  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.
