Search for $t$-channel scalar and vector leptoquark exchange in the high-mass dimuon and dielectron spectra 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 searches for $t$-channel scalar and vector leptoquark exchange in high-mass dilepton spectra, setting stringent 95% confidence level limits on leptoquark-fermion couplings for masses between 1 and 5 TeV.

The Gist

The Great Particle Detective Story: Hunting for Invisible "Leptoquarks"

Imagine the universe as a giant, bustling kitchen where tiny ingredients called quarks (which make up protons and neutrons) and leptons (like electrons and muons) are constantly being tossed around. According to our current recipe book, the Standard Model, these two groups of ingredients rarely mix. Quarks stick with quarks, and leptons stick with leptons.

But what if there's a secret ingredient, a "chameleon" particle called a Leptoquark (LQ), that can turn a quark into a lepton or vice versa? This paper is the story of the CMS team at CERN's Large Hadron Collider (LHC) trying to find these chameleons.

The Setup: A High-Speed Collision Course

The scientists used the LHC, a massive 27-kilometer ring of magnets, to smash protons together at nearly the speed of light. They didn't just look for a "smoking gun" (a brand new particle popping into existence and then immediately decaying). Instead, they looked for a subtle "ghost in the machine."

Think of it like this:

• The Standard Way (Background): Usually, when two protons collide, they exchange a "messenger" (like a photon or a Z boson) that creates a pair of electrons or muons. This is the Drell-Yan process, the background noise of the universe.
• The Leptoquark Way (The Signal): If a Leptoquark exists, it doesn't just sit there; it acts as a bridge. It allows a quark from one proton to swap places with a lepton from the other in a single, invisible handshake. This is called t-channel exchange.

The catch? The Leptoquark might be so heavy (up to 5,000 times the mass of a proton) that we can't create it directly. Instead, we have to look for the echo of its presence in the way the particles scatter.

The Investigation: Looking for a Distorted Shadow

Since the Leptoquark is too heavy to see directly, the team looked at the shape of the collision debris.

Imagine throwing two tennis balls at each other.

• If they just bounce off each other normally (Standard Model), they scatter in a predictable, symmetrical pattern.
• If there's a hidden, invisible magnet (the Leptoquark) influencing the bounce, the balls will scatter in a weird, lopsided way.

The CMS team analyzed 138 "inverse femtobarns" of data (a fancy way of saying they looked at a staggering number of collisions). They focused on events where two muons or two electrons were produced with very high energy (masses above 500 GeV).

They used three main clues to spot the distortion:

1. The Mass: How heavy was the pair of particles?
2. The Angle: Did they fly off straight ahead or at a sharp angle?
3. The Direction: Did they prefer to fly in the direction of the incoming proton or the other way?

They built a "template" (a digital blueprint) of what the collision should look like if only Standard Model physics were at play. Then, they overlaid their real data to see if the "shadow" of the Leptoquark was distorting the blueprint.

The Results: No Ghosts Found (Yet)

After crunching the numbers, the team found no evidence of Leptoquarks. The data matched the Standard Model predictions perfectly. The "ghost" wasn't there.

However, in science, a "null result" is still a huge discovery because it tells us where not to look.

• The Exclusion Zone: They effectively drew a giant "No Entry" sign on the map of particle physics. They proved that if Leptoquarks exist, they cannot be lighter than 1 to 5 TeV (depending on how strongly they interact).
• The Coupling Limit: They also set strict limits on how "sticky" these particles could be. If a Leptoquark exists, it can't interact with regular matter very strongly, or we would have seen it by now.

Why This Matters

This search is special because it looked for a different type of Leptoquark interaction than previous searches.

• Previous searches looked for Leptoquarks being created in pairs (like finding two identical twins).
• This search looked for the Leptoquark acting as a single, invisible bridge (the t-channel exchange).

This method allowed them to probe much heavier masses (up to 5 TeV) than ever before. It's like searching for a mountain by looking at the shadow it casts on the horizon; even if the mountain is too tall to see directly, the shadow tells you it's not there.

The Bottom Line

The CMS team didn't find the Leptoquark, but they successfully cleared a massive chunk of the "particle wilderness." They have told us that if these exotic particles exist, they are hiding in a very heavy, very weakly interacting corner of the universe that we haven't been able to reach until now. The search continues, but the rules of the game have been tightened significantly.

Technical Summary

Technical Summary: Search for t-channel scalar and vector leptoquark exchange in high-mass dimuon and dielectron spectra

Problem and Motivation
This paper presents a search for the $t$-channel exchange of leptoquarks (LQs), hypothetical color-triplet bosons that couple quarks and leptons. While previous searches have focused on resonant pair or single production of LQs, these channels are limited in sensitivity at high LQ masses ($m_{LQ}$) or high coupling strengths. The $t$-channel exchange process, which interferes with the Standard Model (SM) Drell–Yan (DY) production of dileptons, offers superior sensitivity in these regimes because its cross-section decreases more slowly with increasing $m_{LQ}$ compared to production channels.

The analysis targets first- and second-generation LQs coupled to up/down quarks and electrons/muons. Specifically, it probes three LQ families motivated by phenomenological studies: the scalar doublets $R_2$ and $eR_2$, and the vector triplet $U_3$. These models are relevant to potential solutions for the muon anomalous magnetic moment ($g-2$), lepton flavor universality violation, and lepton flavor violation. The study aims to set limits on LQ-fermion coupling strengths ($y_{LQ}$ for scalars, $g_{LQ}$ for vectors) for masses ranging from 1 to 5 TeV, a regime largely unexplored by previous resonant searches.

Methodology
The analysis utilizes proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search focuses on high-mass dilepton events ($m_{\ell\ell} > 500$ GeV) in the dimuon ($\mu\mu$) and dielectron ($ee$) channels.

• Signal Modeling: The signal is modeled as a non-resonant modification of the dilepton angular and invariant mass distributions. The differential cross-section includes the SM DY contribution, the pure $t$-channel LQ exchange, and the interference between the LQ and SM amplitudes.
• Template Construction: Instead of generating dedicated Monte Carlo (MC) samples for every signal hypothesis, the authors employ a reweighting technique. Simulated SM DY events are reweighted using analytical functions of generator-level variables ($m_{\ell\ell}$, $y$, and $\cos\theta^*$) to represent the specific kinematic shapes of the pure LQ exchange and interference terms. This allows for the construction of parameter-independent templates for the signal and background components.
• Variables: The fit utilizes three variables: the dilepton invariant mass ($m_{\ell\ell}$), the rapidity ($y$), and the cosine of the angle between the incoming quark and outgoing lepton in the Collins–Soper frame ($\cos\theta^*$). Due to the unknown direction of the incident quark in $pp$ collisions, an approximation $\cos\theta_R$ is used.
• Background Estimation: The dominant background is SM DY production. Subdominant backgrounds include $t\bar{t}$, $tW$, diboson ($WW, WZ, ZZ$), and photon-induced dilepton production. "Misidentified" (MisID) leptons from jets are estimated using a data-driven "misidentification rate" method in control regions. Background normalizations and shapes are validated using control regions (e.g., $e\mu$ events).
• Statistical Analysis: A binned maximum likelihood fit is performed on the observed distributions of $m_{\ell\ell}$, $|y|$, and $\cos\theta_R$. The fit extracts the coefficients for the SM angular distribution ($A_0, A_4$) and the LQ coupling parameters ($y_{LQ}^2$ or $g_{LQ}^2$). Systematic uncertainties, including those from PDFs, lepton identification, luminosity, and the reweighting procedure, are incorporated via nuisance parameters.

Key Contributions

• First Search of its Kind: This is the first search for $t$-channel LQ exchange coupled to first- and second-generation fermions using the CMS detector.
• Extended Mass Reach: The analysis probes LQ masses up to 5 TeV, significantly extending the sensitivity beyond the limits set by previous pair-production and single-production searches (which typically excluded masses up to $\sim 1.8$ TeV).
• Comprehensive Coupling Limits: The study sets 95% confidence level (CL) limits on eight distinct coupling scenarios (combinations of scalar/vector, up/down quarks, and electron/muon leptons).
• Methodological Refinement: The paper details a robust template reweighting method that accounts for the "dilution" effect of quark direction misassignment and avoids the need for extensive dedicated signal MC generation.

Results
No significant deviation from the Standard Model background expectations was observed in the high-mass dilepton spectra. The observed distributions of $m_{\ell\ell}$, $|y|$, and $\cos\theta_R$ are consistent with SM predictions.

• Scalar LQs: For scalar LQs ($R_2, eR_2$) with masses between 1 and 5 TeV, coupling values $|y_{LQ}|$ in the range of 0.4–1.3 (for muon couplings) and 0.3–1.0 (for electron couplings) are excluded at 95% CL.
• Vector LQs: For vector LQs ($U_3$), coupling values $|g_{LQ}|$ in the range of 0.3–1.4 (for muon couplings) and 0.1–0.5 (for electron couplings) are excluded at 95% CL.
• Comparison to Previous Limits: These results significantly extend the exclusion limits from previous single-production searches (which excluded masses up to 1.73 TeV for specific couplings) and pair-production searches (which excluded masses up to 1.53 TeV independent of coupling). The vector LQ limits are generally stronger than scalar limits due to larger production cross-sections.
• Asymmetry: The analysis notes that for certain vector LQ models (e.g., $V_{ed}, V_{\mu d}$), the interference with the SM is destructive, leading to asymmetric likelihood functions and weaker expected limits compared to other scenarios.

Significance and Claims
The paper claims to establish stringent limits on first- and second-generation leptoquarks in a mass regime (1–5 TeV) that was previously inaccessible to resonant production searches. By utilizing the $t$-channel exchange mechanism, the analysis demonstrates sensitivity to LQs with masses significantly higher than those probed by pair or single production, provided the couplings are within the perturbative regime. The results provide the first constraints on non-resonant $t$-channel exchange for vector LQs coupled to first- and second-generation fermions. The authors emphasize that these limits are crucial for testing BSM scenarios involving leptoquarks, such as those proposed to explain anomalies in $g-2$ or lepton flavor universality, by ruling out specific regions of the parameter space up to 5 TeV.