6 v 1 1 M ar 2 00 0 ITEP - TH - 74 / 99 Confinement and short distance physics

We consider non-perturbative effects at short distances in theories with confinement. The analysis is straightforward within the Abelian models in which the confinement arises on classical level. In all cases considered (compact U (1) in 3D and 4D, dual Abelian Higgs model) there are non–perturbative contributions associated with short distances which are due to topological defects. In QCD case, both classical and quantum effects determine the role of the topological defects and the theoretical analysis has not been completed so far. Generically, the topological defects would result in 1/Q 2 corrections going beyond the standard Operator Product Expansion. We review existing data on the power corrections and find that the data favor existence of the novel corrections, at least at the mass scale of (1-2) GeV. We indicate crucial experiments which could further clarify the situation on the phenomenological side. 1. The perturbative QCD describes basic features of hard processes, i.e. processes characterized by a large mass scale Q. On the other hand, the perturbative QCD does not encode the effects of confinement. Hence there is a growing interest in power corrections to the par-ton model which might be sensitive to the nature of confinement (for a recent review see [1]). Moreover, in the the Abelian Higgs model the leading power correction at short distances does reflect confinement [2]. Namely, there exist short strings which are responsible for a stringy potential between confined charges at vanishing distances r → 0. In this note we are exploring Abelian models with confinement in a more regular way by including into consideration the compact three and four dimensional U(1) theory. In all the cases the confinement mechanism can be understood classically. Moreover, we find that the confinement results in additional terms in the static potential at short distances. How topological defects can be manifested at short distances, is easy to understand on the example of the Dirac string. Naively, its energy diverges quadratically in the ultraviolet but in compact U(1) it is normalized to zero [3] changing the power corrections at short distances. As for non-Abelian theories, the Dirac strings are also allowed because of the compactness of the corresponding U(1) subgroup. In this sense, there is a similarity between non–Abelian and Abelian cases. However, there is an important difference as well. On the classical level, the Dirac strings may end up with monopoles which have a vanishing non-Abelian action. Thus,