In particle physics, the Cornell potential is an effective method to account for the confinement of quarks in quantum chromodynamics (QCD).
It was developed by Estia J. Eichten, Kurt Gottfried, Toichiro Kinoshita, John Kogut, Kenneth Lane and Tung-Mow Yan at Cornell University[1][2] in the 1970s to explain the masses of quarkonium states and account for the relation between the mass and angular momentum of the hadron (the so-called Regge trajectories).
is the effective radius of the quarkonium state,
is the QCD running coupling,
is the QCD string tension and is a constant of
The potential consists of two parts.
dominate at short distances, typically for
[3] It arises from the one-gluon exchange between the quark and its anti-quark, and is known as the Coulombic part of the potential, since it has the same form as the well-known Coulombic potential
in QCD comes from the fact that quarks have different type of charges (colors) and is associated with any gluon emission from a quark.
is the number of color charges.
depends on the radius of the studied hadron.
[4] For precise determination of the short distance potential, the running of
must be accounted for, resulting in a distant-dependent
must be calculated in the so-called potential renormalization scheme (also denoted V-scheme) and, since quantum field theory calculations are usually done in momentum space, Fourier transformed to position space.
, is the linear confinement term and fold-in the non-perturbative QCD effects that result in color confinement.
is interpreted as the tension of the QCD string that forms when the gluonic field lines collapse into a flux tube.
controls the intercepts and slopes of the linear Regge trajectories.
The Cornell potential applies best for the case of static quarks (or very heavy quarks with non-relativistic motion), although relativistic improvements to the potential using speed-dependent terms are available.
[3] Likewise, the potential has been extended to include spin-dependent terms[3] A test of validity for approaches that seek to explain color confinement is that they must produce, in the limit that quark motions are non-relativistic, a potential that agrees with the Cornell potential.
A significant achievement of lattice QCD is to be able compute from first principles the static quark-antiquark potential, with results confirming the empirical Cornell Potential.
[5] Other approaches to the confinement problem also results in the Cornell potential, including the dual superconductor model, the Abelian Higgs model, and the center vortex models.
[3][6] More recently, calculations based on the AdS/CFT correspondence have reproduced the Cornell potential using the AdS/QCD correspondence[7][8] or light front holography.