Search for the single production of vector-like quarks decaying into a W boson and a b quark using single-lepton final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this study searches for single-produced vector-like quarks decaying into a W boson and a b quark in single-lepton final states, finding no significant excess over the Standard Model and setting the most stringent limits to date on their production cross section and coupling strength.

The Gist

The Big Idea: Hunting for the "Heavy Hangers-On"

Imagine the Standard Model of physics as a very strict, well-organized party where only certain guests are allowed: the known particles like electrons, quarks, and the Higgs boson. For decades, physicists have suspected that there might be a few "heavy hangers-on" at this party—massive, mysterious particles that don't quite fit the rules but could explain why the universe is the way it is.

These hypothetical guests are called Vector-Like Quarks (VLQs). They are like the "big brothers" of the top quark (the heaviest known particle), but they are so heavy they haven't been seen yet.

This paper is a report from the CMS experiment at CERN (the Large Hadron Collider), where scientists smashed protons together at record speeds to see if they could kick one of these heavy guests out of the shadows.

The Setup: A High-Speed Collision Course

Think of the Large Hadron Collider (LHC) as a giant, circular racetrack. Scientists shoot two streams of protons (tiny particles) at each other at nearly the speed of light. When they crash, the energy creates a shower of new particles, like a cosmic pinball machine.

The team analyzed 138 "years" worth of data (a massive amount of collision events) from 2016 to 2018. They were specifically looking for a very specific "signature" left behind if a VLQ was created and then immediately fell apart.

The Clue: The "Missing" Piece and the "Forward" Jet

If a VLQ exists, it doesn't stay around long. It instantly decays (breaks apart) into two things:

1. A W boson (which often turns into a single electron or muon).
2. A b-quark (which turns into a jet of particles).

But here's the tricky part: The VLQ is created alongside a "light" quark that shoots off in the opposite direction, usually toward the very front or back of the detector.

So, the scientists were looking for a specific scene in the crash data:

• One lonely electron or muon (the "lepton").
• A lot of missing energy (because the W boson also spits out a neutrino, a ghost-like particle that escapes detection, leaving a "hole" in the energy balance).
• A heavy, b-tagged jet (the debris from the b-quark).
• A "forward" jet (debris shooting off toward the edge of the detector).

The Detective Work: Using AI to Find the Needle in the Haystack

The problem is that normal particle collisions (background noise) happen all the time and can look very similar to this signal. It's like trying to find a specific type of rare coin in a pile of a billion regular coins.

To solve this, the scientists used a Neural Network (AI). Imagine training a dog to sniff out a specific scent. They fed the AI millions of simulated examples of "normal crashes" and "VLQ crashes." The AI learned to spot the subtle differences in the angles, speeds, and energy levels of the particles.

They set up "Control Rooms" (safe zones) to make sure their AI wasn't hallucinating. They checked the data against known physics to ensure their tools were working correctly.

The Result: The Party is Empty (For Now)

After sifting through all the data, the scientists found no evidence of these heavy Vector-Like Quarks.

• The Analogy: Imagine searching a massive forest for a specific, rare blue bird. You have a super-sensitive microphone and a map. You listen for days, but you only hear the wind and the crows. You conclude: "Either the blue bird doesn't exist, or it's hiding in a part of the forest we haven't looked at yet."

What Does This Mean?

Even though they didn't find the particle, this is a huge success for science. Here is why:

1. Ruling Out the "Maybe": Before this, some theories suggested these particles could exist with a certain "strength" of interaction (called a coupling, $\kappa_W$). This paper says, "If they exist, they must be weaker than we thought, or heavier than we thought."
2. Setting the Limits: They established the strictest rules yet.
   • If the particle has a mass of about 1.4 TeV (which is roughly 1,500 times heavier than a proton), its interaction with the standard world must be incredibly weak (less than 0.086).
   • If the interaction is a standard "medium" strength (0.2), the particle must be heavier than 2.4 TeV.
3. The "Goldilocks" Zone: They specifically tested a theory that suggested these particles could fix a small "tension" in our current understanding of the universe (related to the Z boson). This search says, "Nope, that theory doesn't work with the data we have."

The Bottom Line

The CMS team didn't find the heavy Vector-Like Quarks in this round of the hunt. However, by proving they aren't there (at least not in the mass ranges and interaction strengths they tested), they have narrowed the search area significantly.

It's like searching for a lost key. You haven't found it yet, but you've now checked the kitchen, the living room, and the garage. You know for a fact it's not in those rooms. Now, you know exactly where you need to look next: the basement, or perhaps you need a bigger flashlight.

This paper represents the most stringent "search warrant" issued to date for these elusive particles, pushing the boundaries of our knowledge of the universe's building blocks.

Technical Summary

1. Problem and Motivation

Vector-like quarks (VLQs) are hypothetical fermions predicted by various extensions of the Standard Model (SM), such as composite Higgs models, extra dimensions, and supersymmetry. Unlike SM quarks, their left- and right-chiral components transform identically under the SM gauge group, allowing them to acquire mass independently of the Higgs mechanism. VLQs are theoretically motivated to address the hierarchy problem, stabilize the Higgs vacuum, and potentially explain baryogenesis.

While previous LHC searches have placed stringent limits on pair-produced VLQs, these searches are largely insensitive to the VLQ's electroweak (EW) couplings. The single production of VLQs, mediated by EW interactions (mixing with SM quarks), is the primary channel to probe these couplings ($\kappa_W$). This analysis specifically targets the single production of heavy VLQs (labeled $T$ with charge $+2/3$ or $Y$ with charge $-4/3$) decaying into a $W$ boson and a $b$ quark ($VLQ \to Wb$).

2. Methodology

Data Set and Detector

• Data: Proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$ (covering 2016–2018).
• Event Signature: The search targets events with:
  • Exactly one isolated electron or muon ($p_T > 40$ GeV).
  • Large missing transverse momentum ($p_T^{miss} > 60$ GeV) from the neutrino in the $W$ decay.
  • At least one high-$p_T$ $b$-tagged jet ($p_T > 30$ GeV).
  • At least one forward jet ($2.4 < |\eta| < 5.0$) originating from the light-flavor quark in the $Wb$ fusion process.
  • Veto on events containing hadronically decaying top quarks or $W$ bosons to suppress $t\bar{t}$ and single-top backgrounds.

Reconstruction and Selection

• Object Identification: Uses the Particle-Flow (PF) algorithm. Electrons and muons are required to be isolated. Jets are reconstructed using the anti-$k_T$ algorithm ($R=0.4$).
• $b$-tagging: The DeepJet algorithm is used with medium and tight working points to identify $b$-jets.
• Mass Reconstruction: The invariant mass of the VLQ ($m_{rec}$) is reconstructed using the recursive jigsaw algorithm. This technique boosts the event into a reference frame where the $z$-component of the visible VLQ momentum is zero, allowing for the calculation of the missing momentum's $z$-component and the subsequent reconstruction of the VLQ mass.

Background Modeling and Control Regions

• Dominant Backgrounds: Inclusive $t\bar{t}$, single-top production ($tW$ and $t$-channel), and $W$+jets.
• Validation: Dedicated Control Regions (CRs) are defined to validate the simulation of backgrounds:
  • $W$+jets CR: Veto on $b$-jets; used to validate $W$+light-flavor and $W$+heavy-flavor modeling.
  • $t\bar{t}$ CR: Requires $\ge 2$ $b$-jets.
  • Single-top CR: Requires $\ge 2$ $b$-jets with a forward-jet veto.
• Correction Factors: Scale factors are applied to correct mismodeling in $W$+heavy-flavor jets and the $S_T$ (scalar sum of transverse momenta) distribution in $t\bar{t}$ events.

Signal Discrimination

• Machine Learning: An Artificial Neural Network (NN) is trained on 20 kinematic variables (including $p_T$ of leptons/jets, angular separations, and reconstructed masses) to distinguish signal from background.
• Event Categorization: The Signal Region (SR) is split into six exclusive categories based on:
  1. Number of $b$-tagged jets (1 tight, 1 medium, or $\ge 2$ medium).
  2. Lepton charge ($e^+/\mu^+$ vs. $e^-/\mu^-$) to exploit $W$ boson charge asymmetry differences between signal and background.
• Statistical Analysis: A simultaneous binned maximum likelihood fit is performed on the $m_{rec}$ distributions across all six categories. The background shapes are modeled using a 5-parameter analytical function fitted to Monte Carlo (MC) simulations.

3. Key Contributions

• First Direct Probe of EW Couplings: This is the first search to probe VLQ electroweak couplings below the exclusion limits set by indirect constraints (electroweak precision observables) across the entire mass range considered (0.7–2.4 TeV).
• Improved Sensitivity: By utilizing the full 138 fb$^{-1}$ dataset and advanced multivariate techniques (NN) combined with forward jet requirements, the analysis significantly improves sensitivity over previous CMS results (which used 2.3 fb$^{-1}$).
• Comprehensive Categorization: The separation of events by $b$-jet multiplicity and lepton charge allows for a more granular extraction of limits and better background control.

4. Results

• Observation: No significant excess of events was observed over the Standard Model background prediction. The data is consistent with the background-only hypothesis (goodness-of-fit $p$-value = 0.12).
• Upper Limits on Cross Section: 95% Confidence Level (CL) upper limits were set on the single-production cross section of $VLQ \to Wb$.
• Limits on Coupling ($\kappa_W$):
  • For a VLQ decaying exclusively to $Wb$, the upper limit on the coupling $\kappa_W$ depends on the mass.
  • The limits reach as low as $\kappa_W \approx 0.086$ for VLQ masses around 1.4 TeV.
  • For a fixed coupling of $\kappa_W = 0.2$, VLQ masses up to 2.4 TeV are excluded.
• Specific Exclusions:
  • $Y$ quark (charge -4/3): Excluded for $\kappa_W = 0.2$ in the mass range 0.7 to 2.4 TeV.
  • Singlet $T$ quark (charge +2/3): Excluded for $\kappa_W = 0.15$ in the mass range 0.82 to 2.15 TeV.
  • The results disfavor the hypothesis of adding a $(B, Y)$ doublet to the SM with $\kappa_W$ values in the range 0.17–0.23, which were previously preferred by global electroweak fits.

5. Significance

This analysis represents the most stringent limits to date on the single production of vector-like quarks decaying into $Wb$.

• Physics Impact: It effectively rules out a significant portion of the parameter space for VLQs that could explain the tension in the $Zb\bar{b}$ coupling observed in electroweak precision data.
• Methodological Benchmark: The successful application of the recursive jigsaw algorithm for mass reconstruction in single-production topologies and the use of forward jets to tag the $Wb$ fusion process sets a new standard for future searches for heavy resonances and new physics at the LHC.
• Future Outlook: These results guide future theoretical models and experimental strategies, pushing the sensitivity to higher masses and smaller couplings in the upcoming High-Luminosity LHC era.