Energy-energy correlation in N = 4 super Yang-Mills theory at next-to-next-to-leading order

114

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 shortdistance 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.2 In general, the Lorentz indices of the currents in (1.2) should be contracted with the polarization vector of the incoming virtual photon. After averaging over the angular correlations between the final state and the incoming beams in (1.1), the sum over the polarizations gives g µν .3In what follows we refer to J µ and T µν as source and calorimeter operators, respectively.

“…The first three terms of the expansion are in agreement with the NNLO result for the energyenergy correlation in N = 4 SYM [23,24], the O(a 4 ) term is a prediction.…”

Section: Checkssupporting

confidence: 77%

Section: Checksmentioning

confidence: 99%

Section: Checksmentioning

confidence: 99%

Section: Sum Rules For the Energy Correlationsmentioning

confidence: 99%

See 2 more Smart Citations

Energy correlations in the end-point region

Korchemsky

2020

114

“…(4.19). Firstly, EEC in the back-to-back limit obey the leading transcendental principle [84,85], which states that the maximal transcendental part of the QCD results are identical to the same quantity in N = 4 supersymmetric Yang-Mills (SYM) theory, up to trivial overall color factor [86]. In Eq.…”

Section: Jet Function For the Eec In The Back-to-back Limitmentioning

confidence: 99%

Transverse parton distribution and fragmentation functions at NNLO: the quark case

Luo

Wang

et al. 2019

We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to O( 2 ) in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N 3 LL resummation.

The light-ray OPE and conformal colliders

Kologlu

Kravchuk

Simmons-Duffin

et al. 2021

112

194

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).