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Search for scalar leptoquarks produced via muon-quark scattering in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS detector, this study presents the first search for TeV-scale scalar leptoquarks produced via muon-quark scattering, finding no evidence for their existence and setting new exclusion limits that extend previous coverage to masses between 1.5 and 3.6 TeV for LQ(u $\mu$ ) and above 1.8 TeV for LQ(b $\mu$ ).

Original authors: CMS Collaboration

Published 2026-08-31

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CC BY 4.0

Original authors: CMS Collaboration

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

The universe is built from a small set of fundamental ingredients, yet the rules governing how they interact remain one of the great mysteries of modern physics. Scientists have long suspected that the families of particles known as quarks and leptons are not as separate as they appear. Quarks are the building blocks of protons and neutrons, while leptons include the familiar electron and the elusive neutrino. If these two groups are truly related, there should be a bridge connecting them—a particle that can turn a quark into a lepton or vice versa. This hypothetical bridge is called a leptoquark. Finding such a particle would be a monumental discovery, offering a glimpse into a deeper symmetry of nature and potentially explaining why the universe has the specific properties it does today.

For decades, researchers have hunted for these particles, but they have not been found. This absence is puzzling because many theories predicting their existence are compelling. The search has now taken a new turn, moving away from the traditional method of smashing two protons together to create a pair of these particles. Instead, a team of scientists using the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider in Switzerland has looked for a different, more subtle process. They searched for a single leptoquark created when a muon, a heavy cousin of the electron, inside one proton collides with a quark inside the other proton. This scenario relies on the fact that protons are not just simple bags of quarks; they are seething clouds of energy where particles and antiparticles constantly flicker in and out of existence. Occasionally, this quantum activity produces a muon that can act as a projectile in a collision.

The researchers analyzed a massive dataset of collisions recorded between 2016 and 2018, corresponding to an integrated luminosity of 138 inverse femtobarns. They focused on events where the collision produced a high-energy muon and a jet of particles, which is the spray of debris left behind when a quark is knocked loose. They specifically looked for cases where the muon and the jet appeared to come from the decay of a single, heavy particle. The team examined two main possibilities: a leptoquark that decays into a muon and an up quark, and another that decays into a muon and a bottom quark. To find the signal, they used a sophisticated computer program trained to distinguish the subtle patterns of a potential new particle from the overwhelming background of ordinary particle interactions. They looked for a specific mass value where the muon and jet would consistently appear together, which would indicate the presence of a new particle.

After sifting through the data, the scientists found no evidence of a leptoquark. The distribution of the muon and jet masses matched the predictions for known physics perfectly, showing no unexpected peaks or bumps that would signal a new discovery. While this means the leptoquark remains hidden, the study is far from a failure. By not finding the particle, the researchers were able to draw a very precise line in the sand. They determined that if these particles exist, they cannot be lighter than 1.5 to 3.6 trillion electron volts, depending on how strongly they interact with other matter. This range covers masses that were previously unconstrained by other types of searches.

The results effectively rule out the existence of these specific types of leptoquarks within the mass and interaction strength ranges they tested. For the scenario involving an up quark, they excluded particles with masses between 1.5 and 3.6 trillion electron volts and interaction strengths between 0.2 and 0.6. For the scenario involving a bottom quark, they excluded masses above 1.8 trillion electron volts with interaction strengths greater than 1. These limits are significantly more stringent than previous searches, which had focused on creating pairs of leptoquarks rather than single ones. The study demonstrates that the new method of looking for single particles produced by muon-quark collisions is a powerful tool, capable of probing regions of physics that were previously inaccessible.

The absence of a discovery does not mean the search is over; rather, it refines the map of where scientists should look next. By pushing the boundaries of what is possible to detect, this work narrows the field for future experiments. If leptoquarks exist, they must be heavier or interact more weakly than the limits set by this analysis. The next generation of particle accelerators and detectors will need to reach even higher energies or greater sensitivities to find them. For now, the universe keeps its secret, but the path to finding it has become clearer and more defined than ever before.

Technical Summary: Search for Scalar Leptoquarks Produced via Muon-Quark Scattering

Problem and Motivation
The Standard Model (SM) successfully describes elementary particle interactions but leaves unexplained the similarities between quark and lepton families. Leptoquarks (LQs), hypothesized bosons carrying both lepton and baryon numbers, are predicted by various extensions of the SM, including grand unified theories, composite models, and supersymmetry. They are also proposed as potential explanations for anomalies in semileptonic $B$ meson decays and the muon anomalous magnetic moment.

While previous searches at the LHC have focused on pair production or non-resonant single production, the production of LQs via lepton-induced processes (specifically muon-quark scattering) has been historically difficult to study due to uncertainties in the lepton content of the proton. Recent advances in Parton Distribution Functions (PDFs), particularly the LUX formalism, predict a sizable cross-section for single LQ production via the fusion of a muon (generated via quantum fluctuations from a photon within the proton) and a quark from the opposing proton. This paper presents the first search for TeV-scale scalar leptoquarks produced via this specific $\mu q$ scattering mechanism.

Methodology
The analysis utilizes proton-proton collision data recorded by the CMS detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$ collected between 2016 and 2018.

Signal Hypotheses: The search targets scalar LQs with electric charges of $(1/3)e$ and $(2/3)e$ , decaying into a muon and an up quark ( $LQ(u\mu)$ ) or a bottom quark ( $LQ(b\mu)$ ). The analysis assumes the LQ couples to only one lepton flavor.
Event Selection: Events are selected requiring at least one high-transverse momentum ( $p_T$ $p_{T}$ ) muon and at least one jet. The dataset is divided into two Signal Regions (SRs) based on the number of reconstructed muons: a one-muon SR ( $N_\mu = 1$ $N_{μ} = 1$ ) and a two-muon SR ( $N_\mu = 2$ $N_{μ} = 2$ ).
- Kinematic Cuts: The leading muon must have $p_T > 55$ GeV, and the leading jet $p_T > 100$ GeV. The invariant mass of the muon-jet system ( $M_{\mu j}$ ) is required to be $> 300$ GeV. Events with electrons are vetoed to suppress $Z$ -boson backgrounds.
- Background Suppression: A Boosted Decision Tree (BDT) is trained to distinguish signal from background (dominated by $W$ +jets, $t\bar{t}$ +jets, and Drell-Yan processes). The BDT utilizes kinematic variables such as the ratio of muon-to-jet $p_T$ , azimuthal angles, and missing transverse momentum.
- Categorization: Events are further categorized by the BDT score (tight vs. loose) and whether the leading jet is $b$ -tagged, resulting in eight distinct analysis categories.
Statistical Analysis: The primary observable is the $M_{\mu j}$ invariant mass distribution. A maximum likelihood fit is performed simultaneously across all categories. The SM background is modeled using an empirical function ( $B(x) = p_0(1-x)^{p_1}/x^{p_2}$ ), while the signal is modeled using simulated templates interpolated across mass ( $M_{LQ}$ ) and coupling ( $\lambda$ ) parameters. Upper limits are set using the modified frequentist $CL_s$ criterion.

Key Contributions

Novel Production Mechanism: This work constitutes the first experimental search for scalar leptoquarks specifically targeting the resonant production via muon-quark scattering, leveraging the charged-lepton component of the proton.
Extended Parameter Space: The analysis extends the search coverage for LQs in the mass-coupling plane beyond previous limits. It specifically targets regions where the lepton-induced production cross-section dominates over pair production (large $\lambda$ and high $M_{LQ}$ ).
Robust Background Modeling: The study employs a data-driven background estimation using flexible empirical functions validated through signal injection tests, ensuring minimal bias in the extraction of signal limits.

Results
The observed data are found to be in agreement with the background-only predictions. No significant excess is observed in the $M_{\mu j}$ spectrum. Consequently, 95% confidence level (CL) upper limits are set on the product of the LQ production cross-section and its branching fraction to the $\mu q$ final state ( $\sigma \mathcal{B}$ ).

The results exclude specific regions in the $(M_{LQ}, \lambda)$ parameter plane:

For the $LQ(u\mu)$ scenario: Masses between 1.5 and 3.6 TeV are excluded for couplings between 0.2 and 0.6.
For the $LQ(b\mu)$ scenario: Masses above 1.8 TeV are excluded for couplings above 1.

These exclusions improve upon previous CMS searches by extending the coverage into regions where the resonant single-production mechanism is the dominant production mode, a regime where pair-production searches have reduced sensitivity due to phase-space suppression.

Significance
The paper claims that these results represent a significant step in exploring the parameter space of leptoquarks by utilizing a production mechanism that was previously unexplored due to PDF uncertainties. By demonstrating the feasibility of searching for LQs via lepton-induced processes, the analysis provides complementary constraints to those derived from pair production and non-resonant single production. The exclusion of broad regions in the mass-coupling plane for both $u\mu$ and $b\mu$ scenarios tightens the constraints on models predicting leptoquarks coupled to muons, particularly those proposed to explain $B$ -meson anomalies. The author notes that the results are conservative, as they consider only the lepton-induced production mechanism, though cross-checks confirm the analysis remains sensitive even if other production modes are present.

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