Threshold resummation of transverse momentum distributions beyond next-to-leading log

TL;DR

This paper develops a comprehensive formula for threshold resummation of transverse momentum distributions in processes with a colorless final state, extending beyond the next-to-leading log accuracy and validated against existing results.

Contribution

It generalizes the renormalization-group based approach to threshold resummation, enabling all-order logarithmic accuracy for transverse momentum distributions.

Findings

Derived a general all-order threshold resummation expression.

Extended results to next-to-next-to-leading log level.

Validated against known NLL and fixed-order results.

Abstract

We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.