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Gluon Polarimetry with Energy-Energy Correlators

Yu-Kun Song, Shu-Yi Wei, Lei Yang, Jian Zhou

Abstract

We propose a novel method to probe gluon linear polarization via energy correlations in hard scattering processes. This approach exploits the characteristic $\cos 2φ$ azimuthal modulation in single- and two-point energy correlations within jets initiated by polarized gluons. In contrast to conventional techniques that rely on $k_t$ resummation or intricate jet substructure observables, our method offers a theoretically robust and experimentally accessible avenue for gluon polarimetry. We perform an all-order analysis within the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) formalism, incorporating coherent branching effects to achieve improved precision. Our predictions can be tested at current and future facilities, including the LHC, RHIC, HERA, and the EIC.

Gluon Polarimetry with Energy-Energy Correlators

Abstract

We propose a novel method to probe gluon linear polarization via energy correlations in hard scattering processes. This approach exploits the characteristic azimuthal modulation in single- and two-point energy correlations within jets initiated by polarized gluons. In contrast to conventional techniques that rely on resummation or intricate jet substructure observables, our method offers a theoretically robust and experimentally accessible avenue for gluon polarimetry. We perform an all-order analysis within the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) formalism, incorporating coherent branching effects to achieve improved precision. Our predictions can be tested at current and future facilities, including the LHC, RHIC, HERA, and the EIC.

Paper Structure

This paper contains 3 sections, 23 equations, 9 figures.

Table of Contents

  1. Gluon linear polarization in the $q + \bar{q} \to g + Z^0$ process
  2. EEC in $e^+e^-$ annihilations
  3. Fixed order calculation for EEC between $c$ and $\bar{c}$ in $p\bar{p}$ collisions

Figures (9)

  • Figure 1: Illustration of a proton-proton collision where a nearly collinear, linearly polarized gluon is emitted from an incoming parton in a hard scattering event. The gluon's transverse momentum $\vec{P}_\perp$ defines the reference axis. The magnified view shows the resulting EEC within the jet cone, displaying the $\cos 2\phi$ anisotropy, where $\phi$ is the angle between $\vec{P}_\perp$ and the detector pair orientation.
  • Figure 2: Normalized unpolarized angular distributions for the EEC in the region $\theta\in [0.01, 0.3]$, calculated with the boundary conditions $J_{g}(0) = 1$ and $J_{q}(0) = 0$ at $\mu= 30$ GeV. Results are shown for both standard DGLAP evolution and the CCFM formalism with infrared cutoffs $\Lambda = 0.3$ GeV and $\Lambda =0.7$ GeV.
  • Figure 3: Gluon polarization analyzing power $A(\theta)$, representing the maximal azimuthal asymmetry $\langle \cos{2\phi} \rangle$, for single-point and two-point energy correlations with $n_f = 5$, plotted as a function of $\theta$ in the range $0.01$ to $0.3$ at $\mu = P_\perp= 30$ GeV. The error bands show the effect of varying the infrared cutoff $\Lambda$ from $0.3$ GeV to $0.7$ GeV.
  • Figure 4: Schematic illustration of linearly polarized gluons from initial-state radiation in DIS (left) and di-jet production (right), showing characteristic energy patterns in jet cones that enable probing gluon polarization.
  • Figure S1: Gluon linear polarization of the $q + \bar{q} \to g +Z^0$ channel as a function of $\xi$ at different $P_\perp$.
  • ...and 4 more figures