Hamiltonian Analysis of the Deep Inelastic Structure Function

Abstract

We investigate the feasibility of analyzing deep inelastic structure functions in Hamiltonian formalism by combining the light-front BJL limit of high energy amplitudes and the Fock space (multi-parton) description of hadrons. This study is motivated by some of the theoretical questions emerging from the ongoing nonperturbative/perturbative studies in light-front QCD and also by current problems in the interface of perturbative/nonperturbative QCD. In this preliminary study, we address the unpolarized structure function $F_2$. Our starting point is the expression for the quark structure function as the Fourier transform of the expectation value of the {\it good component} of a bilocal current in the target state. By expanding the target state in a set of multi-particle Fock states, the structure function is expressed as the sum of squares of multi-parton wavefunctions integrated over independent longitudinal and transverse parton momenta. Utilizing the fact that the multi-particle Fock states are connected with each other by the light-front QCD Hamiltonian, we study questions of cancellation of collinear singularities, factorization of mass singularities, and the logarithmic scaling violations in the Hamiltonian picture. In this paper the essential features of the formalism are illustrated utilizing the calculation of the structure function of a dressed quark and the evolution of the valence part of the $q {\bar q}$ bound state structure function up to order $g^2$.