Non-global logarithms at finite Nc beyond leading order

TL;DR

This paper analytically computes non-global logarithms at finite Nc up to 4 loops for the hemisphere mass distribution in e+e- to di-jets, confirming exponentiation patterns and discussing finite-Nc effects.

Contribution

It provides the first full analytical calculation of non-global logarithms at finite Nc beyond leading order for this process.

Findings

Non-global logarithms exhibit exponentiation pattern.

Results match large-Nc limit findings in literature.

Finite-Nc corrections have notable phenomenological impact.

Abstract

We analytically compute non-global logarithms at finite Nc fully up to 4 loops and partially at 5 loops, for the hemisphere mass distribution in e+e- to di-jets to leading logarithmic accuracy. Our method of calculation relies solely on integrating the eikonal squared-amplitudes for the emission of soft energy-ordered real-virtual gluons over the appropriate phase space. We show that the series of non-global logarithms in the said distribution exhibits a pattern of exponentiation thus confirming - by means of brute force - previous findings. In the large-Nc limit, our results coincide with those recently reported in literature. A comparison of our proposed exponential form with all-orders numerical solutions is performed and the phenomenological impact of the finite-Nc corrections is discussed.