Soft gluons away from jets: distribution and correlation

TL;DR

This work establishes a detailed dictionary between soft gluon emission in $e^+e^-$ annihilation and high-energy hadron evolution via a conformal stereographic projection. It proves that the timelike dipole picture is the exact counterpart of Mueller's spacelike dipole model, enabling analytic derivations of interjet gluon distributions and energy correlations, including all-orders resummation and nonlinear evolution. The results highlight conformal symmetry guiding the dual descriptions, unveil the structure of dipole densities and correlations, and connect energy correlators to OPE expectations and Regge/Pomeron interpretations, with implications for conformal theories such as $\mathcal{N}=4$ SYM. Overall, the paper provides a unified, analytic framework for interjet radiation that links timelike and spacelike cascades through the stereographic map, offering insights into both perturbative QCD and conformal field theory perspectives.

Abstract

Recently, an exact conformal mapping between soft gluons emitted from jets at large angle in e+e- annihilation and those in the BFKL evolution of a high energy hadron has been proposed. We elucidate some remarkable aspects of this correspondence and use them to analytically compute the distribution and correlation of gluons in the interjet region. We also establish the timelike counterpart of Mueller's dipole model and discuss the resulting linear and nonlinear evolution equations.