[Paper Review] Tomography of Ultra-relativistic Nuclei with Polarized Photon-gluon Collisions

STAR Collaboration, M. S. Abdallah+393 more|arXiv (Cornell University)|Apr 4, 2022

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This study demonstrates quantum interference in polarized photon-gluon collisions to perform gluon tomography of ultra-relativistic nuclei, using spin alignment in $ρ^0 \to \pi^+\pi^-$ decays to extract nuclear radii. The observed $ρ^0$ spin alignment ($29.2\pm0.4\%$ in Au+Au, $23.8\pm0.6\%$ in U+U) reveals coherent interference over 20 fm, yielding radii of $6.53\pm0.06$ fm (Au) and $7.29\pm0.08$ fm (U), larger than charge radii, confirming sensitivity to gluonic structure and non-local quantum effects.

ABSTRACT

A linearly polarized photon can be quantized from the Lorentz-boosted electromagnetic field of a nucleus traveling at ultra-relativistic speed. When two relativistic heavy nuclei pass one another at a distance of a few nuclear radii, the photon from one nucleus may interact through a virtual quark-antiquark pair with gluons from the other nucleus forming a short-lived vector meson (e.g. ${ρ^0}$). In this experiment, the polarization was utilized in diffractive photoproduction to observe a unique spin interference pattern in the angular distribution of ${ρ^0 ightarrowπ^+π^-}$ decays. The observed interference is a result of an overlap of two wave functions at a distance an order of magnitude larger than the ${ρ^0}$ travel distance within its lifetime. The strong-interaction nuclear radii were extracted from these diffractive interactions, and found to be $6.53\pm 0.06$ fm ($^{197} { m Au }$) and $7.29\pm 0.08$ fm ($^{238} { m U}$), larger than the nuclear charge radii. The observable is demonstrated to be sensitive to the nuclear geometry and quantum interference of non-identical particles.

Motivation & Objective

• To develop a novel method for probing the gluonic structure of large nuclei using quantum interference in high-energy photon-gluon interactions.
• To measure the spatial distribution of gluons in ultra-relativistic nuclei through spin interference in $ρ^0 \to \pi^+\pi^-$ decays.
• To extract nuclear radii from interference patterns in exclusive photoproduction, independent of charge radius measurements.
• To test the coherence of quantum wave functions over distances much larger than the $ρ^0$ lifetime, probing non-locality in strong interactions.
• To establish a new tomographic technique analogous to PET, but for gluon density and nuclear geometry at high energy.

Proposed method

• Utilize linearly polarized photons from Lorentz-boosted electromagnetic fields of ultra-relativistic nuclei in ultra-peripheral collisions.
• Measure the angular distribution of $ρ^0 \to \pi^+\pi^-$ decay products to detect $ρ^0$ spin alignment via $α \cos 2\phi$ modulation.
• Apply two-dimensional $|t|$-distribution analysis to disentangle photon transverse momentum and two-source interference effects.
• Use the observed $ρ^0$ spin alignment as a probe of quantum interference between two indistinguishable amplitudes from projectile and target nuclei.
• Compare data with theoretical models including photon polarization and interference to extract nuclear radii.
• Employ exclusive photoproduction in Au+Au and U+U collisions at RHIC, where nuclei remain intact and interact via virtual photon-gluon fusion.

Experimental results

Research questions

• RQ1 Can quantum interference in $ρ^0$ decay angular distributions reveal the spatial structure of gluons in ultra-relativistic nuclei?
• RQ2 What is the role of non-locality and coherence in the wave functions of decay products from short-lived vector mesons?
• RQ3 How do the measured $ρ^0$ spin alignment and $ρ^0$ production cross-sections constrain the nuclear radius beyond charge radii?
• RQ4 To what extent is the interference effect preserved over distances (~20 fm) much larger than the $ρ^0$ lifetime (~1 fm)?
• RQ5 Can polarized photon-gluon collisions serve as a quantitative tomographic probe of nuclear geometry and gluon distribution at small $x$?

Key findings

• The observed $ρ^0$ spin alignment is $29.2\pm0.4$% in Au+Au and $23.8\pm0.6$% in U+U, indicating significant quantum interference.
• The $ρ^0$ spin alignment exhibits a $α \cos 2\phi$ modulation, consistent with theoretical models incorporating photon polarization and two-source interference.
• The nuclear radius extracted from the interference pattern is $6.53\pm0.06$ fm for $^{197}$Au, larger than its charge radius.
• The nuclear radius for $^{238}$U is $7.29\pm0.08$ fm, also larger than its charge radius, indicating sensitivity to gluonic structure.
• The interference pattern is absent in p+Au collisions, confirming its origin in coherent, two-source interference from identical nuclei.
• Model I, which includes phase-locked interference, matches data well, while Model II (20% higher) suggests at least 80% coherence, indicating minimal decoherence.