Probing Transverse Momentum Dependent Structures with Azimuthal Dependence of Energy Correlators

TL;DR

This paper investigates how azimuthal angle dependence of energy correlators in $e^+e^-$ and DIS processes reveals polarization and transverse momentum structures, introducing new observables and extending the formalism for phenomenological studies.

Contribution

It introduces a formalism connecting azimuthal energy correlators with transverse momentum dependent structures, including new jet functions and observables for polarized processes.

Findings

Polarization information propagates into azimuthal dependence.

New EEC observables using lab-frame angles are proposed.

Nonperturbative information is encapsulated by a single number in the OPE region.

Abstract

We study the azimuthal angle dependence of the energy-energy correlators $\langle \mathcal{E}(\hat{n}_1)\mathcal{E}(\hat{n}_2)\rangle$ in the back-to-back region for $e^+e^-$ annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers $\mathbb{S}_i$ in the back-to-back limit $\langle \mathcal{E}_{\mathbb{S}_1}(\hat{n}_1)\mathcal{E}_{\mathbb{S}_2}(\hat{n}_2)\rangle$. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.