Structure functions at small x(Bj) in a Euclidean field theory approach

The small-x(Bj) limit of deep inelastic scattering is related to the high-energy limit of the forward Compton amplitude in a familiar way. We show that the analytic continuation of this amplitude in the energy variable is calculable from a matrix element in Euclidean field theory. This matrix element can be written as a Euclidean functional integral in an effective field theory. Its effective Lagrangian has a simple expression in terms of the original Lagrangian. The functional integral expression obtained can, at least in principle, be evaluated using genuinely non-perturbative methods, e.g., on the lattice. Thus, a fundamentally new approach to the long-standing problem of structure functions at very small x(Bj) seems possible. We give arguments that the limit x(Bj) --> 0 corresponds to a critical point of the effective field theory where the correlation length becomes infinite in one direction. (C) 2000 Elsevier Science B.V. All rights reserved.