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SUMMARY:Cornell Model calibration with NRQCD at N3LO
DTSTART;VALUE=DATE-TIME:20180802T144000Z
DTEND;VALUE=DATE-TIME:20180802T150000Z
DTSTAMP;VALUE=DATE-TIME:20210619T054000Z
UID:indico-contribution-3038191@indico.cern.ch
DESCRIPTION:Speakers: Pablo Garcia Ortega (University of Salamanca)\, Vice
nt Mateu Barreda (University of Salamanca)\, David Rodriguez Entem (Univer
sity of Salamanca)\, Francisco Fernandez (Universidad de Salamanca)\nThe t
ypical energy scale of heavy hadron spectroscopy makes the system accessib
le to perturbative calculations in terms of non-relativistic QCD. Within N
RQCD the predictions of heavy quarkonium energy levels rely on the accurat
e description of the static QCD potential $V_{\\rm QCD}(r)$. Most recent c
alculations computed the energy levels of the lower-lying bottomonium stat
es up to $\\mathcal{O}(\\alpha_s^5 m)$ and $\\mathcal{O}(\\alpha_s^5 m \\l
og \\alpha_s)$ utilizing pNRQCD [1]. A closed expression for arbitrary qua
ntum numbers can be found in Ref [2].\n\nHistorically\, the heavy quarkoni
um spectroscopy was study using phenomenological approaches such as the Co
rnell model $V_{\\rm Cornell}=-\\kappa/r+\\sigma r$\, which assumes a shor
t-distance dominant Coulomb potential plus a liner rising potential that e
merges at long distances. Such model works satisfactorily in describing th
e charmonium and bottomonium spectroscopy. However\, even when there are p
hysically-motivated arguments for the construction of the Cornell model\,
there is no connection a priori between the model and QCD parameters.\n\nB
ased on a previous work on heavy meson spectroscopy [3]\, we calibrate the
Cornell model with NRQCD predictions for the lowest lying bottomonium sta
tes at N$^3$LO\, in which the bottom mass is varied within a wide range. W
e show that the Cornell model mass parameter can be identified with the lo
w-scale short-distance MSR mass at the scale $R = 1$ GeV. This identifica
tion 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 NRQC
D and Cornell static potentials are in head-on agreement when switching th
e pole mass to the MSR scheme\, which allows to simultaneously cancel the
renormalon and sum up large logarithms.\n\n[1] N. Brambilla\, A. Pineda\,
J. Soto and A. Vairo\, Nucl. Phys. B 566\, 275 (2000).\n\n[2] Y. Kiyo and
Y. Sumino\, Nucl. Phys. B 889\, 156 (2014).\n\n[3] V. Mateu and P. G.~Orte
ga\, JHEP 1801 (2018) 122.\nhttps://indico.cern.ch/event/648004/contributi
ons/3038191/
LOCATION:Hall H (Arts Bldg.)
RELATED-TO:indico-event-648004@indico.cern.ch
URL:https://indico.cern.ch/event/648004/contributions/3038191/
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