N jettiness: an inclusive event shape to veto jets

Jet vetoes are essential in many analyses at the LHC and Tevatron. Typical signals have a specific number of hard jets or leptons, while backgrounds have additional jets. Vetoing undesired jets efficiently discriminates signal and background. For a sample with ≥N jets, the veto to give N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space and causes large double logarithms in perturbation theory that must be summed. Jet vetoes are typically implemented using jet algorithms, yielding complicated phase-space restrictions, and reliance on leading-log parton-shower Monte Carlo simulations. We introduce a global event shape "N jettiness" τN, which is defined for events with N signal jets. Requiring τN≪1 constrains radiation between the signal jets and provides a theoretically well-controlled jet veto. N jettiness yields a factorization formula with inclusive jet and beam functions.