On threshold resummation of the longitudinal structure function

Abstract

The validity of a previously proposed momentum space ansatz for threshold resummation of the non-singlet longitudinal structure function F_L is checked against existing finite order three-loop results. It is found that the ansatz, which is an assumption for the large-x behavior of the physical evolution kernel, does not work beyond the leading logarithmic contributions to the kernel even at {\cal O}(1/(1-x)) order (except at large-\beta_0), which is consistent with a recent observation of Moch and Vogt. Corrections down by one power of 1-x are also studied. At {\cal O}((1-x)^0) order, the corresponding ansatz fails already at the leading logarithmic level, where the situation appears similar to that encountered in the case of the F_i (i=1,2,3) structure functions. At the next-to-leading logarithmic level, the same term (with opposite sign) responsible for the failure of the ansatz at {\cal O}(1/(1-x)) order is found to occur.