Azimuthal Modulations in Photon-Induced Processes

TL;DR

The paper investigates azimuthal modulations in photon-induced processes across ultra-peripheral collisions and $e^+e^-$ colliders, focusing on $\cos(n\phi)$ harmonics as probes of linearly polarized photons, final-state radiation, and quantum interference. It synthesizes EPA/TMD, SCET, CGC, and dispersion-framework approaches to describe dilepton production, light-by-light scattering, diffractive dijet and vector-meson production in UPCs, and $\gamma\gamma\to\pi\pi$ in $e^+e^-$ collisions. Key findings include strong agreement with experimental data on $\langle\cos(4\phi)\rangle$ in dilepton UPCs, a mass-dependent separation of initial-state polarization and soft radiation effects, and a detailed mapping of azimuthal harmonics to gluon Wigner distributions and double-slit interference in vector meson production. The work demonstrates that azimuthal modulations are a powerful, multi-dimensional imaging tool for nuclear structure and precision QED/QCD tests, with significant implications for hadronic light-by-light contributions to the muon anomalous magnetic moment and for future high-statistics measurements at Belle II, BESIII, and UPC facilities.

Abstract

We review recent theoretical developments and experimental measurements of azimuthal modulations in photon-induced processes, covering both ultra-peripheral heavy-ion collisions (UPCs) and $e^+e^-$ colliders. The azimuthal asymmetries $\cos(nφ)$ ($n=1,2,3,4$) serve as precision diagnostics that probe the linear polarization of coherent photons, final-state soft radiation effects, and quantum interference phenomena at the femtometer scale. In UPCs, we discuss dilepton production, diffractive dijet and vector meson production, where theoretical predictions show excellent agreement with STAR, ALICE, and CMS measurements. The unique double-slit interference effect in nucleus-nucleus collisions plays a crucial role in describing experimental observations. At $e^+e^-$ colliders, $γγ\toππ$ azimuthal asymmetries enable the direct extraction of helicity amplitude phases, with important implications for hadronic light-by-light scattering and the muon anomalous magnetic moment. Azimuthal modulations establish a powerful tool for multi-dimensional nuclear imaging and precision QED/QCD tests.

Figures (6)

• Figure 1: An illustration of the factorization scheme. The double line represents the gauge link.
• Figure 2: Schematic diagram for diffractive vector meson production in UPC.
• Figure 3: Illustration diagrams for $\cos2\phi$ azimuthal asymmetry
• Figure 4: Illustration diagram for $\cos3\phi$/$\cos\phi$ azimuthal asymmetry
• Figure 5: Illustration diagram for $\cos 4\phi$ azimuthal asymmetry