Baryon Wilson loop area law in QCD

John M. Cornwall
1996 Physical Review D, Particles and fields  
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 [-KA_Y], where K is the qq̅ string tension and A_Y 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 [-(K/2)(A_12+A_13+A_23)], where, e.g., A_12 is the minimal area between quark lines
more » ... and 2 (Δ 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 Δ law from the usual vortex-monopole picture of confine- ment, and show that in any case because of the 1/2 in the Δ 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 Δ law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU(N), with N>3.
doi:10.1103/physrevd.54.6527 pmid:10020654 fatcat:l4oihsl5urhdppctqsqibcziq4