Ultraperipheral Pb+Pb Collisions

• Ultraperipheral Pb+Pb collisions are lead nucleus interactions at impact parameters larger than their radii, where electromagnetic processes dominate over hadronic ones.
• They employ intense, Lorentz-contracted Coulomb fields scaling as Z² and Z⁴ to drive photon-photon and photon-nucleus interactions, enabling tests of rare QED processes.
• These collisions offer precise probes of nuclear gluon densities and shadowing effects through measurements such as exclusive J/ψ photoproduction and dijet production.

Ultraperipheral Pb+Pb collisions (UPCs) are collisions between lead nuclei at impact parameters larger than the sum of their nuclear radii, such that the suppression of hadronic interactions enables electromagnetic processes—governed by the intense Lorentz-contracted Coulomb fields—to become the primary mechanism for particle production. UPCs at the LHC provide a unique environment to investigate photon-induced and two-photon interactions, including photoproduction of vector mesons, light-by-light scattering, dilepton, and dijet production, to probe the partonic structure and quantum electrodynamics (QED) and quantum chromodynamics (QCD) dynamics in nuclei at very low Bjorken-$x$.

1. Fundamental Electromagnetic Processes in Ultraperipheral Collisions

In ultraperipheral Pb+Pb events, one or both nuclei act as sources of quasi-real photons due to their large charge ($Z = 82$), with the equivalent photon flux scaling as $Z^2$ for single-photon processes and $Z^4$ for photon-photon fusion. The resulting interactions can be categorized as:

• Photon-photon ($\gamma\gamma$) fusion, producing dilepton pairs ($e^+e^-$, $\mu^+\mu^-$), light-by-light (LbL) scattering ($\gamma\gamma \to \gamma\gamma$), or multiparticle states.
• Photon–nucleus ($\gamma$A) or photon–proton ($\gamma$p) interactions, leading to exclusive vector meson production (e.g., $J/\psi$, $\psi(2S)$, $\rho^0$, $\phi$), and photon-induced dijet or heavy flavor production.
• Electromagnetic dissociation (EMD), where the nucleus is excited via soft photon absorption and emits one or more neutrons, detected with Zero Degree Calorimeters (ZDCs) (Collaboration, 2022).

Photonuclear reactions such as coherent and incoherent vector meson photoproduction are central to UPC physics. In the coherent case, the photon scatters elastically off the entire target nucleus, leading to a final state with a narrow transverse momentum ($p_T$) spectrum, while in incoherent production, the photon couples to a single nucleon, resulting in a broader $p_T$ distribution and possible nuclear breakup (Kryshen, 2017).

2. Exclusive Vector Meson Photoproduction and Nuclear Gluon Densities

Coherent photoproduction of heavy vector mesons (notably $J/\psi$) is a key probe of the gluon distribution in nuclei at low $x$. In leading-order (LO) QCD, the cross section is proportional to the square of the gluon density: $$\sigma(\gamma + \mathrm{Pb} \to J/\psi + \mathrm{Pb}) \propto [xg_A(x, Q^2)]^2$$ where $x$ is the Bjorken variable and $Q^2$ is set by the meson mass (Kryshen, 2017, Kryshen, 2013, Li et al., 2022).

The ALICE, CMS, and LHCb collaborations have performed high-precision measurements of coherent $J/\psi$ production at both mid- and forward rapidities, enabling direct comparison with theoretical models incorporating different treatments of nuclear shadowing and gluon distributions (Nystrand, 2013, Kryshen, 2013, Li et al., 2022). Results consistently show suppression of the cross section relative to models without nuclear modifications, supporting the existence of significant gluon shadowing at $x \lesssim 10^{-3}$ (Scapparone, 2013, Ragoni, 2019).

Two primary modeling approaches arise:

• Color Dipole Models (CDM): The $\gamma\to q\bar{q}$ fluctuation interacts with the nucleus as a color dipole. The dipole cross section is described by models such as the IIM or IPsat (factorized/fIPsat), each differing in their handling of impact-parameter profiles and saturation dynamics (Lappi et al., 2013).
• Collinear Factorization (pQCD): Uses generalized parton distributions (GPDs) reduced to PDFs in the forward limit, with calculations at LO and, more recently, full NLO (Eskola et al., 2022, Eskola et al., 2022, Eskola et al., 2022). NLO corrections yield substantial contributions, including quark-induced terms, and introduce significant scale and PDF uncertainties. At NLO, the cross section becomes sensitive not only to gluon distributions but also to nuclear quark PDFs, especially at midrapidity where interference between different amplitude components can suppress the gluonic contribution.

Theoretical calculations further incorporate photon flux modeling (via the equivalent photon approximation with appropriate nuclear geometry), nuclear form factors, and corrections due to the real part of the scattering amplitude and skewedness ($R_g$) (Lappi et al., 2013). Model comparisons with LHC data show that parameterizations including moderate gluon shadowing (e.g., EPS09, BGK-I) best reproduce the measured $J/\psi$ cross sections and their rapidity dependence (Nystrand, 2013, Ragoni, 2019).

3. Multi-Particle Electromagnetic Final States

UPCs enable direct observation of rare multi-particle electromagnetic processes, providing stringent tests of QED:

• Two-photon (Breit–Wheeler) $\gamma\gamma\to\ell^+\ell^-$: Dimuon and dielectron production have been extensively measured, with cross sections and kinematic distributions in agreement with STARlight predictions at central rapidities but showing up to $10$–$20\%$ excess at forward rapidities—potentially indicative of underestimated photon fluxes or nonlinear effects near the nuclear periphery (Collaboration, 2020).
• Light-by-light scattering ($\gamma\gamma\rightarrow\gamma\gamma$): ATLAS observed the process in Pb+Pb UPCs at $8.2\sigma$ significance, reporting a fiducial cross section of $78\pm13$ (stat.) $\pm 7$ (syst.) $\pm 3$ (lumi.) nb—higher than theory predictions by a factor 1.5–1.7—confirming the feasibility of studying rare QED processes in this context and opening searches for physics beyond the Standard Model (Collaboration, 2019).
• Single- and double-scattering production of $\mu^+\mu^-\mu^+\mu^-$: The dominant four-muon production mechanism is double-scattering, i.e., two independent $\gamma\gamma\to\mu^+\mu^-$ subevents within a single ion–ion encounter. The cross section for direct $\gamma\gamma\to\mu^+\mu^-\mu^+\mu^-$ is orders of magnitude smaller (Hameren et al., 2017).

For exclusive $K^+K^-$ photoproduction, UPCs at the LHC provide access to resonant (via $\phi(1020)$) and direct continuum contributions, with observed spectra requiring interference models to explain the yield above pure resonance expectations (Kim, 5 May 2024).

4. Collectivity, Azimuthal Correlations, and Initial State Dynamics

UPC photonuclear processes offer crucial insight into the origins of collectivity and flow in small systems:

• Two-particle azimuthal correlations: ATLAS has observed significant second- and third-order Fourier harmonics ($v_2$, $v_3$) in photonuclear Pb+Pb events, after template subtraction of non-flow effects. The measured $v_2$ is systematically below corresponding pp/pPb values, while $v_3$ is largely compatible within uncertainties, reflecting differences in initial geometry and indicating the presence of collective phenomena even in electromagnetic-dominated collisions (Collaboration, 2021).
• Hydrodynamic simulations: Full (3+1)D dynamical simulations demonstrate that quasi-real $\gamma^*$+Pb systems can exhibit fluid behavior akin to that in p+Pb, with radial and elliptic flow. Elliptic flow ($v_2$) is suppressed in $\gamma^*$+Pb relative to p+Pb at fixed multiplicity, caused not by differences in transverse eccentricity but by increased longitudinal decorrelations arising from the asymmetric rapidity geometry (Zhao et al., 2022). The sensitivity of $v_2$ to photon virtuality $Q^2$ makes future electron-ion colliders particularly promising for systematic studies of collectivity.
• CGC calculations: Color Glass Condensate–based approaches explain the emergence of significant $v_2$ from pure initial state gluon correlations, with the magnitude and $p_T$ dependence of the correlations influenced by modeling choices for the nearly real photon’s wavefunction (perturbative dipole vs vector meson) (Duan et al., 2022).

5. Diffractive and Inclusive Hard Processes: Dijet Photoproduction and Nuclear PDFs

UPCs provide access to hard QCD observables, such as:

• Inclusive dijet photoproduction: NLO pQCD predictions, incorporating collinear PDFs and photon fluxes, quantitatively describe ATLAS data for inclusive dijet production in Pb+Pb UPCs and probe nuclear PDFs down to $x_A\sim0.005$ (Guzey, 26 Mar 2024). Comparison with the data allows a factor-of-two reduction in the uncertainty on the small-$x$ nuclear gluon PDF via Bayesian reweighting.
• Diffractive dijet photoproduction: Leading twist nuclear shadowing strongly suppresses the nuclear diffractive PDFs, resulting in the diffractive contribution being only 5–10% of the inclusive cross section. Theoretical implementation of QCD factorization breaking shows that the $x_\gamma$ spectrum of the diffractive dijets can differentiate between global and resolved-only suppression scenarios; current and future measurements can help clarify the dynamics of hard diffraction and the domain of factorization breaking in nuclei.

6. Peripheral Collisions: Coherent Photoproduction and Polarization

While coherent photoproduction is most prominent in non-overlapping UPCs, recent results demonstrate its persistence—and importance—in peripheral Pb+Pb collisions (centrality 70–90%):

• ALICE measurements at forward rapidity show a rapidity-differential cross section for very-low-$p_T$ $J/\psi$ compatible with coherent photoproduction, extending the domain of photonuclear processes to regions of modest nuclear overlap (Massacrier, 12 Jul 2024).
• Polarization measurements: The observed transverse polarization (consistent with $s$-channel helicity conservation) in the very-low-$p_T$ $J/\psi$ corroborates the hypothesis of a photon-induced origin, distinguishing it from hadronic production channels. This provides a robust method to isolate photonuclear events even in complex collision environments.

Significant discrepancies between the observed rapidity dependence of the cross section and current models (including variations with "effective photon flux" or photonuclear cross section treatment) point toward the need for refined modeling of the photon source in nuclear overlap regions.

7. Neutron Emission and Operational Considerations

Electromagnetic dissociation (EMD) in UPC results in one or more nucleon emissions, predominantly neutrons, due to excitation of the Giant Dipole Resonance. Neutron multiplicity distributions, measured using the ALICE ZDCs, inform both fundamental photonuclear reaction models and the design of accelerator components:

• Spectator neutron detection: Multi-Gaussian fits to energy deposit distributions enable extraction of exclusive neutron emission channels, and comparison across $\sqrt{s_{NN}}=2.76$ and $5.02$ TeV demonstrates robustness of the underlying dissociation dynamics (Collaboration, 2022).
• Impact on LHC and FCC design: Produced secondary beams (e.g., $^{207,206,...}$Pb) pose a risk for beam losses and magnet quenching, underscoring the significance of precise neutron emission cross sections for machine protection and collimation system design.

8. Summary and Ongoing Challenges

Ultraperipheral Pb+Pb collisions at the LHC constitute a precision laboratory for investigating QED, QCD, and nuclear structure in the high-energy, small-$x$ regime:

• Exclusive vector meson photoproduction, especially $J/\psi$, provides a window into the small-$x$ behavior of gluons and the emergence of shadowing, while recent NLO studies reveal significant sensitivity to nuclear quark PDFs and require careful scale and PDF uncertainty treatment (Eskola et al., 2022, Eskola et al., 2022, Eskola et al., 2022).
• Multiparticle QED processes, such as light-by-light scattering and four-lepton production, validate the capability of UPCs to probe rare electromagnetic interactions.
• Dijet measurements in UPCs directly constrain nuclear parton densities, especially the poorly known gluon sector, with negligible diffractive contamination in inclusive measurements (Guzey, 26 Mar 2024).
• Collective phenomena in UPC photonuclear events challenge the prevailing understanding of the required conditions for collectivity, and new theoretical treatments combining hydrodynamics and the CGC reproduce many of the salient experimental observables.
• The interplay of resonant and non-resonant production in channels such as $K^+K^-$, along with polarization measurements in peripheral collisions, further demonstrates the richness of photon-induced processes in heavy-ion environments.

Continued experimental and theoretical advances—including improved photon flux and nuclear modeling in overlap regions, higher-order QCD corrections, and precision measurements of rare channels—are essential for refining the understanding of electromagnetic and QCD phenomena in ultraperipheral heavy-ion collisions.