  The N-jettiness event shape divides phase space into N+2 regions, each
containing one jet or beam. These jet regions are insensitive to the
distribution of soft radiation and, with a geometric measure for N-jettiness,
have circular boundaries. We give a factorization theorem for the cross section
which is fully differential in the mass of each jet, and compute the
corresponding soft function at next-to-leading order (NLO). For N-jettiness,
all ingredients are now available to extend NLO cross sections to resummed
predictions at next-to-next-to-leading logarithmic order.
