The Large-x Factorization of the Longitudinal Structure Function
R. Akhoury, M. G. Sotiropoulos
TL;DR
This paper develops a leading-twist factorization for the longitudinal structure function $F_L$ in the large-$x$ limit by introducing a gauge-invariant jet function $J'$ that probes the transverse momentum of the struck parton. Through a detailed diagrammatic analysis and renormalization-group treatment, the authors derive a Sudakov-exponentiated form for $F_L$ in Mellin space and compute the anomalous dimension $\gamma'_{J'}$ to ${\cal O}(\alpha_s)$. The $O(\alpha_s^2)$ fixed-order logarithmic structure of $F_L$ is reproduced by the factorization, validating the approach and enabling resummation of the $O(\ln^k N / N)$ corrections. The framework extends beyond $F_L$ to other structure functions and inclusive processes near the elastic limit, with potential implications for power corrections and renormalon analyses.
Abstract
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 γ_K and the anomalous dimension γ_{J^\prime} of the new jet function. This anomalous dimension is computed to O(α_s). The suggested factorization for F_L reproduces the fixed order results known to O(α_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.