Variable-flavor-number scheme for final state jets in thrust

Abstract

We present results for mass effects coming from secondary radiation of heavy quark pairs related to gluon splitting in the thrust distribution for ${e}^{+}{e}^{\ensuremath{-}}$ collisions. The results are given in the dijet limit where the hard interaction scale and the scales related to collinear and soft radiation are widely separated. We account for the corresponding fixed-order corrections at $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$ and the summation of all logarithmic terms related to the hard, collinear, and soft scales as well as the quark mass at ${\mathrm{N}}^{3}\mathrm{LL}$ order. We also remove the $\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}})$ renormalon in the partonic soft function, leading to an infrared evolution equation with a matching condition related to the massive quark threshold. The quark mass can be arbitrary, ranging from the infinitely heavy case, where decoupling takes place, down to the massless limit, where the results smoothly merge into the well-known predictions for massless quarks. Our results are formulated in the framework of factorization theorems for ${e}^{+}{e}^{\ensuremath{-}}$ dijet production and provide universal threshold corrections for the renormalization group evolution of the hard current, the jet, and the soft functions at the scale where the massive quarks are integrated out. The results represent a first explicit realization of a variable-flavor-number scheme for final-state jets along the lines of the well-known flavor-number-dependent evolution of the strong coupling ${\ensuremath{\alpha}}_{s}$ and the parton distribution functions.