⚛️ phenomenology

ALP pair production at the LHC

This paper investigates ALP pair production at the LHC, demonstrating that the four-photon signature from the non-resonant $gg\to aa$ process can significantly constrain the multidimensional parameter space of dimension-5 and dimension-6 ALP interactions, while also reinterpreting ATLAS Higgs-resonant search results to reveal complex, non-trivial constraints.

Original authors: Ilaria Brivio, Simone Meoni, Davide Pagani

Published 2026-07-27

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CC BY 4.0

Original authors: Ilaria Brivio, Simone Meoni, Davide Pagani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible puzzle. For decades, scientists have been trying to solve it using the "Standard Model," which is like a rulebook listing all the known particles (like electrons and quarks) and how they dance together. But there's a problem: the rulebook has holes. It doesn't explain gravity, why there's more matter than antimatter, or what dark matter is made of. To fill these gaps, physicists dream up "Beyond the Standard Model" theories. One of the most popular ideas involves a mysterious, ghost-like particle called an Axion-Like Particle (ALP). Think of an ALP as a shy, ultra-lightweight ghost that barely interacts with anything. It's so elusive that it might be hiding in plain sight, only revealing itself when it bumps into other particles or decays into flashes of light.

The big question is: How do we catch these ghosts? Usually, scientists look for a single ALP appearing out of nowhere. But this paper asks a bolder question: What if we look for two ALPs appearing together? It's like trying to find a single sneaky cat in a house versus finding two cats playing tag. The authors of this study, working with data from the Large Hadron Collider (LHC)—the world's biggest particle-smashing machine—decided to simulate what would happen if two of these ALPs were created at the same time and then immediately turned into four beams of light (photons). They wanted to see if this "double-ghost" scenario could reveal new secrets about the rules of the universe, specifically looking for interactions that are usually too weak to see.

The Paper's Story: Hunting for Double Ghosts

The researchers, Ilaria Brivio, Simone Meoni, and Davide Pagani, set out to explore a specific corner of physics where two ALPs are born from a collision of protons. In their simulation, they focused on a very clean signal: four isolated photons (particles of light) flying out of the collision. This is like looking for a specific four-color fireworks display in a sky full of noise.

The team investigated two different ways these double-ALP pairs could be created. The first way is the "Higgs-resonant" channel. Imagine the Higgs boson (a heavy particle discovered a decade ago) as a unstable balloon that pops, releasing two ALPs. This has been looked at before, but the authors re-examined it with a fresh set of eyes, allowing for more complex interactions than previous studies. The second way, and the real novelty of this paper, is the "non-resonant" channel. Here, the two ALPs are created directly from the collision without the Higgs balloon in the middle. It's like two ghosts appearing out of thin air, skipping the middleman entirely. This process had never been studied in this specific way before.

What they found is fascinating and a bit tricky. They discovered that looking for these double ALPs is a powerful tool, but it's not a simple "yes or no" test. The universe's parameter space (the map of all possible values for these particles) is a multi-dimensional maze. The authors found that if you only look at one number at a time, you might think you've caught the ghost, but if you look at the whole picture, the ghost can slip away.

For instance, they found that if the ALPs are very heavy (up to 1,000 GeV) and the interaction creating them is strong, the search could be incredibly sensitive. In their simulations, with just 300 fb⁻¹ of data (a measure of how many collisions the LHC has seen), they could potentially rule out certain types of interactions that were previously thought to be safe. They found that the "non-resonant" search could be even more powerful than the "Higgs-resonant" one, potentially constraining the strength of these new interactions by a factor of ten.

However, the paper also highlights a major catch: the ALPs are tricky. If they live too long, they might fly right out of the detector before turning into light, making them invisible to the four-photon search. If they decay too quickly, they might turn into other things. The authors showed that there are "blind spots" in the search. For example, if the interaction that creates the ALPs is huge but the interaction that makes them decay into light is tiny, the signal disappears. This creates a "flat direction" in the data—a path where the ALP parameters can be anything, and the experiment sees nothing. It's like trying to find a needle in a haystack, but the needle can change its color to match the hay perfectly.

The study also re-interpreted existing data from the ATLAS experiment (one of the detectors at the LHC). They took the old results, which assumed a simple scenario, and re-ran the numbers allowing for more complex interactions. They found that the old limits on how heavy or how strongly interacting these particles can be change significantly when you allow for these extra complexities. In some cases, the limits get tighter; in others, they get looser, depending on how the different forces balance each other out.

Ultimately, the paper suggests that hunting for pairs of ALPs is a promising strategy that could open a new window into physics beyond our current understanding. It shows that even with the data we have right now, we can start to map out the rules of these ghostly particles. But it also warns us that the map is complex. We can't just look at one piece of the puzzle; we have to understand how the creation of the particles and their decay are linked. If we get the balance wrong, the ALPs will remain hidden. The authors conclude that while we haven't found the ALPs yet, this new way of looking for them—especially the non-resonant, double-ghost method—gives us a much sharper pair of glasses to spot them in the future. They emphasize that to truly solve the mystery, we need a global analysis that looks at all the different ways ALPs could behave, rather than just checking one box at a time.

Technical Summary: ALP Pair Production at the LHC

Problem Statement
Axion-Like Particles (ALPs) are well-motivated pseudo-Goldstone bosons appearing in various Beyond the Standard Model (BSM) scenarios. While single-ALP production and decay processes have been extensively studied, processes involving the simultaneous production of ALP pairs (di-ALP) remain largely unexplored, particularly in the context of Effective Field Theory (EFT) including dimension-6 operators. Existing literature has primarily focused on the Higgs-resonant decay $h \to aa$ , mediated by a dimension-6 operator. However, the direct non-resonant production of ALP pairs via gluon fusion ( $gg \to aa$ ) involves a complex interplay between dimension-5 operators (coupling ALPs to gluons and photons) and dimension-6 operators (contact interactions and Higgs couplings). A comprehensive understanding of the sensitivity to these simultaneous interactions is lacking, especially regarding the multidimensional nature of the ALP parameter space and the potential for cancellations or flat directions that could evade standard constraints.

Methodology
The authors perform a phenomenological study of ALP pair production at the LHC ( $\sqrt{s} = 13$ TeV) focusing on the final state of four isolated photons ( $pp \to aa \to 4\gamma$ ). The analysis covers two distinct production channels:

Non-resonant production ( $gg \to aa$ ): This process is mediated by dimension-5 operators ( $O_{G1}$ ) and a dimension-6 contact operator ( $O_{G2}$ ). The authors calculate the tree-level amplitude, including $t$ - and $u$ -channel diagrams and the contact vertex.
Higgs-resonant production ( $gg \to h \to aa$ ): This channel is mediated by the dimension-6 operator $O_{ah}$ coupling the Higgs to two ALPs.

The study employs the following technical framework:

EFT Formalism: The analysis utilizes an ALP EFT up to dimension-6, considering CP-even operators. The relevant Wilson coefficients are $C_{G1}$ (dimension-5, $agg $),$ C_{G2}$ (dimension-6, $a^2gg$ ), $C_{ah}$ (dimension-6, $haa$), and $C_{\gamma\gamma}$ (dimension-5, $a\gamma\gamma$ ).
Signal Modeling: Simulations are performed using MadGraph5_aMC@NLO with the NNPDF40 parton distribution functions. The Narrow Width Approximation (NWA) is adopted for the ALPs, factorizing production and decay.
Decay and Branching Ratios: The branching ratio $Br(a \to \gamma\gamma)$ is calculated considering tree-level decays to photons and gluons, as well as kinematically open electroweak decays ( $Z\gamma, WW, ZZ$ ). To avoid introducing unconstrained directions, the authors adopt a "best-case scenario" where the electroweak decay width is minimized for a given mass, maximizing the photon branching ratio.
Detector Effects: The analysis incorporates Finite-Size Detector Effects (FSDE), accounting for the probability that long-lived ALPs escape the detector volume before decaying. Selection cuts mimic those used in ATLAS searches (four isolated photons with specific $p_T$ and $\eta$ requirements).
Reinterpretation: For the Higgs-resonant channel, the authors recast existing ATLAS search results (Ref. [46]) into the multidimensional parameter space $(C_{\gamma\gamma}, C_{G1}, C_{ah})$ , rather than performing a new simulation chain.

Key Contributions

First Study of Non-Resonant $gg \to aa$ : This work presents the first phenomenological investigation of the non-resonant di-ALP production process at the LHC, identifying its sensitivity to dimension-6 operators ( $O_{G2}$ ) alongside dimension-5 couplings.
Multidimensional Parameter Space Analysis: Unlike previous studies that often vary one parameter at a time, this analysis explores the full three-dimensional parameter space. It highlights non-trivial features arising from the interplay between production cross-sections and decay branching ratios, specifically the cancellation effects between production and decay dependencies on $C_{G1}$ .
Reinterpretation of Higgs-Resonant Limits: The authors provide a rigorous reinterpretation of ATLAS Higgs-resonant search limits, relaxing the assumption that $C_{G1}=0$ and exploring the dependence on $C_{ah}$ and $C_{\gamma\gamma}$ simultaneously.
Identification of Flat Directions and Unconstrained Regions: The study demonstrates that di-ALP searches alone cannot fully constrain the ALP parameter space. It identifies specific directions (e.g., large $C_{G1}$ with specific $C_{G2}$ signs, or regions where FSDE dominate) where the signal rate becomes independent of certain Wilson coefficients, leading to unconstrained regions.

Results

Non-Resonant Sensitivity: With an integrated luminosity of $300 \text{ fb}^{-1}$ , the non-resonant search can constrain the dimension-6 coefficient $C_{G2}/\Lambda_a^2$ down to $\sim 10^{-3} \text{ TeV}^{-2}$ for ALP masses up to $1 \text{ TeV}$ , provided $C_{G1}$ is small and $Br(a \to \gamma\gamma)$ is maximized.
Dimension-5 Constraints: The non-resonant channel can also provide competitive constraints on dimension-5 couplings ( $C_{G1}, C_{\gamma\gamma}$ ), particularly in regions where the dimension-6 contribution is negligible.
Higgs-Resonant Sensitivity: The reinterpretation of ATLAS data shows that constraints on $C_{ah}/\Lambda_a^2$ are strongest for $C_{G1} \approx 0$ and $Br(a \to \gamma\gamma) \approx 1$ . The sensitivity drops significantly if $C_{G1}$ is large (suppressing the photon branching ratio) or if $C_{ah}$ is too small to produce a detectable signal.
FSDE Impact: Finite-size detector effects significantly alter the exclusion contours, particularly for small Wilson coefficients where ALPs become long-lived. This effect can lead to upper bounds on $C_{\gamma\gamma}$ in specific regions of parameter space, but also creates "unconstrained" directions where the signal is depleted by the ALP escaping the detector.
Interference Effects: The study reveals that for negative $C_{G2}$ , destructive interference between the dimension-5 and dimension-6 amplitudes can create cusps or thin bands in the allowed parameter space, allowing for larger values of couplings than in the constructive interference case.

Significance and Claims
The paper claims that ALP pair production is a promising and necessary probe for the ALP EFT beyond dimension-5. The authors emphasize that:

Complementarity: Di-ALP searches offer sensitivity to dimension-6 operators that single-ALP searches cannot access, and they provide a complementary probe to existing single-ALP constraints.
Multidimensionality is Crucial: The complex interplay between production and decay, and the dependence on ALP lifetimes, leads to non-trivial shapes in the parameter space (e.g., flat directions, cusps, and unconstrained regions). A global analysis is essential to extract robust constraints, as single-channel searches cannot fully close the allowed parameter space.
Feasibility: Meaningful exploration of the ALP EFT beyond dimension-5 is already possible at the LHC with current or near-future datasets ( $300 \text{ fb}^{-1}$ ), potentially probing dimension-6 coefficients with sensitivities competitive with or stronger than current Higgs-resonant limits.
EFT Validity: The authors note that the most stringent constraints often arise in regions where dimension-6 couplings are large relative to dimension-5 ones, a scenario that may challenge the perturbative validity of the EFT, but which serves as a conservative benchmark for experimental sensitivity.

The work concludes by suggesting that while the current analysis is a significant step, future improvements should include NLO QCD corrections, more detailed background modeling, and extensions to lower ALP masses and other final states.

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