Kinematical bounds on jet variables and the heavy jet mass distribution

Abstract

We investigate the dependence of the bounds of several QCD jet variables on the order of perturbation theory. We show that the ratio of the heavy jet invariant mass squared to the c.m. energy, M H 2/ s, is bounded by 1 3 in every order of perturbation theory. To illustrate the consequences, using the recent gluon loop calculations of Ellis et al. we calculate d σ/ d( M H 2/ s) to order α s 2 and contrast it with the thrust distribution. It is suggested that the perturbation series for M H 2/ s converges faster and agrees better with experiment away from the infrared sensitive region.