Constraining magnetic monopoles and multiply charged particles with diphoton events at the LHC

Using LHC Run 2 central exclusive diphoton production data, this study constrains the existence of magnetic monopoles and high-electric-charge objects by analyzing their virtual contributions to light-by-light scattering within effective field theories and Born-Infeld scenarios, excluding masses up to several tens of TeV.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle accelerator, a giant cosmic racetrack where scientists smash protons together at near-light speeds. The goal? To find new, exotic particles that could explain the universe's biggest mysteries, like dark matter or why electric charge comes in specific "chunks."

This paper is about hunting for two very special, hypothetical creatures: Magnetic Monopoles and High-Electric-Charge Objects (HECOs).

Here is the story of how the scientists looked for them, explained simply.

1. The Missing Puzzle Pieces

• Magnetic Monopoles: You know how magnets always have a North and a South pole? If you break a magnet in half, you get two smaller magnets, each with a North and South. A magnetic monopole would be a particle that is just a North pole or just a South pole. It's like finding a single half of a coin. If they exist, they would make the laws of physics perfectly symmetrical and explain why electric charge is quantized (why it comes in specific amounts).
• HECOs: These are particles that carry a massive amount of electric charge—way more than an electron. Think of an electron as a tiny spark; a HECO would be like a lightning bolt. They might be remnants of black holes or strange clumps of matter that could explain dark matter.

2. The "Ghost" Hunt: Why Not Just Smash Them?

Usually, to find a new particle, you smash things together hard enough to create it directly. But these monsters are likely too heavy to be created directly, even with the LHC's huge energy. It's like trying to find a specific grain of sand on a beach by digging a hole; you might not find it.

So, the scientists used a clever trick: The "Ghost" Search.

Instead of looking for the monsters themselves, they looked for the ripples the monsters would leave behind if they briefly popped into existence and then vanished.

3. The Light-by-Light Scattering Analogy

Imagine two people throwing tennis balls (photons) at each other.

• Normal Physics: In our everyday world, if two light beams cross, they pass right through each other like ghosts. They don't bounce off or interact.
• The Exotic Twist: The scientists looked for a rare event where two photons do bounce off each other (Light-by-Light scattering).

The Analogy:
Imagine two people throwing tennis balls at each other in a foggy room. Usually, the balls pass through the fog without hitting anything. But, if a giant, invisible elephant (the heavy monopole or HECO) briefly materializes in the middle of the room, the tennis balls might bounce off the elephant's invisible skin and change direction.

The scientists didn't see the elephant. They just saw the tennis balls bouncing in a weird way that shouldn't happen unless a giant invisible elephant was there for a split second.

4. The Detective Work: Proton Tagging

To catch this "ghost," the scientists used a specific setup called Central Exclusive Production.

• They watched for events where two protons (the racers) barely grazed each other, sending out two photons (the tennis balls) in the middle, while the protons themselves kept flying forward, intact.
• They used special "forward detectors" (like high-speed cameras placed far down the track) to catch the protons that survived the graze. This confirmed that the protons didn't break apart, meaning the energy went purely into creating the photon interaction.

5. The Results: Setting the "Speed Limit"

The scientists didn't find the monsters. But that's actually a good thing! It allowed them to set strict rules on where these monsters could be hiding.

• The "Effective Field Theory" (EFT) Filter: Since the monsters are too heavy to see directly, the scientists used a mathematical "filter" (EFT) to estimate how heavy they must be based on how much they would have disturbed the photons.
• The Resummation Trick: Because these hypothetical particles have such huge charges, the math gets messy and breaks down. The scientists used a technique called "resummation" (think of it as adding up an infinite series of tiny corrections) to fix the math and get a reliable answer.

The Verdict:

• For HECOs: If they exist, they must be incredibly heavy (thousands of times heavier than a proton) and carry a massive electric charge. If they were lighter or had less charge, the scientists would have seen the "ripples" in the light.
• For Monopoles: They are also ruled out up to very high masses (tens of TeV). Specifically, if they are "spin-1" (vector) particles, they must be heavier than 73 TeV. If they are "spin-0" (scalar), they must be heavier than 30 TeV.

6. The Born-Infeld Scenario: A Special Case

The paper also looked at a specific theory called Born-Infeld, which suggests there's a maximum limit to how strong an electric field can get (like a speed limit for electricity). In this specific scenario, the "monopole" (called a Cho-Maison monopole) must be even heavier—over 61 TeV. This is so heavy that no current or near-future machine could ever create it directly.

Summary

The scientists didn't find the magnetic monopoles or the super-charged particles. However, by watching how light scatters off light, they proved that if these particles exist, they must be incredibly massive and heavy.

It's like saying, "We didn't find the Loch Ness Monster, but we know for a fact that if it's swimming in this lake, it must be the size of a whale, because we would have seen the waves."

This work complements other searches that try to catch these particles directly. It shows that even when we can't see the monster, we can still map out the territory where it's allowed to hide.

Technical Summary

1. Problem Statement

The existence of Magnetic Monopoles (MMs) and High-Electric-Charge Objects (HECOs) remains one of the most significant open questions in particle physics.

• Magnetic Monopoles: Predicted by Dirac (1931) to explain electric charge quantization and proposed in Grand Unified Theories (GUTs) as solitons. Their existence would symmetrize Maxwell's equations.
• HECOs: Hypothetical particles with large electric charges proposed in various Beyond the Standard Model (BSM) scenarios (e.g., Q-balls, micro-black hole remnants, dark matter candidates).
• Challenge: Direct searches for these particles at the Large Hadron Collider (LHC) rely on high ionization energy loss and time-of-flight measurements. However, these methods are limited by kinematic thresholds and trigger capabilities.
• Objective: This paper proposes an indirect search strategy. It investigates how virtual MMs and HECOs contribute to Light-by-Light (LbL) scattering ($\gamma\gamma \to \gamma\gamma$) via box diagrams. By measuring deviations in this process, the authors aim to constrain the mass and charge of these exotic particles, complementing direct search efforts.

2. Methodology

The study utilizes Central Exclusive Production (CEP) of diphoton events in proton-proton ($pp$) collisions at $\sqrt{s} = 13$ TeV, using data from the CMS-TOTEM Precision Proton Spectrometer (CT-PPS) during LHC Run 2.

Experimental Approach

• Process: $p + p \to p + \gamma\gamma + p$.
• Signature: Two intact protons scattered at small angles (detected by forward proton spectrometers) and two back-to-back photons in the central detector.
• Data Selection: Events with diphoton invariant masses ($m_{\gamma\gamma}$) in the range $350 \text{ GeV} < m_{\gamma\gamma} \lesssim 2 \text{ TeV}$.
• Observation: No excess of exclusive $\gamma\gamma$ events was found above the Standard Model background. This null result was used to set limits on anomalous quartic photon couplings.

Theoretical Framework

The analysis employs two main theoretical approaches to interpret the null results:

1. Effective Field Theory (EFT):

   • Assumes new physics particles (MMs/HECOs) are heavy ($M \gg m_{\gamma\gamma}$) and point-like.
   • Describes the interaction via dimension-8 operators in the Lagrangian:
     $$\mathcal{L}_{4\gamma} = \zeta_1 F_{\mu\nu}F^{\mu\nu}F_{\rho\sigma}F^{\rho\sigma} + \zeta_2 F_{\mu\nu}F^{\nu\rho}F_{\rho\lambda}F^{\lambda\mu}$$
   • The coefficients $\zeta_1$ and $\zeta_2$ are related to the mass ($M$) and charge ($Q$ or $g$) of the virtual particles running in the loop.
   • Validity Constraint: The EFT is valid only if $M \gg m_{\gamma\gamma}$. The authors impose a validity threshold of $M \gtrsim 10$ TeV.

2. Born-Infeld (BI) Theory:

   • Specifically applied to MMs to address the non-perturbative nature of the magnetic coupling.
   • Modifies the QED Lagrangian to impose an upper bound on the electric field, providing a framework for finite-energy monopole solutions (Cho-Maison monopoles).

Handling Strong Coupling (Resummation)

A critical technical challenge is that the coupling between HECOs/HEMOs and photons is too strong for standard perturbation theory.

• The authors apply Dyson-Schwinger resummation techniques (tree-level) to calculate reliable cross-sections for spin-0 and spin-1/2 HECOs.
• This modifies the effective coupling constants, leading to more stringent mass limits compared to tree-level calculations.

3. Key Contributions

• Indirect Mass Limits: The paper derives the first indirect exclusion limits for MMs and HECOs using LbL scattering data from CT-PPS, extending sensitivity to mass scales far beyond the direct kinematic reach of the LHC.
• Spin-Dependent Constraints: The analysis explicitly calculates limits for different spin hypotheses ($s=0, 1/2, 1$), demonstrating how the coupling structure varies with spin.
• Resummation Application: It successfully integrates Dyson-Schwinger resummation into the EFT framework for high-charge objects, correcting for the breakdown of perturbation theory at high charges ($Q \gtrsim 11e$).
• Born-Infeld Interpretation: Provides a specific mass bound for Cho-Maison electroweak monopoles using the BI formalism, a scenario often difficult to constrain with standard EFT.

4. Results

The study translates the experimental limits on $\zeta_{1,2}$ (from CMS-TOTEM) into lower bounds on particle masses ($M$) as a function of their charge ($Q_{eff}$ or $g$).

High-Electric-Charge Objects (HECOs)

• EFT Validity: Indirect limits are reliable only for effective charges $Q_{eff} \gtrsim 90$ (scalar), $160$ (fermion), and $220$ (vector). Below these charges, the required mass falls below the EFT validity threshold ($M < 10$ TeV).
• Mass Limits: For valid EFT regions, the excluded mass scales linearly with charge ($M \propto Q_{eff}$).
  • With resummation, limits become more stringent. For example, for spin-1/2 HECOs, the mass limit reaches multi-TeV values for $Q_{eff} \gtrsim 180$.
• Complementarity: Indirect searches exclude high-mass, high-charge regions that are inaccessible to direct production searches.

Magnetic Monopoles (MMs)

• EFT Limits: Assuming point-like monopoles with Dirac charge $g_D$:
  • Spin-0: Excluded for $M > 2.86$ TeV (valid for $g \ge 4g_D$).
  • Spin-1/2: Excluded for $M > 4.05$ TeV (valid for $g \ge 3g_D$).
  • Spin-1: Excluded for $M > 7.33$ TeV (valid for $g \ge 2g_D$).
  • At $g = 10g_D$, mass limits reach up to 30 TeV (scalar), 40 TeV (fermion), and 73 TeV (vector).
• Born-Infeld Scenario: For the specific Cho-Maison electroweak monopole (mass $\sim$ TeV scale), the BI analysis sets a lower mass limit of $M_{CM} > 61$ TeV.

5. Significance

• Complementarity: This work demonstrates that precision measurements of LbL scattering provide a powerful, complementary probe to direct searches. While direct searches are sensitive to low-mass, slow-moving particles, indirect EFT methods can probe extremely high masses (tens of TeV) if the particles carry sufficient charge.
• Theoretical Validation: The application of resummation techniques validates the use of EFT for high-charge objects, refining the reliability of exclusion limits in the strong-coupling regime.
• Future Prospects: The results set a benchmark for future colliders. The authors note that future $e^+e^-$, $\gamma\gamma$, and muon colliders, as well as heavy-ion runs at the LHC (where photon flux is enhanced by $Z^4$), will further tighten these constraints or potentially discover these exotic states.
• Exclusion of Parameter Space: The study effectively rules out specific regions of the mass-charge parameter space for MMs and HECOs, guiding theoretical model building and future experimental strategies.

In summary, the paper establishes that the absence of anomalous diphoton events in exclusive production at the LHC places robust, model-independent constraints on the existence of heavy magnetic monopoles and highly charged particles, pushing the exclusion limits into the multi-TeV regime.