Searches for axion-like particles in proton-proton and ion-ion collisions at energies in the center of mass system of 5.02 TeV and 13 TeV

This paper presents a theoretical modeling of axion-like particle production and decay into photons in proton-proton and lead-lead collisions at 5.02 TeV and 13 TeV, utilizing Good-Walker eigenstate models to calculate cross-section dependencies on collision energy, ALP mass, and event numbers based on ATLAS light-by-light scattering data.

The Gist

Imagine the universe is a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. Physicists at the Large Hadron Collider (LHC) crash these particles together to see what happens, hoping to find clues about the mysterious "dark matter" that makes up most of the universe but remains invisible to us.

This paper is like a detective's report from two scientists, T.V. Obikhod and S.B. Chernyshenko, who are trying to catch a ghost: a hypothetical particle called an Axion-Like Particle (ALP). They suspect these ALPs might be the dark matter we've been looking for.

Here is the story of their investigation, broken down into simple concepts:

1. The Setup: The "Light-Box" Collision

Usually, when physicists smash protons (the building blocks of atoms) or heavy lead ions together, it's like a massive demolition derby. Everything explodes, and it's hard to see anything clearly.

However, sometimes the particles don't hit head-on. They just graze past each other. The scientists call this an "ultra-peripheral collision."

• The Analogy: Imagine two fast cars driving past each other on a highway. They don't crash, but their headlights flash so brightly that the light from one car hits the other. In this experiment, the "headlights" are actually intense clouds of energy (photons) surrounding the particles. When these light clouds collide, they can create new particles out of pure energy. This is called "light-by-light scattering."

2. The Suspect: The Axion-Like Particle (ALP)

The scientists are looking for a specific "ghost" that might appear when these light clouds collide.

• What is it? An ALP is a theoretical particle that is very light and interacts weakly with normal matter. If it exists, it could be the "dark matter" holding galaxies together.
• How do they find it? They can't see the ALP directly. Instead, they wait for it to be created and then immediately decay (break apart) into two flashes of light (gamma rays). It's like looking for a magician who vanishes instantly, leaving behind two sparkles.

3. The Investigation: Running the Simulation

The scientists didn't just wait in the lab; they used a powerful computer program called SuperChic to run millions of virtual collisions. Think of this as a video game simulator where they can tweak the rules to see what happens.

They looked at two types of crashes:

1. Proton-Proton collisions: Like two small pebbles grazing past each other.
2. Lead-Lead collisions: Like two massive boulders grazing past each other.

They tested two different "speeds" (energies):

• 5.02 TeV: A very fast speed.
• 13 TeV: An even faster, record-breaking speed.

4. The Findings: What the Computer Told Them

After crunching the numbers, the scientists found some interesting patterns:

• The "Single vs. Double" Breakup: When the particles graze each other, sometimes one of them breaks apart (Single Dissociation) and sometimes both do (Double Dissociation).

  • The Result: The computer showed that it is much more likely (about 10 times more likely) for just one particle to break apart than for both to break apart. It's like if you flick a billiard ball; it's more likely to chip off a tiny piece than to shatter completely.

• The Speed Trap (Energy Levels):

  • In Proton collisions: As they increased the speed (energy), the chance of creating an ALP went up. The faster they went, the more likely they were to find the ghost.
  • In Lead collisions: This was the surprise. As they increased the speed, the chance of creating an ALP went up at first, but then it started to drop when the energy got too high (between 7 and 8 TeV).
  • The Analogy: Imagine trying to catch a butterfly. If you run a little faster, you might catch it. But if you run too fast, the wind from your speed blows the butterfly away before you can grab it. In lead collisions, the "wind" (the complex interaction of the heavy nuclei) gets too strong at high speeds, making it harder to create the ALP.

• The Weight Limit (Mass): They also checked if heavier ALPs were easier to find.

  • The Result: As the ALPs got heavier (up to 1,400 times the mass of a proton), the chance of finding them dropped dramatically—by a factor of one million (six orders of magnitude). It's much harder to create a heavy ghost than a light one.

5. The Conclusion: Are We Close?

The scientists compared their computer results with real data collected by the ATLAS collaboration (a huge team of physicists at the LHC).

• The Good News: The number of "ghost sightings" (events) they predicted matches what the real experiments have seen so far (between 10 and 100 events). This means their theory is on the right track.
• The Takeaway: While they haven't found the ALP yet, their calculations help narrow down the search. They know exactly where to look (in the 5 to 30 GeV mass range) and how the physics behaves when the particles are heavy lead ions versus light protons.

In summary: This paper is a roadmap. It tells us that while heavy particles (Lead) might make it harder to find these dark matter ghosts at very high speeds, the search is promising. The computer models confirm that the "ghosts" are hiding in a specific spot, and the real-world experiments are starting to see the same clues.

Technical Summary

1. Problem Statement

The paper addresses the urgent and complex task of searching for Axion-Like Particles (ALPs), which are candidates for dark matter, across a wide mass range (from several eV to 2 TeV). While experimental data from the ATLAS collaboration has confirmed light-by-light scattering in Pb+Pb and proton-proton (pp) collisions with high significance (8.2$\sigma$), the theoretical modeling of ALP production mechanisms in these specific ultra-peripheral collision (UPC) environments requires clarification.

The authors aim to:

• Model the cross-sections for ALP production and subsequent decay into gamma quanta.
• Clarify the kinematic details and features of ultra-peripheral processes in both pp and Pb-Pb collisions.
• Determine the optimal conditions (energy, mass region, event counts) for detecting ALPs, specifically investigating the dependence of production cross-sections on collision energy and ALP mass.

2. Methodology

The study employs a combination of theoretical formalism and Monte Carlo simulation:

• Theoretical Framework:

  • Ultra-Peripheral Collisions (UPC): For ion-ion (Pb-Pb) collisions, the interaction is described using the Weizsäcker-Williams equivalent photon method, treating Lorentz-squeezed Coulomb fields as photon streams.
  • Proton-Proton Interactions: Modeled using the Good-Walker (GW) formalism. This treats high-energy diffractive interactions via pomeron exchange, which can distort the incoming proton's wave function.
  • Dipole Model: The cross-section for pomeron exchange between two dipoles is calculated using form factors ($F_i$) and a cutoff induced by the pomeron. The authors utilize a two-channel eikonal approximation with parametrized form factors to describe elastic scattering data.
  • Dissociation Components: The total diffractive cross-section is decomposed into elastic, single dissociation (SD), and double dissociation (DD) components. The probability of diffractive dissociation is analyzed to determine if wave function coherence is destroyed.

• Simulation Tools:

  • SuperChic v4.2: A modern Monte Carlo event generator used to simulate QCD-initiated ALP formation.
  • Parameters: Four distinct models (Table 1) specifying GW eigenstate parameters ($|a|^2, b, c, d$) were used to tune the calculations.
  • Input Data: The modeling incorporates experimental constraints from ATLAS (2015/2018 Pb+Pb data, $\sqrt{s}=5.02$ TeV, integrated luminosity 2.2 nb$^{-1}$) and selects two-photon events with pseudorapidity $|\eta| < 2.37$ and invariant mass $m_{\gamma\gamma} = 5-30$ GeV.

3. Key Contributions

• Comprehensive Cross-Section Modeling: The authors calculated ALP production cross-sections for both proton-proton and lead-lead collisions at center-of-mass energies of 5.02 TeV and 13 TeV.
• Dissociation Analysis: A detailed breakdown of Single Dissociation (SD) vs. Double Dissociation (DD) components was performed using four different GW eigenstate models.
• Mass Region Comparison: The study explicitly compares ALP production in two mass regions: a low-mass region (5–30 GeV) and a high-mass region (5–1400 GeV).
• Energy Dependence Characterization: The paper establishes the contrasting behavior of cross-sections in pp vs. Pb-Pb collisions as energy increases.

4. Key Results

• Event Count Dependence: At 5.02 TeV, the cross-section dependence on the number of ALP events was modeled. The optimal number of observed particles for detection is estimated to be between 10 and 100 events, aligning with the order of magnitude of recent ATLAS experimental data.
• Dissociation Magnitude: The calculations confirm that Single Dissociation (SD) is approximately one order of magnitude larger than Double Dissociation (DD) at 5.02 TeV. This is attributed to the lack of dispersion and the preservation of wave function coherence in the incoming protons.
• Energy Dependence (pp vs. Pb-Pb):
  • Proton-Proton: The cross-section increases with increasing collision energy.
  • Lead-Lead (Pb-Pb): The cross-section initially increases (3–7 GeV in the center of mass) but then decreases significantly in the 7–8 GeV range. This decline is attributed to the multiplicity of the process associated with the formation of quark-gluon plasma, which suppresses ALP formation in heavy-ion collisions at higher energies.
• Mass and Energy Scaling:
  • When the ALP mass region is extended to 1400 GeV and the energy increases to 13 TeV, the production cross-section drops by six orders of magnitude.
  • Tables 2 and 3 provide specific cross-section values (in mb or similar units, though units are implied by context) for SD and DD components across the four models at both energies.

5. Significance

• Experimental Guidance: The study provides crucial theoretical benchmarks for experimentalists at the LHC (ATLAS and CMS) searching for ALPs. By identifying the optimal event counts (10–100) and highlighting the suppression of ALP production in Pb-Pb collisions at higher energies, it helps refine search strategies.
• Validation of Models: The successful application of the Good-Walker formalism and SuperChic v4.2 to reproduce expected behaviors (such as the dominance of SD over DD) validates the theoretical approach for modeling diffractive ALP production.
• Dark Matter Constraints: By modeling the cross-sections across a vast mass range (up to 1.4 TeV) and comparing them with experimental limits, the paper contributes to narrowing down the parameter space for ALPs as dark matter candidates.
• Insight into QCD Dynamics: The observed decrease in Pb-Pb cross-sections at higher energies offers insights into the interplay between ultra-peripheral photon interactions and the underlying quark-gluon plasma dynamics.