---
title: Nucleon Energy Correlators (NECs) Overview
url: https://www.emergentmind.com/topics/nucleon-energy-correlators-necs
type: topic
---

# Nucleon Energy Correlators (NECs) Overview

Nucleon Energy Correlators (NECs) are operator-defined, energy-weighted angular correlation observables introduced to encode the microscopic details of a nucleon, including the parton angular distribution in a nucleon, the collinear splitting to all orders, and the internal transverse dynamics of the nucleon. In their original formulation, NECs are measured in lepton-nucleon deep inelastic scattering (DIS) through weighted energy flow in the target fragmentation region, without introducing non-perturbative fragmentation functions or jet clustering algorithms. Subsequent work developed polarized, small-$x$, semi-inclusive, and jet-based extensions, so the literature now uses both “nucleon energy correlators” and “nucleon energy-energy correlators” for closely related constructions [2209.02080, 2303.01530].

## 1. Definition and operator structure

The basic NEC is built from a partonic bilocal operator with an insertion of the energy flow operator. A general quark $n$-point definition is
\[
f_{q,n}(x,\{\Omega_i\}) = \int \frac{dy^-}{2\pi}\, e^{-ixy^-P^+}
\left\langle P,s \left| \bar{\xi}(y^-,0)\,\mathcal{L}(\infty)\,
\mathcal{E}(\Omega_1)\cdots \mathcal{E}(\Omega_n)\,\Gamma\,
\mathcal{L}(\infty,0)\,\xi(0) \right| P,s \right\rangle ,
\]
where $

Source: https://www.emergentmind.com/topics/nucleon-energy-correlators-necs