On soft gluon effects in deep-inelastic structure functions

TL;DR

This paper combines soft-gluon resummation with fixed-order calculations to accurately determine large-x logarithmic coefficients in deep-inelastic scattering, enhancing the precision of quark coefficient functions at high Bjorken x.

Contribution

It provides the first all-orders determination of the four leading large-x logarithmic coefficients, including two additional terms for three-loop functions, improving theoretical predictions.

Findings

Derived coefficients for four leading large-x logarithms to all orders.

Included two additional terms for three-loop coefficient functions.

Estimated the impact of the fifth logarithmic contribution.

Abstract

The behaviour of the quark coefficient functions in deep-inelastic scattering is investigated for large values of the Bjorken variable x. By combining results of soft-gluon resummation and fixed-order calculations, we determine the coefficients of the four leading large-x logarithms, alpha_s^k [{ln(1-x)}^{2k-l}/(1-x)]_+, l = 1, ...4, to all orders in the strong coupling constant alpha_s. This result includes two more terms for the three-loop coefficient functions than previously specified in the literature. The effect of the fifth logarithmic contribution is approximately evaluated. The terms derived here are required, but also seem to be sufficient, for a reliable representation of the coefficient functions at large x.