Timelike Single-logarithm-resummed Splitting Functions

TL;DR

This paper derives all-order single logarithmic contributions to timelike splitting functions in QCD, improving theoretical precision for particle production processes by fixing scheme ambiguities through physical assumptions.

Contribution

It provides a novel all-order calculation of single logarithmic terms in timelike splitting functions, fixing scheme ambiguities using relations with massive-gluon regularization and physical assumptions.

Findings

Results agree with NNLO fixed-order calculations.

Scheme transformation determined from double logarithmic contributions.

Enhanced understanding of timelike splitting functions at all orders.

Abstract

We calculate the single logarithmic contributions to the quark singlet and gluon matrix of timelike splitting functions at all orders in the modified minimal-subtraction (MSbar) scheme. We fix two of the degrees of freedom of this matrix from the analogous results in the massive-gluon regularization scheme by using the relation between that scheme and the MSbar scheme. We determine this scheme transformation from the double logarithmic contributions to the timelike splitting functions and the coefficient functions of inclusive particle production in e+ e- annihilation now available in both schemes. The remaining two degrees of freedom are fixed by reasonable physical assumptions. The results agree with the fixed-order results at next-to-next-to-leading order in the literature.