Non-global and rapidity logarithms in narrow jet broadening

Understand

We derive an all-order factorization theorem for the narrow jet broadening event shape, a measure of the transverse momentum in jet events.

• This is a non-global observable which receives logarithmically enhanced contributions associated with the large rapidity difference between soft and collinear radiation and which is also sensitive to soft recoil effects.
• Our work is the first factorization analysis of an observable of this type and we show that with regard to the non-global nature, the rapidity logarithms do not constitute an essential complication since they can be tied to the jet function, which is the same as for global observables.
• As a consequence, the leading non-global logarithms in narrow jet broadening are encoded in the same overall factor relevant for the hemisphere soft function and light jet mass.