Diffractive and photon-induced processes at the LHC: from the odderon discovery, the evidence for saturation to the search for axion-like particles

This paper reviews recent LHC results, highlighting the discovery of the odderon, evidence for gluon saturation in heavy-ion collisions, and the potential for detecting axion-like particles through photon-induced processes.

The Gist

Imagine the Large Hadron Collider (LHC) not just as a giant particle smasher, but as a massive, high-speed billiard table where scientists are trying to understand the rules of the game, the nature of the balls, and even looking for "ghosts" that shouldn't exist.

This paper, written by physicist Christophe Royon, is a report on three major discoveries and searches happening at this table: finding a new type of "force," seeing how crowded the balls get, and hunting for invisible particles.

Here is the breakdown in simple terms:

1. The "Odd" Force: Discovering the Odderon

The Concept:
In the world of subatomic particles, protons can bounce off each other without breaking apart (elastic scattering). For decades, physicists thought they understood the "glue" holding this interaction together. They believed it was carried by a particle called the Pomeron (think of it as a smooth, invisible cushion).

However, there was a prediction of a "twin" to this cushion called the Odderon. The name comes from "odd" because it behaves differently depending on whether you are smashing two protons together or a proton and an antiproton.

The Analogy:
Imagine two people shaking hands.

• Scenario A (Proton vs. Proton): They shake hands normally.
• Scenario B (Proton vs. Antiproton): They shake hands, but one person is wearing a mirrored glove.

For a long time, the "smooth cushion" (Pomeron) explained both scenarios perfectly. But the Odderon is like a hidden, bumpy texture that only shows up when you compare the two scenarios. If the handshake feels different in the mirror world, the Odderon is there.

The Discovery:
The paper describes how the TOTEM experiment (at the LHC) and the D0 experiment (at the older Tevatron collider) compared their data. They looked at how protons bounced off each other at different speeds.

• They found a distinct "dip" and "bump" in the data for proton-proton collisions that simply didn't exist in proton-antiproton collisions.
• This difference was the smoking gun. It proved the existence of the Odderon, a particle made of an odd number of gluons (the carriers of the strong force), which had been predicted for 50 years but never caught until now.

2. The "Traffic Jam": Gluon Saturation

The Concept:
Inside a proton, there are tiny particles called gluons that act like the glue holding the proton together. As you smash protons together faster and faster, you create more and more gluons.

The Analogy:
Think of a proton as a small room.

• At low energy, the room has a few people (gluons) walking around. They have plenty of space.
• At the LHC's high energy, the room is packed with thousands of people. They are so crowded that they can't move freely anymore. They start bumping into each other and merging. This is called saturation. It's like a traffic jam where cars stop moving because there are too many of them.

The Evidence:
The paper discusses two ways they are looking for this traffic jam:

1. The "Gap" Test: They look for collisions where two jets of particles fly out, but the space between them is empty (a "gap"). If the space is empty, it means the gluons didn't scatter everywhere. The data suggests that at high energies, this "gap" behavior matches the theory of a dense, saturated gluon cloud.
2. Heavy Ion Collisions (Pb-Pb): They smash Lead ions (which are like giant, heavy rooms) instead of just protons. Because Lead is so heavy, the "traffic jam" (saturation) should happen much more easily. They found that when they produce specific particles (like J/Ψ mesons) in these heavy collisions, the results match the "saturation" model perfectly, confirming that gluons are indeed piling up and merging.

3. The "Ghost Hunters": Axion-Like Particles (ALPs)

The Concept:
The Standard Model of physics is great, but it doesn't explain everything (like dark matter). Scientists are looking for "Axion-Like Particles" (ALPs), which are hypothetical, very light, and invisible particles.

The Analogy:
Imagine the LHC as a giant camera taking photos of collisions. Usually, the camera sees the debris (jets, photons). But sometimes, a "ghost" (an ALP) might be created. The ghost is invisible, but it leaves a clue: it might turn into two flashes of light (photons) that appear out of nowhere.

The Method:
The LHC acts as a photon-photon collider.

• Normally, protons smash and break.
• But sometimes, the protons just "graze" each other, exchanging photons (light particles) and staying intact.
• The detectors (like CMS and TOTEM) have special "proton spectrometers" (Roman Pots) that catch these intact protons.
• By catching the intact protons, scientists know exactly how much energy was used. If they see two flashes of light (photons) in the center that match that energy perfectly, but no other debris, it could be an ALP that decayed into light.

The Result:
The paper shows that by using these "intact proton" detectors, they can filter out the "noise" (background events) incredibly well. They have set new, very strict limits on where these ALPs could be hiding. If they exist, they are likely heavier or interact differently than previously thought, but this method is the best way to hunt for them.

Summary

This paper is a celebration of three things:

1. We found the Odderon: We proved that the "odd" force exists by comparing how protons and antiprotons bounce.
2. We saw the Traffic Jam: We found evidence that gluons get so crowded at high speeds that they merge and saturate, changing how they behave.
3. We are hunting Ghosts: We are using the LHC as a precise light-collider to hunt for invisible particles (ALPs) that could solve the mysteries of the universe.

It's a story of moving from understanding the basic rules of the billiard table to realizing the table itself is changing shape, and finally, looking for the ghosts that might be playing on the side.

Technical Summary

1. Problem Statement

The paper addresses three fundamental challenges in high-energy Quantum Chromodynamics (QCD) and Beyond Standard Model (BSM) physics at the Large Hadron Collider (LHC):

1. The Odderon: Verifying the existence of the odderon, a $C$-odd (charge-parity odd) colorless exchange object composed of an odd number of gluons, by comparing elastic scattering in proton-proton ($pp$) and proton-antiproton ($p\bar{p}$) collisions.
2. Gluon Saturation: Determining if the LHC can probe the high gluon density regime where non-linear QCD effects (saturation) become dominant, particularly in heavy-ion (Pb-Pb) collisions, distinguishing between linear evolution (BFKL/DGLAP) and non-linear evolution (Balitsky-Kovchegov).
3. BSM Physics via Photon-Photon Interactions: Utilizing the LHC as a $\gamma\gamma$ collider to search for Axion-Like Particles (ALPs) and constrain quartic anomalous couplings (e.g., $\gamma\gamma\gamma\gamma$, $\gamma\gamma WW$) by detecting intact protons in the final state.

2. Methodology

The author synthesizes data from the TOTEM, D0, CMS, and ATLAS collaborations, employing the following methodologies:

• Elastic Scattering Analysis:

  • Comparison of the differential elastic cross-section ($d\sigma/dt$) measured by TOTEM ($pp$ at $\sqrt{s} = 2.76, 7, 8, 13$ TeV) and D0 ($p\bar{p}$ at $\sqrt{s} = 1.96$ TeV).
  • Extrapolation of TOTEM data down to 1.96 TeV using a two-parameter fit for characteristic points (dip, bump, mid-points) to enable direct comparison with D0 data.
  • Normalization at the optical point ($t=0$) assuming equal total cross-sections for $pp$ and $p\bar{p}$ if only $C$-even exchanges exist.
  • Application of a new geometric scaling variable $t^{**}$ to test universality in elastic data.

• Jet Gap Analysis:

  • Measurement of the "jet gap jet" cross-section in CMS, requiring a large rapidity interval devoid of charged particles ($p_T > 200$ MeV) between two jets.
  • Comparison of data against Next-to-Leading Order (NLO) DGLAP and BFKL evolution models.
  • Tagging of intact protons in Roman Pots to isolate diffractive events and suppress multi-parton interactions.

• Saturation in Heavy Ions:

  • Calculation of exclusive vector meson ($J/\Psi$, $\Upsilon$) and heavy quark ($c\bar{c}$, $b\bar{b}$) production cross-sections in $\gamma p$ and $\gamma Pb$ interactions.
  • Comparison of predictions using the BFKL equation (linear, no saturation) versus the Balitsky-Kovchegov (BK) equation (non-linear, includes saturation).
  • Use of impact parameter dependence ($b$-dependence) in the dipole amplitude to model nuclear thickness.

• Photon-Induced BSM Searches:

  • Utilization of the Precision Proton Spectrometer (PPS) and ATLAS Forward Proton (AFP) detectors to tag intact protons.
  • Kinematic matching between the central system (e.g., diphotons, $WW$, $t\bar{t}$) and the forward protons to reject pile-up background.
  • Calculation of limits on effective operators for quartic anomalous couplings and ALP production.

3. Key Contributions and Results

A. Discovery of the Odderon

• Observation: The paper confirms a significant difference between the elastic $pp$ and $p\bar{p}$ cross-sections. While $pp$ data shows a distinct "dip-bump" structure, $p\bar{p}$ data (D0) is flat in the same $|t|$ region.
• Statistical Significance: A $\chi^2$ test comparing extrapolated TOTEM $pp$ data to D0 $p\bar{p}$ data yields a $p$-value of 0.00061 ($3.4\sigma$). Combined with independent TOTEM measurements of the $\rho$ parameter and total cross-section, the total significance reaches 5.3 to 5.7$\sigma$, constituting a discovery.
• Scaling: A new scaling variable $t^{**} = (s/|t|)^A \times |t| / s^B$ is introduced, showing that elastic cross-sections at different energies ($\sqrt{s} = 2.76$ to $13$ TeV) collapse onto a single curve, suggesting a universal behavior of dense gluonic objects.

B. High Gluon Density and Saturation

• Jet Gaps: The "jet gap jet" fraction measured by CMS is consistent with BFKL resummation (high gluon density) but inconsistent with standard NLO DGLAP predictions, which underestimate the gap survival probability.
• Pb-Pb Saturation:
  • Exclusive $J/\Psi$: Data from ALICE and CMS in $\gamma Pb$ interactions strongly favors the BK (saturation) model over the linear BFKL model. The nuclear suppression factor $R_A$ is significantly lower in data than linear predictions.
  • Exclusive $\Upsilon$: Due to the higher mass scale ($M_\Upsilon^2 \gg Q_s^2$), saturation effects are negligible, and BFKL/BK predictions converge, matching CMS data.
  • Heavy Quarks: The ratio of diffractive to inclusive $c\bar{c}$ production in $\gamma Pb$ is predicted to be $\sim 21\%$ (BK) vs. lower values for nuclear PDFs, offering a clean test for future data.

C. $\gamma\gamma$ Physics and BSM Searches

• Background Rejection: The technique of matching central system kinematics (mass, rapidity) with forward proton tags effectively suppresses pile-up background, allowing for clean measurements even at high luminosity.
• Anomalous Couplings:
  • Quartic $\gamma\gamma\gamma\gamma$: CMS limits on anomalous couplings $\zeta_1$ and $\zeta_2$ are improved to $\sim 10^{-14}$ GeV$^{-4}$, representing a sensitivity gain of 2-3 orders of magnitude over standard searches.
  • $\gamma\gamma WW/ZZ$: Limits on quartic couplings involving $W$ and $Z$ bosons are established with negligible background.
• Axion-Like Particles (ALPs): The analysis sets stringent limits on ALP production in the mass range of a few GeV to several TeV. Heavy-ion runs (Pb-Pb) are highlighted as complementary to $pp$ runs, covering the intermediate mass region ($Z^4$ enhancement) where $pp$ sensitivity is lower.

4. Significance

• Fundamental QCD Validation: The paper provides the first definitive experimental evidence for the odderon, a prediction of QCD that had eluded confirmation for decades. It also demonstrates the transition from linear to non-linear QCD evolution (saturation) in heavy-ion collisions.
• New Scaling Laws: The identification of geometric scaling in elastic scattering and the behavior of the profile function $\Gamma$ in impact parameter space offer new phenomenological tools for understanding the proton's internal structure at high energies.
• BSM Sensitivity: By leveraging the LHC as a $\gamma\gamma$ collider with forward proton tagging, the work opens a unique window for discovering new physics (ALPs, resonances) and testing the Standard Model's QED sector with unprecedented precision, significantly surpassing the sensitivity of inclusive searches.
• Future Outlook: The results underscore the necessity of high-luminosity data and dedicated forward detectors (Roman Pots) to fully explore the saturation regime and probe the high-mass frontier of BSM physics.