Effective field theory approach to structure functions at small $x_{\mathrm{Bj}}$

Abstract.

We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P ⁰-(1-r)P ³, with P⁰ the usual Hamiltonian and P³ the third component of the momentum operator. We show that a small $x_{\mathrm{Bj}}$ in the structure functions corresponds to the small r limit of the effective theory. We argue that for $r\to 0$ there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations of the structure functions at small $x_{\mathrm{Bj}}$ for arbitrary Q².