Threshold Resummation of the Structure Function F_L

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.

9 pages, LaTeX, 1 eps-figure