The Baryon Wilson Loop Area Law in QCD

Abstract

There is still confusion about the correct form of the area law for the baryonic Wilson loop (BWL) of QCD. Strong-coupling (i.e., finite lattice spacing in lattice gauge theory) approximations suggest the form exp[−KAY], where K is the q¯q string tension and AY is the global minimum area, generically a three-bladed area with the blades joined along a Steiner line (Y configuration). However, the correct answer is exp[−(K/2)(A12 + A13 + A23)], where, e.g., A12 is the minimal area between quark lines 1 and 2 ( ∆ configuration). This second answer was given long ago, based on certain approximations, and is also strongly favored in lattice computations. In the present work, we derive the ∆ law from the usual vortex-monopole picture of confinement, and show that in any case because of the 1/2 in the ∆ law, this law leads to a larger value for the BWL (smaller exponent) than does the Y law. We show that the three-bladed strong-coupling surfaces, which are infinitesimally thick in the limit of zero lattice spacing, survive as surfaces to be used in the non-Abelian Stokes ’ theorem for the BWL, which we derive, and lead via this Stokes ’ theorem to the correct ∆ law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU(N), wit

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