  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.
