Threshold Resummation of the Structure Function F_L

TL;DR

This paper investigates the behavior of the longitudinal structure function F_L in deep-inelastic scattering at large x, deriving all-order coefficients for leading logarithms and highlighting potential limitations for exponentiation at higher accuracy.

Contribution

It combines a conjecture on the large-x limit with three-loop results to derive all-order coefficients for leading large-x logarithms in F_L and related functions, revealing possible obstacles for higher-order exponentiation.

Findings

Derived all-order coefficients for leading large-x logarithms in F_L.

Identified potential limitations for exponentiation with higher logarithmic accuracy.

Extended results to related gluon and quark coefficient functions.

Abstract

The behaviour of the quark coefficient function for the longitudinal structure function F_L in deep-inelastic scattering is investigated for large values of the Bjorken variable x. We combine a highly plausible conjecture on the large-x limit of the physical evolution kernel for this quantity with our explicit three-loop results to derive the coefficients of the three leading large-x logarithms, alpha_s^n ln^(2n-1-k) (1-x), k = 1, 2, 3, to all orders in the strong coupling constant alpha_s. Corresponding results are derived for the non-C_F part of the gluon coefficient function suppressed by a factor 1-x, and for the analogous subleading (1-x) ln^k (1-x) contributions in the quark case. Our results appear to indicate an obstacle for an exponentiation with a higher logarithmic accuracy.