Factorization of Jet Mass Distribution in the small $R$ limit

TL;DR

This paper develops a factorization theorem for jet mass distributions in the small radius limit, enabling precise calculations and resummation of large logarithms for high transverse momentum jets.

Contribution

It introduces a new factorization framework for jet mass distributions at small R, separating the cross section into universal functions for quark and gluon jets.

Findings

Jet mass distributions are well-normalized and scale invariant.

The factorization allows extraction from cross section ratios.

Resummation of large logarithms improves theoretical predictions.

Abstract

We derive a factorization theorem for the jet mass distribution with a given $p_T^J$ for the inclusive production, where $p_T^J$ is a large jet transverse momentum. Considering the small jet radius limit $(R\ll 1)$ we factorize the scattering cross section into a partonic cross section, the fragmentation function to a jet, and the jet mass distribution function. The decoupled jet mass distributions for quark and gluon jets are well-normalized and scale invariant. And they can be extracted from the ratio of two scattering cross sections such as $d\sigma/(dp_T^JdM_J^2)$ and $d\sigma/dp_T^J$. When $M_J \sim p_T^J R$, the perturbative series expansion for the jet mass distributions works well. As the jet mass becomes small, the large logarithms of $M_J / (p_T^J R)$ appear, and they can be systematically resummed through more refined factorization theorem for the jet mass distribution.