⚛️ phenomenology

Direct constraints on the agnostic $\nu$ SMEFT from heavy-neutrino searches at the LHC

This paper presents the first experimental exclusion limits on the agnostic neutrino Standard Model Effective Field Theory ( $\nu$ SMEFT) parameter space by recasting a CMS search for heavy Majorana neutrinos in the same-sign dimuon plus two jets channel, constraining effective coupling strengths for heavy-neutrino masses between 200 GeV and 15 TeV.

Original authors: Luc\'ıa Duarte, Agust\'ın Guillenea

Published 2026-07-27

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Luc\'ıa Duarte, Agust\'ın Guillenea

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, incredibly complex video game. For decades, physicists have been playing with the "Standard Model," which is like the game's official rulebook. It explains almost everything we see: why things have mass, how particles interact, and how the universe holds together. But there's a glitch in the code. We know neutrinos—tiny, ghostly particles that zip through everything—have a little bit of mass, but the rulebook says they shouldn't. It's like finding a character in the game that moves when the rules say it should be frozen. This mystery has forced scientists to imagine "New Physics," a hidden layer of the game that we haven't unlocked yet.

To hunt for this hidden layer without knowing exactly what it looks like, scientists use a clever strategy called an "Effective Field Theory." Think of it like trying to figure out what's inside a sealed, heavy box by shaking it. You can't see the contents, but you can feel how it rattles and predict what might be inside based on the vibrations. In this paper, the scientists are shaking a specific box called the "neutrino Standard Model Effective Field Theory" (or νSMEFT). They are looking for "Heavy Neutral Leptons"—imaginary, super-heavy cousins of the neutrinos that might be hiding in the box. If these heavy cousins exist, they would leave a unique fingerprint on the universe, and the scientists want to know exactly how heavy they could be and how strongly they might interact with the rest of the game before we find them.

The Great Heavy-Neutrino Hunt

In this study, two researchers, Lucía Duarte and Agustín Guillenea, decided to play detective with a massive amount of data from the Large Hadron Collider (LHC), the world's biggest particle-smashing machine. They took a specific search that the CMS experiment (one of the detectors at the LHC) had already done and gave it a fresh pair of glasses.

The original search was looking for a very specific scenario: a "Type-I Seesaw" model where heavy neutrinos are produced in a very particular way, like two particles colliding and fusing into a heavy one. But the authors asked a bold question: "What if the heavy neutrinos are being made in many different ways, not just the one the original search was designed for?" They decided to be "agnostic," which is a fancy way of saying "open-minded." Instead of betting on just one theory of how these heavy particles behave, they assumed that every possible way they could interact (described by a list of mathematical rules called dimension-six operators) was happening at the same time.

The Simulation and the Search

To see if this open-minded approach worked, the team built a digital simulation. They imagined a universe where these heavy neutrinos exist with masses ranging from 200 GeV all the way up to 15,000 GeV (that's 15 TeV, or about 15,000 times heavier than a proton). They then ran a virtual version of the CMS experiment, smashing protons together and looking for a very specific "smoking gun" signature: two muons (a type of heavy electron) with the same electric charge, accompanied by two jets of particles.

In the real world, finding two same-sign muons is rare and exciting because it breaks a fundamental rule of physics called "lepton number conservation." It's like finding two left-handed gloves in a box that should only contain right-handed ones. The CMS experiment had already looked for this signal, but they were only looking for it in the "Type-I Seesaw" style. Duarte and Guillenea re-ran the analysis, but this time they let the heavy neutrinos be produced by all the different interaction rules in their agnostic list simultaneously. They even checked if the results changed if they forced some of the rules to obey strict limits from a different experiment called "neutrinoless double beta decay" (a rare process that hasn't been seen yet but sets strict rules for how heavy neutrinos can behave).

The Findings: A New Map of the Unknown

The results of this digital detective work are a new set of "exclusion limits." Think of these limits as a map of a treasure hunt where the treasure is the heavy neutrino. The map doesn't show where the treasure is; instead, it shows the vast areas where the treasure definitely isn't.

The team found that for heavy neutrinos with masses between 200 GeV and 15 TeV, the strength of their interaction with the rest of the universe (called the effective coupling) must be weaker than a very specific number. The strongest limit they found was around 5.8 × 10⁻⁷ GeV⁻², occurring when the heavy neutrino mass is about 1.5 TeV. If the interaction were stronger than this, the CMS detector would have seen the signal by now. Since they didn't see it, they can rule out any theory that predicts stronger interactions in that mass range.

Interestingly, when they added the strict rules from the "neutrinoless double beta decay" experiment, the map didn't change much. The exclusion limits stayed almost the same. This suggests that the LHC search is sensitive to a wide variety of interactions, not just the ones constrained by the low-energy experiments. It's like finding that a metal detector is so sensitive it finds gold even if you tell it to ignore the most common type of metal.

Why This Matters

This paper is a milestone because it's the first time anyone has taken a dedicated LHC search for heavy neutrinos and re-interpreted it specifically for this "agnostic" framework. Before this, scientists mostly looked at one interaction at a time. By looking at them all together, the authors show that the LHC is a powerful tool for hunting these heavy particles, even if we don't know exactly which "flavor" of new physics is hiding them.

The authors are careful to note that these results come from a detailed simulation and statistical analysis of existing data, not a new discovery of a particle. They haven't found the heavy neutrino yet; they've just drawn a tighter circle around where it can't be. They suggest that future work should look at how these heavy neutrinos might mix with the light ones we already know, and how different interaction rules might interfere with each other. But for now, this study provides the first solid, experimental boundaries for the agnostic νSMEFT parameter space, giving future explorers a clearer map of the territory they need to cover.

Technical Summary: Direct Constraints on the Agnostic $\nu$ SMEFT from Heavy-Neutrino Searches at the LHC

Problem and Motivation
The observation of neutrino oscillations and masses necessitates extensions of the Standard Model (SM), often involving right-handed neutrinos ( $N_R$ ). While the Standard Model Effective Field Theory (SMEFT) describes new physics at scales beyond direct experimental reach, it typically integrates out heavy neutral leptons (HNLs). However, if HNLs exist within the accessible energy spectrum, they should be treated as explicit dynamical degrees of freedom. This leads to the neutrino SMEFT ( $\nu$ SMEFT) framework, which systematically parametrizes low-energy effects of ultraviolet (UV) physics in the presence of heavy neutrinos.

Despite extensive phenomenological studies of specific $\nu$ SMEFT operators, direct constraints on the parameter space derived from dedicated reinterpretations of Large Hadron Collider (LHC) searches remain largely unexplored. Most existing analyses focus on individual operators or specific UV completions (e.g., Type-I Seesaw), potentially missing the collective impact of multiple effective interactions. This work addresses the gap by providing direct constraints on an "agnostic" $\nu$ SMEFT benchmark using LHC data.

Methodology
The authors perform a dedicated recast of a CMS search for heavy Majorana neutrinos in the same-sign dimuon plus two jets ( $\mu^\pm \mu^\pm jj$ ) final state [36]. The analysis proceeds through the following steps:

Theoretical Framework:
- Agnostic Benchmark: The study adopts a model-independent scenario where all dimension-six operators in the $\nu$ SMEFT basis (involving SM fields and a right-handed neutrino $N$ ) are assumed to contribute simultaneously. A common effective coupling, $\alpha/\Lambda^2$ , is assigned to all operators. This reduces the parameter space to two variables: the heavy neutrino mass ( $m_N$ ) and the overall coupling strength ( $\alpha/\Lambda^2$ ).
- $0\nu\beta\beta$ -Constrained Benchmark: A second scenario imposes bounds from neutrinoless double-beta decay ( $0\nu\beta\beta$ ) on operators contributing to the $udNe$ vertex (involving first-generation fermions), while keeping other operators agnostic.
- Lagrangian: The analysis considers the renormalizable dimension-4 Lagrangian extended with a Majorana mass term and the dimension-5 and dimension-6 effective operators listed in Table I of the paper. The heavy-active mixing ( $V_{\ell N}$ ) is neglected to focus on new physics effects beyond the minimal seesaw mechanism.
Event Simulation and Recast:
- Signal Generation: Signal events for the process $pp \to \mu^\pm \mu^\pm jj$ are generated using MadGraph5_aMC@NLO 3.6.2 at $\sqrt{s} = 13$ TeV. The simulation includes tree-level Feynman diagrams for various production topologies, including Vector Boson Fusion (VBF) mediated by the $O_{Nl\phi}$ operator, as well as four-fermion contact interactions ( $O_{duNl}$ , $O_{QuNL}$ , etc.). Interference effects between different amplitudes are fully included.
- Detector Simulation: Events are processed through Pythia 8.313 for parton showering and hadronization, followed by a fast detector simulation using Delphes 3.5.0 with the CMS card.
- Selection: The analysis replicates the CMS selection criteria [36], including requirements for two same-sign muons ( $p_T > 30$ GeV, $|\eta| < 2.4$ ), two jets ( $p_T > 30$ GeV, $|\eta| < 4.7$ ), large dijet invariant mass ( $m_{jj} > 750$ GeV), large pseudorapidity separation ( $|\Delta\eta_{jj}| > 2.5$ ), and specific Zeppenfeld variable cuts to isolate VBF-like kinematics. Veto criteria for electrons, hadronic taus, and $b$ -jets are applied.
- Statistical Analysis: A counting experiment is performed using a Poisson likelihood. The observed number of events ( $n$ ) and expected background ( $b$ ) from the original CMS analysis are used to derive the 95% Confidence Level (CL) upper limit on the number of signal events ( $s_{up}$ ). The exclusion limit is set where the predicted signal yield $s = \mathcal{L} \sigma_{MC} \epsilon_{MC}$ exceeds $s_{up}$ .

Key Contributions

First Direct Exclusion: This work presents the first experimental exclusion limits on the agnostic $\nu$ SMEFT parameter space obtained from a dedicated recast of an LHC heavy-neutrino search.
Agnostic Benchmark Implementation: It introduces and applies a benchmark where all dimension-six operators contribute simultaneously with a common coupling, capturing collective effects and interference that single-operator studies miss.
Comprehensive Operator Inclusion: The analysis accounts for a broad class of production topologies (VBF, contact interactions) rather than restricting the search to the specific VBF topology optimized for the Type-I Seesaw model.

Results

Exclusion Limits: For heavy neutrino masses in the range $200 \text{ GeV} \le m_N \le 15 \text{ TeV}$ , the observed upper limits on the effective coupling strength range from $5.8 \times 10^{-7} \text{ GeV}^{-2}$ to $2.3 \times 10^{-6} \text{ GeV}^{-2}$ .
Mass Dependence: The exclusion contours exhibit a characteristic U-shaped behavior. The strongest limits are achieved around $m_N \sim 1.5 \text{ TeV}$ , where the selected signal yield is maximized. Sensitivity decreases for both lower and higher masses.
Impact of $0\nu\beta\beta$ Constraints: Imposing $0\nu\beta\beta$ bounds on first-generation operators results in only a modest modification of the exclusion contour. This is because the same-sign dimuon signal receives significant contributions from operators involving second-generation leptons, which remain unconstrained by $0\nu\beta\beta$ . Consequently, the search retains substantial sensitivity even under these strong low-energy constraints.
Comparison to Original Search: While the exclusion contour shape resembles the original CMS limits (optimized for Type-I Seesaw), the position of the minimum is shifted, reflecting the richer signal composition in the agnostic $\nu$ SMEFT scenario.

Significance and Claims
The paper claims that these results constitute the first direct collider exclusion of the agnostic $\nu$ SMEFT parameter space. The authors emphasize that the CMS VBF analysis is sensitive not only to the specific t-channel topology it was designed for but also to a broader class of $\nu$ SMEFT interactions. The proximity of the limits obtained in the fully agnostic scenario and the $0\nu\beta\beta$ -constrained scenario suggests that current LHC searches are robust against the strongest available low-energy constraints on first-generation operators. The derived limits on effective couplings ( $\sim 10^{-6} \text{ GeV}^{-2}$ ) indicate that $\nu$ SMEFT contributions could be phenomenologically relevant in the same parameter space region traditionally explored via heavy-light neutrino mixing.

The authors note that a quantitative comparison with mixing-induced processes and the study of their interplay are left for future work, as is the disentanglement of individual operator contributions. The work serves as a proof-of-concept for using LHC data to constrain the collective parameter space of effective theories involving heavy neutrinos.

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