From squared amplitudes to energy correlators

The leading order \(N\)-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the \(N\) detectors are collinear can be expressed as an integral of the \(1\to N\) splitting function, which is given by the \((N{+}3)\)-point squared super-amplitudes at tree level. Th...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: He, Song, Jiang, Xuhang, Yang, Qinglin, Yao-Qi, Zhang
Format: Article
Language:English
Subjects:
Amplitudes
Canonical forms
Correlation
Correlators
Curves
Yang-Mills theory
Online Access:Get full text
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Summary:The leading order \(N\)-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the \(N\) detectors are collinear can be expressed as an integral of the \(1\to N\) splitting function, which is given by the \((N{+}3)\)-point squared super-amplitudes at tree level. This provides yet another example that the integrand of certain physical observable -- \(N\)-point energy correlator -- is computed by the canonical form of a positive geometry -- the (tree-level) "squared amplituhedron". By extracting such squared amplitudes from the \(f\)-graph construction, we compute the integrand of energy correlators up to \(N=11\) and reveal new structures to all \(N\); we also show important properties of the integrand such as soft and multi-collinear limits. Finally, we take a first look at integrations by studying possible residues of the integrand: our analysis shows that while this gives prefactors in front of multiple polylogarithm functions of \(N=3,4\), the first unknown case of \(N=5\) already involves elliptic polylogarithmic functions with many distinct elliptic curves, and more complicated curves and higher-dimensional varieties appear for \(N>5\).
ISSN:2331-8422