a previous work on heavy meson spectroscopy, we calibrate the Cornell model with NRQCD predictions for the lowest lying bottomonium states at N${}^3$LO, in which the bottom mass is varied within a wide range. We show that the Cornell model mass parameter can be identified with the low-scale short-distance MSR mass at the scale $R=1$ GeV. This identification holds for any value of ${\alpha }_s$ or the bottom mass. For moderate values of $r$, the NRQCD and Cornell static potentials are in head-on agreement when switching the pole mass to the MSR scheme, which allows to simultaneously cancel the renormalon and sum up large logarithms.

Comments: 12 pages, 5 figures. XIII Quark Confinement and the Hadron Spectrum. arXiv admin note: text overlap with arXiv:1811.01982