Designing gapped soft functions for jet production

Distributions in jet production often depend on a soft function, S, which describes soft large angle hadronic radiation between the jets. Near kinematic thresholds S encodes nonperturbative information, while far from thresholds S   can be computed with an expansion in operators. We design soft functions for jet factorization theorems that serve this dual purpose, reducing to the perturbative result in the tail region and to a consistent model in the nonperturbative region. We use the MS¯ scheme, and in both regions S   displays the appropriate renormalization group scale dependence. We point out that viable soft functions in jet production should have a gap associated with the minimum soft hadronic energy deposit. This gap is connected to the leading O(ΛQCD)O(ΛQCD) renormalon ambiguity in massless jet event shapes. By defining the gap in a suitable scheme we demonstrate that the leading renormalon can be eliminated. This improves the convergence of perturbative results, and also the stability by which nonperturbative parameters encode the underlying soft physics.