Exclusive dimuon production and coherent charmonium photoproduction at forward rapidity in ultra-peripheral Pb$-$Pb collisions at $\mathbf{\sqrt{s_{\rm NN}}=5.36}$ TeV

Using 2023 ALICE data from ultra-peripheral Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.36$ TeV, this paper presents forward rapidity measurements of coherent J/$\psi$ and $\psi$(2S) photoproduction and exclusive dimuon production, revealing significant nuclear shadowing effects in quarkonium production and highlighting the sensitivity of dimuon measurements to photon flux modeling near the nuclear radius.

The Gist

The Big Picture: A High-Speed Dance of Ghosts

Imagine two massive, heavy lead balls (atomic nuclei) zooming toward each other at nearly the speed of light. Usually, if they hit head-on, it's a catastrophic crash, shattering everything into a million pieces.

But in this experiment, the scientists set up the race so the balls missed each other. They passed by like two speeding trains on parallel tracks, just close enough that their "electric fields" (invisible force fields surrounding them) brushed against one another.

Because these lead balls are so heavy and charged, they carry a massive cloud of "virtual" light particles (photons). When the balls pass close by, these clouds collide. It's like two people walking past each other and their umbrellas brushing together, creating a tiny spark. This is called an Ultra-Peripheral Collision (UPC).

The ALICE team at CERN's Large Hadron Collider used these "near-miss" collisions to study two specific things:

1. How light creates heavy particles (making a J/ψ or ψ(2S) particle).
2. How light creates pairs of muons (heavy cousins of electrons).

They did this with a huge amount of data collected in 2023, looking specifically at the "forward" direction (the front of the collision).

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Part 1: The Heavy Hitters (Coherent Charmonium)

The Analogy: The "Ghost" vs. The "Brick"

When the light from one lead ball hits the other, it can create a heavy particle called J/ψ (or its slightly heavier cousin, ψ(2S)).

• The "Brick" Hit (Incoherent): Imagine throwing a pebble at a brick wall. Sometimes, the pebble hits just one brick. The wall gets a little chipped, and that one brick flies off. In physics, this is when the light hits a single proton inside the nucleus. The result is messy, and the new particle flies off at a high speed sideways.
• The "Ghost" Hit (Coherent): Now, imagine the pebble is a ghost that passes through the whole wall without hitting any single brick, but instead "feels" the entire wall as one big object. The whole wall wobbles slightly, but nothing breaks. The new particle is created gently and moves very slowly sideways.

What the Paper Found:
The scientists focused on the "Ghost" hits (coherent production). They wanted to see how the light interacts with the entire nucleus.

• The Shadow Effect: They compared their results to a simple prediction that assumes the nucleus is just a pile of individual bricks (the "Impulse Approximation"). The prediction said there should be more particles than they actually found.
• The Result: They found about 25% fewer J/ψ particles and 30% fewer ψ(2S) particles than the simple prediction.
• The Metaphor: Imagine shining a flashlight through a dense forest. If the trees were just individual sticks, you'd expect a certain amount of light to get through. But because the trees are packed so tightly, they cast shadows on each other, blocking more light than expected. This is called nuclear shadowing. The gluons (the glue holding the nucleus together) are so dense that they "shadow" each other, making it harder for the light to create new particles.

Key Takeaway: The experiment confirmed that at high speeds, the inside of a lead nucleus acts like a dense, shadowy forest, not just a pile of loose bricks.

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Part 2: The Light Pairs (Exclusive Dimuons)

The Analogy: The "Perfect" vs. "Messy" Spark

The second part of the study looked at dimuons (a pair of heavy electrons). This happens when the light from one ball hits the light from the other ball, fusing to create a pair of muons. This is a pure "light vs. light" collision.

• The Simple Model (STARlight): One computer model (STARlight) treats the lead nucleus like a single, tiny point of light. It assumes that if the light passes inside the physical size of the nucleus, it doesn't count. It puts a "hard stop" at the edge of the ball.
• The Refined Model (Upcgen & SuperChic): Newer models treat the nucleus like a fuzzy cloud. They realize that light can interact even if it passes slightly inside the edge of the nucleus.

What the Paper Found:

• At lower speeds (lower rapidity): The simple "point-like" model worked okay.
• At higher speeds (forward rapidity): The simple model started to fail. It predicted fewer muon pairs than the scientists actually saw. The data showed up to 40% more pairs than the simple model predicted.
• The Problem: The newer models (which allow for interactions inside the nucleus) actually predicted too many pairs (about 1–2 times more than observed).

Key Takeaway: The data shows that the simple "point-like" model is too rough for high-speed collisions. We need to understand exactly how the "fuzziness" of the nucleus affects the light. The fact that the data sits between the simple model and the complex models suggests our current understanding of how light flows around heavy nuclei isn't quite perfect yet.

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Summary of the "Story"

1. The Setup: Two lead nuclei zoom past each other without crashing, letting their light fields collide.
2. The Heavy Particles: When light creates heavy particles (J/ψ), the nucleus acts like a dense forest, blocking some of the light (shadowing). The simple "pile of bricks" theory overestimates how many particles are made.
3. The Light Pairs: When light creates light-particles (muons), the simple theory that treats the nucleus as a tiny dot fails at high speeds. It misses the "fuzzy" interactions happening near the edge of the nucleus.
4. The Conclusion: The experiment provides a very precise map of these interactions. It tells theorists, "Your simple models are too simple, and your complex models are a bit too complex. We need a better description of how light and heavy nuclei interact at the very edge."

This paper is essentially a high-precision measurement that helps physicists tune their mathematical models of the universe's building blocks, specifically how light behaves when it grazes the edge of a heavy atom.

Technical Summary

Technical Summary: Exclusive Dimuon Production and Coherent Charmonium Photoproduction at Forward Rapidity in Ultra-Peripheral Pb–Pb Collisions

Problem and Motivation
Ultra-peripheral collisions (UPCs) of heavy ions provide a unique environment to study photon-photon and photon-nucleus interactions via the strong electromagnetic fields generated by the nuclei. This paper addresses two primary physics objectives in the forward rapidity region ($-4 < y < -2.5$) of Pb–Pb collisions at a center-of-mass energy of $\sqrt{s_{NN}} = 5.36$ TeV:

1. Coherent Charmonium Photoproduction: Measuring the production of $J/\psi$ and $\psi(2S)$ mesons where the photon interacts coherently with the entire nucleus. These measurements serve as probes of the nuclear gluon density, specifically testing nuclear shadowing and gluon saturation effects at low Bjorken-$x$ ($10^{-5} \lesssim x \lesssim 10^{-2}$).
2. Exclusive Dimuon Production: Measuring the $\gamma\gamma \to \mu^+\mu^-$ process to test the modeling of photon fluxes within the Equivalent Photon Approximation (EPA). Recent discrepancies between data and theoretical models (specifically regarding impact parameters smaller than the nuclear radius) necessitate precise differential measurements.

Methodology
The analysis utilizes data recorded by the upgraded ALICE detector during the 2023 LHC Run 3, corresponding to an integrated luminosity of $L = 1170 \pm 50 \, \mu\text{b}^{-1}$.

• Event Selection: Ultra-peripheral events are selected by requiring a pair of muon tracks in the forward muon spectrometer ($-4 < \eta < -2.5$) and vetoing hadronic activity using the Fast Interaction Trigger (FIT) system, specifically the FV0 detector. The absence of a hardware trigger on single-muon transverse momentum ($p_T$) in the continuous readout mode allows access to low invariant masses ($m_{\mu\mu} \sim 1.5$ GeV/$c^2$).
• Track Reconstruction and Matching: Muon tracks are reconstructed in the Muon Tracking Chambers (MCH) and matched with segments in the Muon Identifier (MID) to determine the precise bunch crossing and timing.
• Signal Extraction:
  • Charmonium: Raw yields for $J/\psi$ and $\psi(2S)$ are extracted from invariant mass fits using double-sided Crystal Ball functions for the resonances and an exponential function for the non-resonant background. The analysis corrects for feed-down contributions from $\psi(2S) \to J/\psi$ decays and separates coherent from incoherent production by fitting the transverse momentum ($p_T$) distributions. Incoherent components are modeled using H1 parametrizations.
  • Dimuons: Exclusive $\gamma\gamma \to \mu^+\mu^-$ yields are extracted in five invariant mass intervals ($1.5 < m_{\mu\mu} < 10$ GeV/$c^2$) by fitting $p_T$ distributions, excluding the charmonium mass regions. Backgrounds from incoherent photon emission and beam-gas interactions are estimated using side-band methods and Monte Carlo templates.
• Simulation and Efficiency: A full detector simulation within the ALICE O2 framework is used to determine reconstruction efficiencies. Monte Carlo generators (STARlight, Upcgen, SuperChic 4) are employed to model signal and background processes, including nuclear form factors and impact parameter dependencies.

Key Results

1. Coherent $J/\psi$ and $\psi(2S)$ Cross Sections:

   • Rapidity-differential cross sections were measured for both mesons.
   • The ratio of the measured cross section to the impulse approximation prediction (which neglects nuclear effects) yields a suppression factor. The square root of this ratio is approximately 0.76 for $J/\psi$ and 0.71 for $\psi(2S)$ at $y \approx -3$ (typical $x \sim 10^{-2}$).
   • Theoretical Comparison:
     • The Impulse Approximation (STARlight) significantly overestimates the data, confirming the necessity of nuclear shadowing.
     • Leading-Order pQCD models (EPS09 and Leading Twist Approximation) describe the $\psi(2S)$ data well but underestimate the $J/\psi$ cross section by $1\text{--}2\sigma$ in the range $-3.75 < y < -2.5$.
     • The Color Glass Condensate (CGC) model (Mäntysaari, Salazar, and Schenke) agrees with both $J/\psi$ and $\psi(2S)$ measurements within its validity range ($|y| < 2.85$).
   • The measured $\psi(2S)$-to-$J/\psi$ cross-section ratio is $0.131 \pm 0.012$ (stat) $\pm 0.013$ (syst) in the full forward rapidity range, consistent with previous ALICE and LHCb measurements at $\sqrt{s_{NN}} = 5.02$ TeV.

2. Exclusive Dimuon Production Cross Sections:

   • Invariant-mass differential cross sections were measured in three rapidity intervals.
   • Theoretical Comparison:
     • The STARlight generator, which models photon fluxes as point-like sources with a hard cutoff at the nuclear radius, agrees with data in the lowest rapidity range ($-3.0 < y < -2.5$) but underestimates the cross section by up to 40% at higher rapidities and masses.
     • Generators incorporating nuclear form factors (Upcgen and SuperChic 4), which allow for photon emission at impact parameters smaller than the nuclear radius, predict cross sections 1–2$\sigma$ higher than the measured central values across all intervals.
   • The results highlight a discrepancy between data and current theoretical descriptions of photon fluxes, particularly at large rapidities where small impact parameters become significant.

Significance and Claims
The paper claims that the observed suppression of coherent charmonium production provides clear evidence for nuclear gluon shadowing effects, with the magnitude of suppression varying between $J/\psi$ and $\psi(2S)$. The data supports the CGC model's description of saturation effects within its kinematic validity.

Regarding exclusive dimuon production, the paper asserts that the measurements highlight the sensitivity of such processes to the precise modeling of photon fluxes, specifically the treatment of impact parameters near and inside the nuclear radius. The discrepancy with STARlight at forward rapidities suggests that the point-like source approximation is insufficient, while the overestimation by form-factor-based models (Upcgen, SuperChic 4) indicates that current implementations may overestimate the flux or that higher-order QED corrections are required. The authors conclude that these results provide crucial constraints for theoretical models of low-$x$ nuclear dynamics and photon-nucleus interactions.