  The energy-energy correlation (EEC) measures the angular distribution of the
energy that flows through two calorimeters separated by some relative angle in
the final state created by a source. We study this observable in the limit of
small and large angles when it describes the correlation between particles
belonging, respectively, to the same jet and to two almost back-to-back jets.
We present a new approach to resumming large logarithmically enhanced
corrections in both limits that exploits the relation between the energy
correlations and four-point correlation functions of conserved currents. At
large angle, we derive the EEC from the behaviour of the correlation function
in the limit when four operators are light-like separated in a sequential
manner. At small angle, in a conformal theory, we obtain the EEC from
resummation of the conformal partial wave expansion of the correlation function
at short-distance separation between the calorimeters. In both cases, we obtain
a concise representation of the EEC in terms of the conformal data of twist-two
operators and verify it by comparing with the results of explicit calculation
at next-to-next-to-leading order in maximally supersymmetric Yang-Mills theory.
As a byproduct of our analysis, we predict the maximal weight part of the
analogous QCD expression in the back-to-back limit.
