# XIIIth Quark Confinement and the Hadron Spectrum

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
20m
Hall H (Arts Bldg.)

### Hall H

#### Arts Bldg.

Invited talk C: Heavy quarks

### Speaker

Dr Pablo Garcia Ortega (University of Salamanca)

### 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.

### 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)