Evolution Equations for Nonlocal Hadron Operators

Abstract

The study of high-energy scattering processes of hadrons involving transfer of large momenta can be carried out with the help of the operator-product expansion (OPE) (Wilson, 1969) for products of local operators. Such an expansion has often been given in terms of local operators of different twists at short or light-like distances. However, as indicated by several calculations (Geyer, 1982; Balitsky, 1983; Braunschweig et al., 1984; Geyer et al., 1985), it is more effective to use a nonlocal light-cone expansion (LCE) called the string operator expansion (SOE), which is given in terms of gauge-invariant nonlocal operators. This expansion enjoys the fact that it is a true identity in the Fock space (Anikin and Zavialov, 1978), whereas a local LCE is valid only on a dense subset of the Fock space (Bordag and Robaschik, 1980). Moreover, the use of the SOE is physically very appealing, since hadrons, whose dynamics can be very well described by quantum chromodynamics (QCD), are extended objects and should be more naturally described by appropriate gauge-invariant nonlocal operators (Graigie and Dorn, 1981). Thus, nonlocal operators can play an important role both in our understanding of QCD and in practical computations. Therefore, it is hoped that the SOE can provide a more effective and systematic approach to the understanding of nonleading twist effects in QCD.