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Spin-dependent azimuthal asymmetry of coherent J/ $\psi$ photoproduction in hadronic PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.36 TeV

Using CMS data from 5.36 TeV PbPb collisions, this study reports the first observation of a significant negative spin-dependent azimuthal asymmetry in coherently photoproduced J/ $\psi$ mesons, confirming a theoretical model where the meson inherits the incident photon's linear polarization and suggesting a novel method for reaction plane determination.

Original authors: CMS Collaboration

Published 2026-09-07

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CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the realm of high-energy physics, scientists often look at the universe not just as a collection of particles, but as a stage where light and matter interact in extreme ways. When heavy atomic nuclei, such as lead, are accelerated to nearly the speed of light and smashed together, they generate immense electromagnetic fields. These fields act like a flood of real photons, or particles of light, that can strike other nuclei without the nuclei themselves touching. This process allows researchers to create short-lived particles called vector mesons, which are essentially heavy cousins of the particles that make up ordinary matter. A key question in this field is how the spin, or intrinsic rotation, of these newly created particles influences the way they break apart. By studying the direction in which the fragments fly, physicists hope to understand the fundamental rules governing how light transforms into matter and how the geometry of a collision shapes the outcome.

A researcher using the CMS detector at the Large Hadron Collider has now provided a clear answer to this question by observing a specific type of particle decay in lead-lead collisions. The experiment took place at a collision energy of 5.36 trillion electron volts, a scale where the laws of quantum mechanics and relativity play out in dramatic fashion. The team focused on a particle called the J/psi, which is a type of vector meson made of a charm quark and its antimatter partner. In this study, the J/psi mesons were created not by the violent collision of the nuclei themselves, but by a photon from one nucleus interacting with the other. These particles then decayed into a pair of muons, which are heavy versions of electrons. The researcher measured the angles at which these muons were emitted relative to the orientation of the collision, specifically looking for a pattern that would reveal the influence of the J/psi's spin.

The analysis relied on data collected from 1.26 inverse nanobarns of collisions, a specific amount of data that allowed the researcher to isolate the rare events where the J/psi mesons were produced coherently, meaning the photon interacted with the entire nucleus as a single unit rather than with individual protons or neutrons. The scientist examined the distribution of the muons' flight paths and found a distinct, repeating pattern. Instead of the muons flying out in random directions, they showed a preference for specific angles relative to the plane of the collision. This pattern was quantified by a value representing the strength of the modulation, which the researcher measured to be negative. This negative value appeared with a high level of statistical certainty, exceeding five standard deviations, which is the threshold physicists use to claim a definitive discovery.

Crucially, the study found that this pattern did not change based on how central the collision was or where the J/psi meson was produced within the collision zone. The consistency of the result across different conditions suggests a robust underlying physical mechanism. The findings align with a theoretical model where the J/psi meson inherits the polarization, or directional alignment, of the photon that created it. Because the photon's polarization is tied to the geometry of the collision, the decay products of the J/psi effectively map out the orientation of the original impact. This observation confirms that the spin of the decay products matters; the muons, which have a specific type of spin, behave differently than the pions produced in similar studies of other particles.

This work marks the first time such a spin-dependent effect has been clearly observed in the decay of coherently produced vector mesons within hadronic collisions. It validates the idea that the polarization of the initial photon is preserved through the creation of the meson and imprinted on its decay products. Furthermore, the study demonstrates that the orientation of the collision, often difficult to determine precisely, can be inferred from the polarization of these particles. This offers a new, independent method for measuring the geometry of heavy-ion collisions, which could be particularly useful for studying smaller collision systems where traditional methods struggle. The results provide a direct window into the spin dynamics of photon-induced interactions, confirming that the direction of the light that creates a particle dictates the direction in which that particle falls apart.

Technical Summary: Spin-Dependent Azimuthal Asymmetry of Coherent J/ψ Photoproduction in Hadronic PbPb Collisions

Problem and Motivation
In ultrarelativistic heavy-ion collisions, the intense electromagnetic fields of the nuclei can be modeled as fluxes of quasi-real photons. These photons can fluctuate into virtual quark-antiquark pairs and interact with another nucleus via color-singlet gluon exchange to produce real vector mesons (e.g., $J/\psi$ , $\rho^0$ ). While coherent photoproduction has been extensively studied in ultraperipheral collisions (UPCs), where the impact parameter exceeds the sum of nuclear radii, this process also occurs in hadronic collisions.

A key theoretical prediction is that the linearly polarized photons from the Lorentz-contracted electromagnetic fields transfer their polarization to the coherently produced vector meson. This polarization should manifest as a second-order harmonic modulation ( $\cos(2\phi)$ ) in the azimuthal distribution of the meson's decay products relative to the polarization axis. Previous measurements in UPCs relied on quantum interference between indistinguishable production paths (where either nucleus acts as the photon source) to correlate the meson's transverse momentum ( $p_T$ ) with its polarization. However, this interference is suppressed at large rapidities or in asymmetric systems, and the high $p_T$ of decay leptons from heavy mesons like $J/\psi$ makes precise $p_T$ direction determination difficult.

The central problem addressed is the direct observation of spin-dependent azimuthal asymmetry in coherently photoproduced vector mesons within hadronic collisions, independent of quantum interference effects. The paper proposes using the second-order event plane ( $\Psi_2$ ), reconstructed from the flow of charged particles, as a robust proxy for the impact parameter direction and, consequently, the photon polarization axis.

Methodology
The analysis utilizes data from the CMS experiment at the LHC, corresponding to lead-lead (PbPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}} = 5.36$ TeV, collected in 2023 with an integrated luminosity of 1.26 nb $^{-1}$ .

Event Selection: Events are selected using a minimum-bias trigger requiring energy deposits in forward hadron calorimeters (HF) and neutron candidates in zero-degree calorimeters (ZDC). Offline, events are restricted to the 50–80% centrality class to ensure a significant coherent contribution while managing background. Primary vertices are required to be within 25 cm of the interaction point along the beam axis.
Signal Reconstruction: $J/\psi$ mesons are reconstructed via their decay into muon pairs ( $J/\psi \to \mu^+\mu^-$ ). Muons must satisfy "soft muon" identification criteria and lie within a fiducial phase space defined by an $\eta$ -dependent lower $p_T$ boundary. The invariant mass of the muon pairs is required to be between 2.6 and 4.2 GeV.
Event Plane Determination: The second-order event plane angle ( $\Psi_2$ ) is reconstructed using the flow vector ( $Q_2$ ) derived from tracks with $0.3 < p_T < 3.0$ GeV and $|\eta| < 2.4$ , excluding tracks associated with the selected muon pairs to avoid autocorrelations. The event plane resolution is determined using the three-subevent method with the HF calorimeters.
Asymmetry Measurement: The azimuthal angle of the positive muon ( $\phi_{\mu^+}$ ) is measured in the $J/\psi$ rest frame. The variable of interest is $\Delta\phi = \phi_{\mu^+} - \Psi_2$ . The distribution of $\Delta\phi$ is binned and fitted to the form $N(\Delta\phi) = C(1 + 2A_2^{obs}\cos(2\Delta\phi))$ .
Background and Efficiency Correction:
- The coherent $J/\psi$ signal is isolated by selecting low transverse momentum ( $p_T < 0.2$ GeV) candidates, where the coherent contribution dominates.
- Contributions from incoherent and hadronic production are estimated by extrapolating the $p_T$ spectrum from high- $p_T$ regions (where hadronic processes dominate) and subtracted.
- Detector acceptance and reconstruction efficiencies are corrected using simulations (STARLIGHT for coherent, PYTHIA for hadronic) embedded in HYDJET events, with data-to-simulation scale factors applied.
- The observed amplitude $A_2^{obs}$ is corrected for event plane resolution to obtain the physical asymmetry amplitude $A_2$ .

Key Results
The analysis yields a statistically significant negative azimuthal asymmetry for muons from coherently photoproduced $J/\psi$ mesons:

Measured Amplitude: $A_2 = -0.194 \pm 0.022 \text{ (stat)} \pm 0.018 \text{ (syst)}$ .
Significance: The result deviates from zero by more than five standard deviations.
Dependence: The $A_2$ values show no significant dependence on the $J/\psi$ rapidity ( $1.6 < |y| < 2.4$ ) or the collision centrality (50–80%).
Theoretical Comparison: The measured negative amplitude is consistent with theoretical models (Wu et al. and Shao et al.) that predict the $J/\psi$ inherits the linear polarization of the incident photon, which is correlated with the impact parameter (and thus the event plane). The Wu et al. model, which accounts for partial coherence loss due to participating nucleons, provides a good description of the data across all centrality and rapidity intervals. In contrast, the Shao et al. model, based on an impact-parameter dependent saturation model, predicts negative $A_2$ values arising from interference between different photon helicity states; however, the predicted modulation amplitudes are systematically larger than the measurements by approximately a factor of two.

Significance and Claims
The paper claims the first observation of a negative modulation in the azimuthal asymmetry of spin-1/2 muons produced in the decay of coherently photoproduced vector mesons in heavy-ion collisions. This finding, when combined with previous measurements of positive modulation for spin-0 pions from $\rho^0$ decays, provides direct experimental evidence of spin-state dependence in the azimuthal asymmetries of decay products from coherently photoproduced vector mesons.

Furthermore, the paper asserts that the observed correlation between the decay products and the second-order event plane demonstrates that the event plane can serve as an experimentally robust proxy for the polarization direction of coherently photoproduced vector mesons in hadronic collisions. Unlike methods relying on quantum interference, this approach is applicable over a broad rapidity range and across different collision systems. The author suggests this correlation offers a novel approach to reaction plane determination that is largely independent of nonflow effects and event-by-event fluctuations, potentially proving valuable for studying collective behavior in smaller collision systems (e.g., proton-nucleus collisions).

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