Structure functions at small x_Bj in a Euclidean field theory approach

TL;DR

This paper proposes a novel Euclidean field theory approach to calculate structure functions at small Bjorken-x in deep inelastic scattering, enabling non-perturbative evaluations potentially on the lattice.

Contribution

It introduces a new method linking small-x structure functions to Euclidean functional integrals, offering a non-perturbative computational framework.

Findings

Analytic continuation of the Compton amplitude is expressible as a Euclidean matrix element.

The effective Lagrangian is simply related to the original Lagrangian.

The small-x limit corresponds to a critical point with infinite correlation length.

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.