July 31, 2018 to August 6, 2018
Maynooth University
Europe/Dublin timezone

Cornell Model calibration with NRQCD at N3LO

Aug 2, 2018, 3:40 PM
Hall H (Arts Bldg.)

Hall H

Arts Bldg.

Invited talk C: Heavy quarks Heavy quarks


Dr Pablo Garcia Ortega (University of Salamanca)


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.

Primary authors

Dr Pablo Garcia Ortega (University of Salamanca) Dr Vicent Mateu Barreda (University of Salamanca) David Rodriguez Entem (University of Salamanca) Francisco Fernandez (Universidad de Salamanca)

Presentation materials