Abstract
Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in mathcal{N} = 4 super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In mathcal{N} = 4, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.
Highlights
Factorization in the collinear limitTo compute the behavior of the EEEC in the collinear limit, we will use timelike collinear factorization, and extend the factorization formula presented in [26] for the EEC
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In this paper we have presented a calculation of the three point energy correlator in the collinear limit
Summary
To compute the behavior of the EEEC in the collinear limit, we will use timelike collinear factorization, and extend the factorization formula presented in [26] for the EEC. We can write the result for the EEEC jet function at the lowest non-trivial order as This expression is true for a generic measurement function, M, but in general it is hard to perform the integral analytically. This particular factorization of the measurement function into energies and angles is non-standard in jet substructure, but we find that it is extremely convenient and leads to many of the nice properties of the result.
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