Factorization of the Jet Mass Distribution in the Small R Limit

We derive a factorization theorem for the jet mass distribution with a given pTJ for the inclusive production, where pTJ is a large jet transverse momentum. Considering the small jet radius limit (R ≪ 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 dσ/(dpTJdMJ2) and dσ/dpTJ. When MJ∼pTJR, the perturbative series expansion for the jet mass distributions works well. As the jet mass becomes small, large logarithms of MJ/(pTJR) appear, and they can be systematically resummed through a more refined factorization theorem for the jet mass distribution.