Phenomenology developments in UPC: $\gamma \gamma \to \gamma \gamma$ scattering

This paper proposes extending the study of $\gamma \gamma \to \gamma \gamma$ scattering in ultraperipheral heavy ion collisions to lower invariant masses and inelastic processes involving individual nucleons, while also calculating cross sections for associated neutron production and single photon production to guide future investigations with detectors like FOCAL and ALICE 3.

The Gist

Imagine two massive, heavy trains (lead nuclei) speeding toward each other on parallel tracks. They are so close that they almost touch, but they don't crash. Instead, they pass by each other at a high speed.

In the world of particle physics, these trains are surrounded by a powerful "aura" of light (photons). Usually, when these trains pass, the light from one train might interact with the light from the other. This is called Ultraperipheral Collision (UPC).

For about ten years, scientists have been watching what happens when two beams of light collide and bounce off each other to become two new beams of light. This is called Light-by-Light scattering ($\gamma\gamma \to \gamma\gamma$). It's like two flashlights shining at each other, and instead of passing through, they bounce off and change direction.

This paper by Paweł Jucha and Antoni Szczurek is like a "future roadmap" for scientists. They are saying, "We've been looking at this phenomenon for a decade, but we think we're missing some pieces of the puzzle. Here is how we can find them."

Here are the main ideas of the paper, explained with simple analogies:

1. The "Missing Strength" Mystery

For a long time, scientists have been measuring how often these light beams bounce off each other. They have a theory (a mathematical recipe) that predicts how often this should happen.

• The Problem: The theory predicts a certain amount of "bouncing," but the actual experiments (by ATLAS and CMS) show more bouncing than the theory says. It's like a recipe for a cake that says it should weigh 1kg, but when you bake it, it weighs 1.2kg.
• The Old Guess: Some people thought maybe a mysterious new particle (a "tetraquark") was causing the extra weight.
• The New Idea: The authors suggest we might be looking at the wrong things. They propose we need to look at lower energy collisions (slower trains) and new types of interactions that we haven't studied much yet.

2. The "Whole Train" vs. "Individual Passengers"

This is the most exciting part of the paper.

• The Old View (Coherent): Imagine the train is a solid block of steel. When the light hits it, it hits the entire train at once. This is what scientists have studied so far.
• The New View (Inelastic): The authors say, "Wait, trains are made of individual cars (nucleons)." Sometimes, the light doesn't hit the whole train; it hits just one single passenger inside the train.
  • The Analogy: If you throw a ball at a solid wall, it bounces back cleanly. If you throw it at a crowd of people, it might hit just one person, knock them over, and cause a bit of chaos before bouncing back.
  • The Result: The authors calculate that these "hit-one-person" events might happen 20% to 30% of the time. This could explain the "missing strength" in the data.

3. The "Neutron Smoke Signal"

How do we know if the light hit the whole train or just one passenger?

• The Analogy: If you hit a solid wall, nothing happens. But if you hit a person in a crowd, they might stumble and drop something.
• The Physics: When a photon hits a single nucleon (a "passenger") inside the nucleus, it often knocks a neutron out of the nucleus.
• The Plan: The authors suggest that if we detect these "kicked-out" neutrons alongside the bouncing light, we can prove that the "inelastic" (hit-one-passenger) process is happening. They have calculated exactly how many neutrons we should expect to see for different types of collisions.

4. Looking for "Single" Photons

So far, everyone has been looking for two photons bouncing off each other.

• The New Idea: What if we look for just one photon?
• The Analogy: Imagine two people throwing balls at each other. Usually, we watch both balls bounce back. But what if one ball gets absorbed or scattered in a weird way, and we only see the other one?
• The authors predict that we might be able to see these "single photon" events with future, super-sensitive detectors (like ALICE 3). This would be a brand-new way to study how light interacts with matter.

5. The Future Tools

The paper mentions new detectors (like FoCal and ALICE 3) that will be built soon.

• The Analogy: It's like upgrading from a pair of binoculars to a high-powered telescope. These new tools will allow scientists to see "fainter" events (lower energy collisions) that were previously too dim to notice. This is where the new "hit-one-passenger" mechanisms might show up.

Summary: What's the Big Takeaway?

The authors are telling the scientific community: "Stop looking only at the big, clean bounces. Start looking at the messy, partial hits."

They believe that by:

1. Looking at lower energies.
2. Checking for "kicked-out" neutrons.
3. Studying single photons.

...we can finally solve the mystery of why the experiments show more light-bouncing than our current theories predict. It's a call to expand the search to find the hidden parts of the puzzle.

Technical Summary

1. Problem Statement

The paper addresses the persistent discrepancy between theoretical predictions and experimental data regarding light-by-light (LbL) scattering ($\gamma\gamma \to \gamma\gamma$) in ultraperipheral heavy-ion collisions (UPC), specifically observed by the ATLAS and CMS collaborations at the LHC.

• The Gap: Despite precise measurements and improvements in theoretical calculations (including Next-to-Leading Order corrections), a "missing strength" in the cross-section remains unexplained.
• Limitations of Current Models: Previous studies focused almost exclusively on coherent processes where photons couple to the entire nucleus. The potential contribution of inelastic processes (where photons couple to individual nucleons) and associated nuclear breakup has been largely ignored or not fully quantified.
• Future Opportunities: With the development of new detectors (ALICE FoCal, ALICE 3) capable of lowering photon energy cuts, there is an opportunity to explore lower diphoton invariant masses and new kinematic regions where these missing mechanisms might become visible.

2. Methodology

The authors employ the Equivalent Photon Approximation (EPA) in impact parameter space to calculate nuclear cross-sections. The methodology involves several key theoretical components:

• Cross-Section Formalism: The differential cross-section is calculated by integrating the elementary $\gamma\gamma \to \gamma\gamma$ cross-section over photon fluxes ($N(\omega, b)$) and a survival factor ($S^2_{abs}$) which accounts for the probability of no hadronic interaction. Two models for the survival factor are compared: a sharp nuclear edge and a smeared nuclear surface (using nuclear thickness functions).
• Mechanism Analysis:
  • Coherent Processes: Re-evaluation of standard mechanisms including fermionic box diagrams (leptons, quarks, W bosons), light-meson resonances, and double vector meson fluctuations (Vector Dominance Model - VDM).
  • Inelastic Processes: A novel calculation of processes where one or both photons couple to individual nucleons (protons/neutrons) rather than the whole nucleus. This utilizes photon parton distribution functions (PDFs) from CTEQ18QED, solving modified DGLAP equations.
  • Interference: The study explicitly calculates interference effects between different contributions (e.g., box diagrams vs. vector meson fluctuations).
• Associated Neutron Production: The authors model the simultaneous excitation of nuclei and neutron emission. They calculate the mean number of absorbed photons and apply a probability function for neutron emission ($P_{Xn}$) versus non-emission ($P_{0n}$) based on impact parameter ($b$).
• Single Photon Production: The paper extends the analysis to single photon production ($AA \to AA\gamma$) via Compton scattering and Delbrück scattering, utilizing the Vector Dominance Model to relate photon scattering to vector meson scattering.

3. Key Contributions

• Quantification of Inelastic Contributions: The paper provides the first theoretical estimates for inelastic $\gamma\gamma \to \gamma\gamma$ contributions in Pb-Pb UPCs. It demonstrates that these processes can account for 20–30% of the total cross-section without special exclusivity cuts.
• Refined VDM-Regge Model: The authors refine the calculation of double vector meson fluctuations (Regge trajectories), proposing a smooth switching off of $t/u$-dependent terms at high momentum transfers to avoid artificial suppression.
• Neutron Correlation Predictions: A detailed breakdown of cross-sections for different neutron emission categories ($0n0n$, $Xn0n$, $XnXn$) is presented. This provides a specific experimental signature to distinguish between coherent and inelastic processes.
• Single Photon Phenomenology: The authors present preliminary results for single photon production, identifying rescattering mechanisms as dominant over incomplete two-photon final states in specific kinematic regions.

4. Key Results

• Inelastic vs. Elastic Ratio: The ratio of inelastic to elastic contributions ($R_{inel}$) increases with diphoton invariant mass ($M_{\gamma\gamma}$) and rapidity difference ($y_{diff}$). At high masses, inelastic contributions become significant.
• Interference Effects:
  • Interference between box diagrams and double vector meson fluctuations results in a negative interference, reducing the total box result by approximately 10%.
  • The box mechanism remains the dominant contribution but still fails to fully explain the ATLAS data strength.
• Neutron Emission Signatures:
  • The total cross-section is dominated by the $0n0n$ (no neutron emission) category (~75%).
  • However, the $XnXn$ (both nuclei break up) and mixed categories contribute significantly (~15% combined).
  • The shape of the rapidity difference distribution ($y_{diff}$) shows only a weak dependence on the neutron category, suggesting that deviations in this shape could signal the presence of inelastic contributions.
• Single Photon Production: For single photon detection, the rescattering mechanism (analogous to vector meson production) dominates over the "incompletely measured" two-photon final state where one photon is lost.

5. Significance and Future Outlook

• Resolving the Discrepancy: The study suggests that the "missing strength" in ATLAS data may not be due to exotic states like the $X(6900)$ tetraquark (which the authors argue against based on refined calculations) but rather due to inelastic contributions and associated nuclear breakup that have not been fully accounted for in current experimental cuts.
• Experimental Strategy: The paper proposes that future measurements should:
  • Utilize Zero Degree Calorimeters (ZDC) to detect associated neutrons, which serves as a tag for inelastic processes.
  • Lower photon energy cuts using ALICE FoCal and ALICE 3 to access lower invariant masses where new mechanisms (like VDM fluctuations) are more prominent.
  • Study single photon production and acoplanarity distributions to isolate inelastic effects.
• Theoretical Challenges: The authors highlight open questions regarding the modeling of the final state (gap survival factors for inelastic processes) and the distinction between final states excited by extra photon exchange versus one-step inelastic processes.

In conclusion, this paper expands the phenomenological framework of UPC physics by rigorously incorporating inelastic mechanisms and nuclear breakup correlations, offering a new pathway to resolve long-standing discrepancies between LbL scattering theory and experiment.