Spin-string interaction in QCD strings

Abstract

I consider the question of the interaction between a QCD string and the spin of a quark or an antiquark on whose worldline the string terminates. The problem is analyzed from the point of view of a string representation for the expectation value of a Wilson loop for a spin-half particle. A string representation of the super Wilson loop is obtained starting from an effective string representation of a Wilson Loop. The action obtained in this manner is invariant under a worldline supersymmetry and has a boundary term which contains the spin-string interaction. For rectangular loops the spin-string interaction vanishes and there is no spin-spin term in the resulting heavy quark potential. On the other hand if an allowance is made for the finite intrinsic thickness of the flux tube by assuming that the spin-string interaction takes place not just at the boundary of the string world sheet but extends to a distance of the order of the intrinsic thickness of the flux tube then we do obtain a spin-spin interaction which falls as the fifth power of the distance. Such a term was previously suggested by Kogut and Parisi in the context of a flux-tube model of confinement.