Speaker
Description
The typical energy scale 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 $V_{\rm QCD}(r)$. Most recent calculations computed the energy levels of the lower-lying bottomonium states up to $\mathcal{O}(\alpha_s^5 m)$ and $\mathcal{O}(\alpha_s^5 m \log \alpha_s)$ utilizing pNRQCD [1]. A closed expression for arbitrary quantum numbers can be found in Ref [2].
Historically, the heavy quarkonium spectroscopy was study using phenomenological approaches such as the Cornell model $V_{\rm Cornell}=-\kappa/r+\sigma r$, which assumes a short-distance dominant Coulomb potential plus a liner rising potential that emerges at long distances. Such model works satisfactorily 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 connection a priori between the model and QCD parameters.
Based on a previous work on heavy meson spectroscopy [3], 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. Furthermore we show that a) the “string tension” parameter is completely independent of the bottom mass, and b) the Coulomb strength $\kappa$ of the Cornell model can be related to the QCD strong coupling constant $\alpha_s$ at a certain scale. Finally we show that 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.
[1] N. Brambilla, A. Pineda, J. Soto and A. Vairo, Nucl. Phys. B 566, 275 (2000).
[2] Y. Kiyo and Y. Sumino, Nucl. Phys. B 889, 156 (2014).
[3] V. Mateu and P. G.~Ortega, JHEP 1801 (2018) 122.
