Photon-initiated enhancements in the pair production of highly charged coloured particles

This paper demonstrates that mixed QCD-QED contributions from gluon-photon initial states significantly enhance the pair production of highly charged leptoquarks by up to 33%, thereby strengthening mass exclusion limits derived from LHC data and establishing a new precision standard for bounding such states.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle smasher. Scientists use it to look for new, heavy particles that might be hiding in the universe. Usually, when they try to create pairs of these heavy, "colored" particles (particles that interact via the strong nuclear force, like quarks), they assume the collision is driven almost entirely by gluons.

Think of gluons as the "heavy trucks" of the particle world. They are everywhere inside the proton and are very good at smashing things together.

However, this paper points out that scientists have been ignoring a smaller, quieter force: photons (light particles). While photons are much rarer inside a proton than gluons, they act like "speeding sports cars." If the new heavy particles they are looking for have a very strong electric charge, these "sports cars" can actually help create them just as effectively as the "trucks," especially when the particles are very heavy.

Here is a breakdown of the paper's main discoveries using simple analogies:

1. The "Sports Car" vs. The "Truck"

Usually, scientists calculate how often these new particles are made by only counting the collisions between two gluons (Truck vs. Truck).

• The Paper's Insight: They realized that collisions between a gluon and a photon (Truck vs. Sports Car) are being missed.
• Why it matters: If the new particle has a high electric charge (like a "super-charged" battery), the photon hits it much harder. The paper shows that for certain particles called Leptoquarks (which are like hybrid particles that can turn into both a quark and a lepton), this "Truck vs. Sports Car" collision can increase the production rate by up to 33%.
• The Analogy: Imagine you are trying to fill a bucket with water. You've been using a fire hose (gluons) and ignoring a garden hose (photons). You thought the fire hose did 100% of the work. But if the garden hose is aimed at a very sensitive spot (a highly charged particle), it turns out the garden hose is actually adding a huge splash, making the bucket fill up 33% faster than you thought.

2. The "Traffic Pattern" Change

It's not just about how many particles are made; it's also about how they are made.

• The Old Way (Gluon-Gluon): When two gluons collide, they are both "colored" (carrying a specific charge). This creates a symmetrical, chaotic spray of other particles (jets) flying out in all directions. It's like two trucks crashing head-on; debris flies everywhere.
• The New Way (Gluon-Photon): A photon has no color charge. When it collides with a gluon, the "debris" pattern is different. The spray of particles is lopsided and less chaotic.
• The Result: The paper shows that events created by this mixed collision look "cleaner" and have fewer extra jets of debris than the standard collisions. This is a unique fingerprint that helps scientists tell the difference between the two types of collisions.

3. Raising the "Speed Limit"

Because scientists previously ignored the photon contribution, they underestimated how often these particles are made.

• The Consequence: If you think you are making 100 particles, but you are actually making 133, your math for finding them is wrong.
• The Fix: The authors took the latest data from the ATLAS experiment (a giant detector at the LHC) and recalculated the limits. By including the "Truck vs. Sports Car" collisions, they found that the rules for excluding these particles are stricter.
• The Takeaway: If a particle hasn't been seen yet, we can now say with more confidence that it must be heavier than we previously thought. The "exclusion limit" (the minimum weight a particle must have to have escaped detection so far) has been pushed higher.

4. Why Leptoquarks?

The paper focuses on Leptoquarks because they are the perfect candidates for this effect.

• They are "fundamental" particles (like the basic building blocks), which makes the math work out in their favor.
• They can carry a very high electric charge (up to 5/3 times the charge of an electron).
• Because the "photon boost" scales with the square of the charge, these highly charged Leptoquarks get the biggest bonus from the photon collisions.

Summary

In simple terms, this paper tells us that for a long time, scientists were looking for new heavy particles using a map that only showed the main highways (gluons). They forgot about the fast side roads (photons).

When they finally added the side roads to the map, they realized:

1. More cars are arriving: The production rate for certain highly charged particles is significantly higher (up to 33% more) than previously calculated.
2. The traffic looks different: The collisions leave a distinct, cleaner trail of debris.
3. The rules have changed: Because more particles are being made, the "safety zone" where we thought these particles didn't exist has shrunk. We now know these particles must be even heavier to have remained hidden.

The authors conclude that to get precise measurements in the future, we must stop ignoring the "side roads" and treat these photon collisions with the same seriousness as the main highway collisions.

Technical Summary

Technical Summary: Photon-Initiated Enhancements in the Pair Production of Highly Charged Coloured Particles

Problem Statement
Direct searches for TeV-scale coloured particles at the Large Hadron Collider (LHC) typically rely on pair production (PP) mechanisms dominated by strong interactions (QCD). Consequently, mass exclusion limits are derived using QCD cross-sections, often assuming insensitivity to unknown couplings. However, for new states carrying significant electric charge, electromagnetic interactions mediated by photons become phenomenologically relevant. Specifically, mixed QCD-QED contributions arising from gluon-photon ($g\gamma$) initial states can modify total production rates. While the photon parton distribution function (PDF) is smaller than the gluon PDF, the $g\gamma$ contribution scales with the square of the particle's electric charge ($Q^2$) and the Dynkin index of its colour representation. This effect is particularly pronounced for colour-triplet states (fundamental representation) and particles with large electric charges, where the relative importance of the $g\gamma$ channel can rival next-to-leading-order (NLO) QCD corrections.

Methodology
The authors systematically quantify the impact of mixed QCD-QED contributions on the pair production of coloured particles with varying spins and colour representations.

• Theoretical Framework: The study calculates tree-level cross-sections for $g\gamma \to X_R X_R$ processes, where $X_R$ is a coloured particle in representation $R$. The analysis establishes that the $g\gamma$ channel is constrained to produce a colour-octet final state, with cross-sections scaling linearly with the Dynkin index $T(R)$.
• Model Application: The framework is applied to Leptoquarks (LQs), specifically the canonical scalar and vector species defined by the Buchmüller-Rückl-Wyler classification. These are chosen because they are colour triplets and, in certain extensions, can carry charges up to $Q=5/3$ (or higher in BSM scenarios).
• Computational Tools: Interactions were implemented in FeynRules to generate UFO models. Cross-sections were evaluated using MadGraph5_aMC@NLO with a dynamic scale choice. For scalar LQs, NLO QCD corrections were computed using NLOCT and matched to the Pythia parton shower.
• PDF Sets: To address uncertainties in photon density, the authors utilized the LUXqed PDF set, which offers improved precision over standard sets like NNPDFqed for high-$x$ regimes.
• Experimental Recasting: The latest ATLAS search for $\mu\mu jj$ final states (pair production of LQs decaying to quarks and leptons) was recast. The analysis assumed the limit where LQ-lepton-quark couplings ($\lambda_{\ell q}$) are negligible, isolating gauge-mediated production. Experimental cut efficiencies were assumed consistent across $gg$, $q\bar{q}$, and $g\gamma$ subprocesses.

Key Contributions and Results

1. Colour and Charge Scaling: The paper demonstrates that the ratio of the $g\gamma$ cross-section to the pure QCD cross-section ($R = \sigma_{g\gamma} / (\sigma_{gg} + \sigma_{q\bar{q}})$) is maximized for the lowest-dimensional colour representations (triplets) and increases with electric charge. For a scalar colour-triplet with $Q=5/3$ at a mass of 2 TeV, the $g\gamma$ contribution enhances the total pair-production rate by approximately 33%. This enhancement is comparable in magnitude to NLO QCD corrections.
2. Kinematic Distinctions: The asymmetric colour flow of the $g\gamma$ initial state (where only the gluon carries colour) leads to distinct radiation patterns compared to symmetric $gg$ or $q\bar{q}$ channels. Specifically, $g\gamma$ events exhibit:
   • Suppressed initial-state radiation, resulting in lower jet multiplicities.
   • A harder transverse momentum ($p_T$) spectrum for radiated jets due to the $g\gamma X_R X_R$ contact interaction.
   • A less central angular distribution for radiation jets, as they are preferentially pulled along the beamline by the single incoming gluon.
3. Updated Mass Limits: By incorporating the tree-level $g\gamma$ contribution alongside NLO QCD corrections, the authors derived updated mass exclusion limits for various LQ species.
   • For models containing states with $Q=5/3$ (e.g., $R_2$, $U_3$), the inclusion of QED effects significantly strengthens the exclusion limits compared to pure QCD predictions.
   • For example, in the $R_2$ model (assuming 100% branching ratio to $\mu j$), the mass limit increases from 1545 GeV (pure QCD LO) to 1682 GeV (LO QCD+QED).
   • The study confirms that neglecting these QED effects leads to systematically weaker bounds on highly charged coloured states.

Significance and Claims
The paper establishes that photon-initiated contributions are not merely subleading corrections but are essential for precision constraints on highly charged coloured particles. The authors argue that for states with large electric charges, the mixed QCD-QED effects are comparable in size to higher-order QCD corrections (such as NLO or NNLO). Therefore, accurate theoretical predictions and reliable mass exclusion limits require the inclusion of these tree-level QED effects.

The work serves as a proof of principle, demonstrating that accounting for QED-induced contributions is a necessary step toward precision-driven constraints on Beyond the Standard Model (BSM) scenarios. Furthermore, the authors note that these effects highlight the potential of future $\gamma p$ colliders (such as LHeC or FCC-eh), where photon-parton interactions would be the primary production mechanism, offering enhanced sensitivity to highly charged states compared to proton-proton collisions. The paper concludes that as photon PDFs improve and future datasets emerge, these processes will play an increasingly vital role in constraining BSM physics.