On the resummation of non-global logarithms at finite ${\mathbf{N}}_{\mathbf{c}}$

Abstract

We present a calculation of non-global logs at finite ${\mathrm{N}}_{\mathrm{c}}$ 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 ${\mathrm{N}}_{\mathrm{c}}$, recently reported in literature, we find an agreement. We additionally compare our findings with the numerical all-orders resummation at large ${\mathrm{N}}_{\mathrm{c}}$ and discuss the significance of neglected finite-${\mathrm{N}}_{\mathrm{c}}$ corrections on the said distribution.

Comments: To appear in the proceedings of the XXIII International Workshop on Deep-Inelastic Scattering and Related Subjects, April 27 - May 1, 2015, Dallas, Texas, USA