Three point energy correlators in the collinear limit: symmetries, dualities and analytic results

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 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 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.

Rethinking jets with energy correlators: Tracks, resummation, and analytic continuation

“…Weighted observables are therefore directly expressible as matrix elements of energy flow operators. As mentioned in the introduction, the simple field theoretic definition of these objects has allowed significant recent progress in their understanding [24,[28][29][30][32][33][34][35][36].…”

“…Here 0 ≤ x ≤ 1, and the track function satisfies the sum rule 4 Although we should emphasize that the perturbative simplicity of energy correlator observables has enabled a number of analytic calculations [24,29,[34][35][36] that were not possible for standard δ-function observables, leading to valuable perturbative data for improving our understanding of event shapes [55]. Although, as mentioned above, their moments are directly related to the energy flow polynomials which are a basis of tagging observables [39].…”

“…Taking the concrete case of the projected threepoint correlator, this definition involves integrating the three-point correlator (whose analytic form was computed at LO in Ref. [29]) over the configuration space of three points shown in Fig. 5.…”

“…The threepoint correlator in the collinear limit was computed in Ref. [29] in N ¼ 4 SYM theory and in QCD for both quark and gluon jets. It depends on three variables: the longest side x L and a complex variable z 3 defining the position of the third point, as illustrated in Fig.…”

“…(2) are in a sense the simplest observables in a field theory that measure the flow of energy. In particular, they inherit a number of simple theoretical properties from their direct representation as a matrix element: They have manifest symmetry properties [22,23,28,29], enjoy simple factorization properties in limits [28][29][30][31][32][33], have simple nonperturbative behavior even away from singular regions of phase space [19], can be analytically calculated to high perturbative orders [24,[34][35][36], and can be directly studied using sophisticated techniques from conformal field theory (CFT) [28,33,37,38], including at strong coupling in N ¼ 4 super Yang-Mills (SYM) using the AdS/CFT correspondence [21]. Furthermore, all infrared and collinear safe energy flow observables can be expressed in terms of these basic objects [17,18] (for recent work, see [39,40]).…”