To resolve various outstanding issues associated with the twist four longitudinal structure function $F_L^{\tau =4\mathrm{}}\mathrm{}\left(x\right)\mathrm{}$ we perform an analysis based on the BJL expansion for the forward virtual photon-hadron Compton scattering amplitude and equal (light-front) time current algebra. Using the Fock space expansion for states and operators, we evaluate the twist four longitudinal structure function for dressed quark and gluon targets in perturbation theory. With the help of a new sum rule which we have derived recently we show that the quadratic and logarithmic divergences generated in the bare theory are related to the corresponding mass shifts in old-fashioned light-front perturbation theory. We present numerical results for the $F_2$ and $F_L$ structure functions for the meson in two-dimensional QCD in the one pair approximation. We discuss the relevance of our results for the problem of the partitioning of the hadron mass in QCD.

• Received 30 April 1998

DOI:https://doi.org/10.1103/PhysRevD.58.114022