⚛️ phenomenology

Neutron tagging of heavy lepton pair production at RHIC and LHC energies

This paper presents a LO QED Monte Carlo calculation of heavy lepton pair production cross sections in ultraperipheral gold and lead collisions at RHIC and LHC energies, incorporating neutron emission probabilities to categorize results into specific neutron classes and comparing them with experimental data from STAR, ALICE, ATLAS, and CMS under detector-specific fiducial constraints.

Original authors: Atacan Fatih Candar, Mehmet Cem Güçlü

Published 2026-07-14

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Atacan Fatih Candar, Mehmet Cem Güçlü

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

Imagine two massive, super-charged trains (heavy atomic nuclei) zooming past each other at nearly the speed of light. They are so close that their magnetic fields brush against one another, but they never actually crash. This is called an "ultraperipheral collision." In this paper, the authors act like cosmic detectives, trying to figure out what happens when these invisible fields smash together to create new particles: pairs of electrons, muons, and even the heavy, short-lived tau particles.

The Main Discovery: The "Neutron Tag"
The biggest trick in this study is how they figure out exactly what happened during the collision. When the two trains pass each other, their intense electric fields can sometimes "jiggle" the nuclei, knocking loose one or more neutrons (tiny, neutral particles inside the atom).

The authors realized they could use these flying neutrons as "tags" or receipts for the event.

0n0n: No neutrons flew off either side. The collision was very gentle.
0nXn: One side lost a neutron, the other didn't.
XnXn: Both sides lost neutrons. The collision was a bit more energetic.

By counting these neutrons, the team could sort their data into specific categories, just like sorting mail by zip code. They calculated exactly how many electron, muon, and tau pairs should appear in each category and compared their numbers to real data collected by giant experiments like STAR, ALICE, ATLAS, and CMS.

The Results: A Good Match
The authors ran complex computer simulations (using a method called Monte Carlo) to predict these numbers.

For Electrons: At the Relativistic Heavy Ion Collider (RHIC), they predicted that in the "both sides lost a neutron" (XnXn) category, there should be about 274.5 µb (microbarns) of electron pairs. The real experiment (STAR) measured 261 ± 4stat ± 13sys µb. That's a very close match!
For Muons: At the Large Hadron Collider (LHC), they predicted an inclusive total of 36.5 µb for muon pairs. The ATLAS experiment measured 34.1 ± 0.3stat ± 0.7sys µb. Again, the numbers are very close.
For Taus: This is the heavy hitter. Taus are much heavier than electrons or muons. The authors predicted an inclusive total of 1043 µb for tau pairs. This is higher than the CMS experiment's direct measurement (which was only 4.8 ± 0.6stat ± 0.5sys µb in a restricted area), but it lines up almost perfectly with other theoretical estimates that tried to guess the total number for the whole universe of possibilities (around 580–850 µb or up to 1060 µb depending on the model).

What They Explicitly Ruled Out
The paper is very clear about what they are not doing. They are not claiming that the "strong force" (the glue that holds nuclei together) is doing the heavy lifting here. They explicitly state that because the nuclei don't touch, all the messy "hadronic interactions" are eliminated. The only thing driving this show is electromagnetism (light and electric fields).

They also rule out the idea that they have solved the problem of "higher-order" effects. They admit they only used the "lowest order" math (the simplest version of the rules). They note that adding more complex corrections (like final state radiation) would only change the total numbers by a tiny amount (a "K factor" of 1.01), so their simpler math is good enough for now.

How Sure Are They?
The authors are confident in their method, but they are careful not to call it a final, unchangeable truth.

They simulated the probabilities using a specific mathematical trick: they treated the collision path as a smooth curve and used a "Poisson statistics" model (like rolling dice to see how many neutrons might fly off) to guess the neutron counts.
They suggest that their method works well because their simulated numbers match the real-world measurements from the big experiments within a few percent.
However, they admit that for the heaviest particles (taus), the numbers are still a bit fuzzy because the experiments can only see a tiny slice of the action, and they have to "extrapolate" (guess the rest) to compare with the theory.

The Takeaway
Think of this paper as a master chef testing a new recipe. They didn't invent the ingredients (the laws of physics), but they figured out a new way to measure the dish by looking at the crumbs (the neutrons) left on the table. Their recipe predicts that if you cook up these heavy-ion collisions, you should get a specific amount of electron, muon, and tau "dough." When they compared their predictions to the actual "taste tests" done by the world's biggest particle detectors, the flavors matched up surprisingly well. It's not a perfect, solved puzzle, but it's a very strong hint that their way of looking at the universe is on the right track.

Technical Summary: Neutron Tagging of Heavy Lepton Pair Production at RHIC and LHC Energies

Problem and Motivation
The production of lepton-antilepton pairs via photon-photon fusion ( $\gamma\gamma \to \ell^+\ell^-$ ) in ultraperipheral collisions (UPCs) of heavy ions serves as a stringent test of Quantum Electrodynamics (QED) in strong electromagnetic fields. While electron-positron pair production has been extensively studied, theoretical descriptions of heavier lepton pairs (muons and taus) in conjunction with specific neutron emission topologies remain less developed in the literature. In UPCs, where nuclei pass each other at impact parameters larger than the sum of their radii, the intense Lorentz-boosted Coulomb fields act as sources of virtual photons. These photons can induce mutual electromagnetic excitation of the nuclei, leading to the emission of neutrons via Giant Dipole Resonance (GDR) and other mechanisms. Experimental collaborations (STAR, ALICE, ATLAS, CMS) categorize events based on neutron detection in Zero Degree Calorimeters (ZDCs) into classes such as $0n0n$ (no neutrons), $0nXn$ (neutrons in one ZDC), and $XnXn$ (neutrons in both ZDCs). A consistent theoretical framework is required to calculate cross sections for these specific neutron-tagged classes to enable direct comparison with experimental data across different center-of-mass energies ( $\sqrt{s_{NN}} = 200$ GeV, 2.76 TeV, and 5.02 TeV).

Methodology
The authors perform lowest-order QED (LO QED) calculations for $\gamma\gamma \to \ell^+\ell^-$ ( $\ell = e, \mu, \tau$ ) production in Au+Au and Pb+Pb collisions. The methodology involves three primary components:

Free Pair Production Probability: The process is treated by considering ion trajectories as classical external electromagnetic sources. The cross section is derived from S-matrix elements involving direct and crossed Feynman diagrams. To handle the multidimensional integrals involving Bessel functions, which exhibit rapid oscillations, the authors employ a Monte Carlo technique. They calculate a function $F(q)$ (related to the momentum transfer) and fit it to a single exponential form, $F(q) = F(0)e^{-aq}$ , using non-linear least-squares fitting. This allows for the analytical integration of the impact parameter ( $b$ ) dependence to determine the probability of pair production, $P_{\ell^+\ell^-}(b)$ .
Neutron Emission and Nuclear Excitation: The probability of nuclear excitation is modeled by integrating the photon flux multiplied by the total photoabsorption cross section ( $\sigma_{tot}$ ). The photoabsorption cross section is constructed by combining a Lorentzian fit for the GDR region (using recent experimental data for $^{197}$ Au and $^{208}$ Pb) with the Kossov model for non-GDR contributions (quasi-deuteron, $\Delta$ resonance, Roper resonance, and Regge-Pomeron). The mean number of absorbed photons is used within a Poisson statistics framework to determine the probabilities for emitting zero ( $0n$ ), one ( $1n$ ), or at least one ($Xn$) neutron. This allows the categorization of events into $0n0n$ , $0n1n$ , $1n1n$ , $0nXn$, and $XnXn$ classes.
No-Hadronic Interaction Probability: To ensure the collisions remain ultraperipheral, the probability of no hadronic interaction, $P_{nohad}(b)$ , is calculated using the Glauber model with Woods-Saxon nuclear density distributions. This probability is multiplied with the pair production and excitation probabilities to obtain the final tagged cross sections.

The calculations are performed within the fiducial phase space restrictions defined by the STAR, ALICE, ATLAS, and CMS experiments, including cuts on pseudorapidity ( $|\eta|$ ), transverse momentum ( $p_T$ ), invariant mass ( $M_{\ell\ell}$ ), and pair transverse momentum ( $p_{T,\ell\ell}$ ).

Key Results
The study presents differential and integrated cross sections for electron, muon, and tau pair production, broken down by neutron emission classes:

Electron Pairs (STAR, $\sqrt{s_{NN}}=200$ GeV): The calculated inclusive cross section is 5850 $\mu$ b. The $XnXn$ tagged cross section is calculated as 274.5 $\mu$ b, which is approximately 4-5% higher than the STAR measurement (261 $\mu$ b) and 24.5% higher than the STARLight prediction. The differential distributions for invariant mass and transverse momentum show good agreement with STAR data, though the model slightly underestimates the high- $p_T$ region.
Electron Pairs (ALICE, $\sqrt{s_{NN}}=2.76$ TeV): For low and high mass regions, the calculated inclusive cross sections (147 $\mu$ b and 87.7 $\mu$ b) are 3-5% below ALICE measurements but 13-15% above STARLight predictions. The $0n0n$ channel dominates the cross section.
Electron and Muon Pairs (ATLAS, $\sqrt{s_{NN}}=5.02$ TeV):
- For electrons, the inclusive cross section is 233 $\mu$ b, which is 8.3% above the ATLAS measurement (215 $\mu$ b).
- For muons, the inclusive cross section is 36.5 $\mu$ b, 7.0% above the ATLAS measurement (34.1 $\mu$ b).
- In both cases, the $0n0n$ channel provides the dominant contribution. The differential distributions in invariant mass and rapidity generally agree well with ATLAS data, with ratios close to unity, though deviations increase at higher invariant masses.
Tau Pairs (CMS, $\sqrt{s_{NN}}=5.02$ TeV): The authors calculate an inclusive cross section of 1043 $\mu$ b for $\tau^+\tau^-$ production. This result is in close agreement with the Shao and d'Enterria LO calculation using the nuclear charge form factor (1060 $\mu$ b) but is significantly higher than the extrapolated CMS fiducial results (580–850 $\mu$ b). The $0n0n$ channel contributes 802 $\mu$ b.

Significance and Claims
The paper claims to provide a consistent theoretical framework for calculating neutron-tagged lepton pair production across a wide range of lepton masses and collision energies. A primary contribution is the extension of neutron tagging analysis from electron-positron pairs to heavier muon and tau pairs, which have received less attention in the literature. The authors demonstrate that their LO QED approach, combined with a Poisson-based neutron emission model and Glauber-based hadronic exclusion, yields results that are generally consistent with experimental data from STAR, ALICE, ATLAS, and CMS within expected theoretical uncertainties.

The authors modestly note that they do not include higher-order QED corrections (such as final state radiation), though they cite literature suggesting these effects are minor for total cross sections. They also acknowledge that their treatment of neutron emission fractions as constant across kinematic bins is a simplification, which may explain slight discrepancies in the shape of differential distributions at higher invariant masses. Nevertheless, the study validates the utility of this simplified approach for describing the bulk of lepton pair production in UPCs and provides a baseline for future precision studies.

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