Deep inelastic structure functions in light-front QCD: Radiative corrections

Recently, we introduced a unified theory to deal with perturbative and non-perturbative QCD contributions to hadronic structure functions in deep inelastic scattering. This formulation is realized by combining the coordinate space approach based on light-front current algebra techniques and the momentum space approach based on Fock space expansion methods in the Hamiltonian formalism of light-front field theory. In this work we show how a perturbative analysis in the light-front Hamiltonian formalism leads to the factorization scheme we have proposed recently. The analysis also shows that the scaling violations due to perturbative QCD corrections can be rather easily addressed in this framework by simply replacing the hadron target by a dressed parton target and then carrying out a systematic expansion in the coupling constant ${\alpha }_s$ based on the perturbative QCD expansion of the dressed parton target. The tools employed for this calculation are those available from light-front old-fashioned perturbation theory. We present a complete set of calculations of unpolarized deep inelastic structure functions to order ${\alpha }_s.$ We extract the relevant splitting functions in all the cases. We explicitly verify all the sum rules to order ${\alpha }_s.$ We demonstrate the validity of approximations made in the derivation of the new factorization scheme. This is achieved with the help of detailed calculations of the evolution of structure function of a composite system carried out using multi-parton wave functions.