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.
Structure functions at small x(Bj) in a Euclidean field theory approach
MEGGIOLARO, ENRICO;
2000-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.