Calibrating the Naïve Cornell Model with NRQCD

Abstract

Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predictions for the lowest-lying bottomonium states up to N${}^3$LO, in which the bottom mass is varied within a wide range. We find that the Cornell model mass parameter can be identified, within perturbative uncertainties, with the MSR mass at the scale $R=1$GeV. This identification holds for any value of ${\alpha }_s$ or the bottom mass, and for all perturbative orders investigated. Furthermore, we show that: a) the "string tension" parameter is 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 characteristic non-relativistic scale. We also show how to remove the $u=1/2$ renormalon of the static QCD potential and sum-up large logs related to the renormalon subtraction by switching to the low-scale, short-distance MSR mass, and using R-evolution. Our R-improved expression for the static potential remains independent of the heavy quark mass value and agrees with lattice QCD results for values of the radius as large as $0.8$fm, and with the Cornell model potential at long distances. Finally we show that for moderate values of $r$, the R-improved NRQCD and Cornell static potentials are in head-on agreement.

22 pages, 13 figures, 3 tables

References in corpus (16)

• PYTHIA 6.4 Physics and Manual
• An Introduction to PYTHIA 8.2
• The equation of state in (2+1)-flavor QCD
• Infrared Renormalization Group Flow for Heavy Quark Masses
• Fermionic contributions to the three-loop static potential
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• Spin-dependent potentials from lattice QCD
• Equation of State in 2+1 Flavor QCD at High Temperatures
• Top Quark Mass Calibration for Monte Carlo Event Generators
• The QCD static energy at NNNLL
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• The charm/bottom quark mass from heavy quarkonium at N${}^3$LO
• Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N${}^3$LO
• P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• QQ-onia package: a numerical solution to the Schrodinger radial equation for heavy quarkonium
• Higher-order condensate corrections to ${\rm Y}$ masses, leptonic decay rates and sum rules

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• Precise determination of ${\alpha }_s$ from relativistic quarkonium sum rules
• Bottomonium spectroscopy motivated by general features of pNRQCD
• Charmonium Properties Using the Discrete Variable Representation (DVR) Method
• Renormalons beyond the Borel plane
• Heavy quark correlators in Instanton Liquid Model with perturbative corrections
• Complete analytical solution to the Cornell potential and heavy quarkonium structure
• Gluons, Light and Heavy Quarks in the Instanton Vacuum
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