On the resummation of non-global logarithms at finite $\mathbf{N_c}$

TL;DR

This paper calculates non-global logarithms at finite N_c for the hemisphere mass distribution in e+e- collisions, providing insights into their all-orders resummation and finite-N_c effects at single logarithmic accuracy.

Contribution

It offers the first calculation of non-global logs at finite N_c up to fifth order, suggesting an exponential resummation and comparing finite-N_c results with large-N_c approximations.

Findings

Finite N_c corrections are significant for the hemisphere mass distribution.

Results agree with large N_c calculations, validating the resummation approach.

Finite N_c effects can influence precision predictions in jet physics.

Abstract

We present a calculation of non-global logs at finite $\mathrm{N_c}$ for the hemisphere mass distribution in $e^+e^-\to 2$ jets at single log accuracy up to fifth order in the strong coupling constant. Our results suggest a possible all-orders resummation of these large logs into an exponential. Comparing our results to those at large $\mathrm{N_c}$, recently reported in literature, we find an agreement. We additionally compare our findings with the numerical all-orders resummation at large $\mathrm{N_c}$ and discuss the significance of neglected finite-$\mathrm{N_c}$ corrections on the said distribution.