On the renormalization and short-distance properties of hadronic operators in QCD

Abstract

We discuss the renormalization of the contour-dependent gauge-invariant composite bilocal or string operator q(2) exp |g ∫ 1 2 A dz|q(1) in QCD, which one would naturally associated with the hadronic bound states. We then discuss the short-distance expansion of this operator as the end points merge. We argue that some functional average overall possible paths between x 1 and x 2 may be the appropriate operator to describe the mesonic modes in QCD and that the short-distance expansion may provide a valuable insight into the nature of this functional average. Most of our considerations are for smooth contours; however, we propose a simple way of treating on the same footing the additional divergences pointed out by Polyakov due to sharp bends in the contour. This latter confirms the conclusions reached for smooth contours.