Energy correlations in heavy states

TL;DR

This paper investigates energy correlations in heavy states within conformal field theories, revealing a transition from power-like to flat angular dependence influenced by the operator's scaling dimension and theory dynamics, analyzed in planar ${ m f N}=4$ SYM at various couplings.

Contribution

It provides a detailed analysis of the transition in energy correlations from power-law to flat regimes in heavy states, connecting conformal field theory predictions with QCD phenomena.

Findings

Identifies two regimes of energy correlations: power-like at small angles and flat at large angles.

Shows the transition is governed by the scaling dimension of the heavy operator and the theory's dynamics.

Analyzes the phenomenon in planar ${ m f N}=4$ SYM at both weak and strong coupling.

Abstract

We study energy correlations in states created by a heavy operator acting on the vacuum in a conformal field theory. We argue that the energy correlations in such states exhibit two characteristic regimes as functions of the angular separations between the calorimeters: power-like growth at small angles described by the light-ray OPE and slowly varying, or ``flat'', function at larger angles. The transition between the two regimes is controlled by the scaling dimension of the heavy operator and the dynamics of the theory. We analyze this phenomenon in detail in the planar ${\cal N}=4$ SYM theory both at weak and strong coupling. An analogous transition was previously observed in QCD in the measurement of the angular energy distribution of particles belonging to the same energetic jet. In that case it corresponds to the transition from the light-ray OPE, perturbative regime described in terms of correlations between quarks and gluons to the flat, non-perturbative regime described in terms of correlations between hadrons.