The Large-x Factorization of the Longitudinal Structure Function

A leading-twist factorization formula is derived for the longitudinal structure function in the x -->1 limit of deeply inelastic scattering. This is achieved by defining a new jet function which is gauge independent and probes the transverse momentum of the struck parton in the target. In moment space, terms of order (\ln^k N)/N, which are the leading ones for F_L, are shown to be resummable through the cusp anomalous dimension \gamma_K and the anomalous dimension \gamma_{J^\prime} of the new jet function. This anomalous dimension is computed to O(\alpha_s). The suggested factorization for F_L reproduces the fixed order results known to O(\alpha_s^2). The general ideas for resumming the terms of order (\ln^k N)/N in moment space may be extended to the other structure functions and to other inclusive processes near the elastic limit.