Relating $e^+e^-$ annihilation to high energy scattering at weak and strong coupling
Yoshitaka Hatta
TL;DR
The work establishes a nontrivial timelike/spacelike duality between the final state in $e^+e^-$ annihilation and the transverse structure of high-energy hadrons, valid at both weak and strong coupling. At strong coupling, it demonstrates an exact mapping via AdS$_5$ shock-wave geometry between spherical energy/charge distributions on the boundary and the transverse profiles of a color-singlet state, with explicit expressions for energy and charge densities and their Fourier form factors. At weak coupling, it shows that interjet soft-gluon dynamics encoded in the dipole evolution equations maps under a stereographic projection to the angular distribution of soft gluons in the interjet region, yielding an explicit angular distribution and the known BFKL growth, with the projection enabling an exact solution transfer. The results extend to energy-energy correlations, suggesting a unified geometric origin for timelike and spacelike soft radiation that persists beyond perturbation theory and could inform multi-dipole correlation studies and phenomenology of jet structure across coupling regimes.
Abstract
We explore the correspondence between the final state in e^+e^- annihilation and the small-x hadronic wavefunction in the transverse plane both in weakly coupled QCD and strongly coupled N=4 SYM. At strong coupling, the virtual and static photon produced in e^+e^- annihilation can be treated as a shock wave propagating in AdS space leaving spherical energy and charge distributions on the boundary. This is shown to be mathematically identical to the computation of energy and charge distributions in the transverse plane generated by a high energy color singlet state. At weak coupling, the correspondence is useful in studying interjet observables. By performing the stereographic projection to the BFKL equation, we construct an exact solution to the evolution equation derived by Marchesini and Mueller, and find the angular distribution of small-x gluons in the interjet region. Finally we argue that the correspondence holds also for the energy correlation functions.