On the QCD analysis of Jet Broadening

TL;DR

Addresses the small-B jet-broadening distribution in e+e- annihilation, aiming for single-logarithmic accuracy by correcting quark recoil effects neglected in the CTW approach. The authors combine independent gluon emission with a coherent-branching framework, introducing a recoil-dependent scaling λ that shifts the double-log radiator from B to 2B/λ and yields compact expressions for Σ_R, Σ_T, and Σ_W. They demonstrate that gluon branching is subleading at this accuracy and show that CTW predictions are recovered up to a rescaling factor (2/λ)^{R'}, with numerical checks against fixed-order results supporting the improvement. The work provides a more precise perturbative description of jet broadening distributions and clarifies how recoil and single-log terms modify CTW’s exponentiation.

Abstract

The perturbative all-order analysis of the jet-broadening B-distribution in the small-B region is carried out with single-logarithmic accuracy, which requires the control of both the sum of the moduli and the modulus of the sum of the transverse momenta of soft gluons. We confirm the master equation for the B-distribution derived by Catani, Turnock and Webber (CTW). Proper treatment of quark recoil is necessary at this accuracy. This effect was neglected in the CTW solution. We show that the answer can be expressed in terms of the CTW result but evaluated at a properly rescaled B value.