Cornell potential

The potential consists of two parts. The first one, -\frac{4}{3}\frac{\alpha_s}{\;r\;} dominate at short distances, typically for r fm. For precise determination of the short distance potential, the running of \alpha_s must be accounted for, resulting in a distant-dependent \alpha_s(r). Specifically, \alpha_s 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. ==Long distance potential==

The second term of the potential, \sigma\,r, is the linear confinement term and fold-in the non-perturbative QCD effects that result in color confinement. \sigma is interpreted as the tension of the QCD string that forms when the gluonic field lines collapse into a flux tube. Its value is \sigma \sim 0.18 GeV^2. \sigma controls the intercepts and slopes of the linear Regge trajectories. ==Domains of application==

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. Likewise, the potential has been extended to include spin-dependent terms ==Calculation of the quark-quark potential==

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. 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. More recently, calculations based on the AdS/CFT correspondence have reproduced the Cornell potential using the AdS/QCD correspondence or light front holography. ==See also==