Search for single vector-like quark production in opposite-sign dilepton final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration presents the first search for single vector-like top quark (T) production decaying into a top quark and Higgs boson in opposite-sign dilepton final states using 138 fb⁻¹ of 13 TeV proton-proton collision data, finding no evidence of new physics and setting 95% confidence level upper limits on the production cross section ranging from 2.0 pb at 600 GeV to 0.1 pb at 1000 GeV.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It takes two beams of protons (tiny building blocks of matter) and smashes them together at nearly the speed of light. When they collide, the energy of the crash can briefly turn into new, heavy particles that don't exist in our everyday world.

This paper is a report from the CMS experiment, one of the giant detectors watching these collisions. The scientists are on a treasure hunt for a specific type of "heavy gold": a particle called a Vector-Like Quark, specifically a heavy version of the top quark, which they call "T".

Here is the story of their search, explained simply:

1. The Mystery Guest: The "Vector-Like" Quark

In our standard understanding of physics (the Standard Model), quarks come in pairs with specific "handedness" (left or right). But physicists suspect there might be a "fourth generation" of quarks that are different. These are called Vector-Like Quarks.

Think of the Standard Model quarks like a pair of shoes: one left, one right. They are distinct. A Vector-Like Quark is like a shoe that is both left and right at the same time. Because of this special nature, it can be incredibly heavy without breaking the rules of physics. If these particles exist, they could help explain why the universe has the mass it does and solve some deep mathematical puzzles.

2. The Hunt: Looking for a "T" Quark

The scientists are looking for a specific heavy guest: the T quark. They aren't looking for it to appear alone; they are looking for it to be created singly (one at a time) and then immediately decay (fall apart) into two other things:

1. A standard Top Quark (a heavy, known particle).
2. A Higgs Boson (the particle that gives other particles mass).

The Analogy: Imagine a heavy, unstable balloon (the T quark) popping in mid-air. When it pops, it doesn't just disappear; it releases two specific items: a heavy bowling ball (the Top quark) and a glowing orb (the Higgs boson). The scientists want to catch the debris of this specific pop.

3. The Clues: The "Opposite-Sign Dilepton" Trail

When the Top quark and the Higgs boson fall apart, they create a messy trail of debris. The scientists focused on a very specific, rare pattern of debris to find their T quark:

• Two Leptons: They looked for two particles that are like electrons or muons (lightweight, fast-moving particles).
• Opposite Signs: One must be positive (+) and one negative (-).
• Missing Energy: Because some invisible particles (neutrinos) fly away, there is a "missing" amount of energy in the detector.
• Jets: They also looked for sprays of particles (jets) coming from the heavy quarks.

The Metaphor: Imagine a crime scene. The scientists are looking for a very specific set of footprints: a left shoe print and a right shoe print (the two leptons) that are facing opposite directions, surrounded by a pile of rubble (jets), with a noticeable gap in the floor where something invisible slipped away (missing energy). This specific combination is the "signature" of the T quark decaying.

4. The Search: Sifting Through the Noise

The LHC produces billions of collisions. Most of them are boring background noise—like rain falling on a roof. The scientists needed to filter out the rain to find the one rare diamond.

• They analyzed data from 2016 to 2018, which is like looking at a massive library of 138 "books" (units of data called inverse femtobarns).
• They used powerful computer algorithms to reconstruct the collisions, trying to piece together the "T" particle from the debris.
• They calculated what the "background noise" (standard physics) should look like and compared it to what they actually saw.

5. The Result: No Diamonds Found (Yet)

After sifting through all that data, the scientists found no evidence of the T quark.

• The number of "diamonds" (events with the specific signature) they found matched exactly what they expected from the "rain" (standard background processes).
• There was no surprise spike or "excess" that would indicate a new particle.

6. The Conclusion: Setting the Boundaries

Even though they didn't find the particle, the search wasn't a failure. It was a successful "fence-building" exercise.

• Because they didn't find the T quark, they can now say: "If this particle exists, it must be heavier than we thought, or it is much harder to create than we hoped."
• They set a "limit" on how likely it is to find this particle. They ruled out the existence of T quarks with masses between 600 and 1200 GeV (a specific range of heaviness).
• This is the first time anyone has looked for this specific particle in this specific "opposite-sign dilepton" pattern.

In Summary:
The CMS team looked for a heavy, exotic particle (the T quark) by smashing protons together and looking for a very specific, rare pattern of debris. They didn't find it. This means that if this particle exists, it is hiding in a heavier, more elusive range than they could reach with this specific search. The hunt continues, but the map of where it isn't has just gotten a lot more detailed.

Technical Summary

Technical Summary: Search for Single Vector-Like Quark Production in Opposite-Sign Dilepton Final States

Problem and Motivation
Vector-like quarks (VLQs) are hypothetical fermions where the left- and right-handed chiral components transform identically under the Standard Model (SM) electroweak group. Unlike chiral quarks, VLQs can possess gauge-invariant mass terms independent of the SM Higgs boson, allowing them to be heavy states that evade current Higgs coupling constraints. They are theoretically motivated as potential solutions to the hierarchy problem and as explanations for observed hints of deviations from Cabibbo–Kobayashi–Maskawa (CKM) matrix unitarity. In models of physics beyond the SM, VLQs can appear as singlets, doublets, or triplets. This paper focuses on the single production of a vector-like top quark ($T$) with electric charge $+2/3$, specifically the process $pp \to Tbq$ via $t$-channel $W$ boson exchange. The study targets the decay chain $T \to tH$, where the top quark decays hadronically and the Higgs boson decays primarily into a pair of $W$ bosons ($H \to WW$), with subsequent leptonic decays of the $W$ bosons yielding an opposite-sign (OS) dilepton final state.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at a center-of-mass energy of $\sqrt{s} = 13$ TeV during the 2016–2018 run periods, corresponding to an integrated luminosity of up to 138 fb$^{-1}$.

• Event Selection: The search targets final states with two opposite-sign leptons (electrons or muons), at least three jets (including at least one $b$-tagged jet), and missing transverse momentum ($p^{\text{miss}}_T$). The selection requires exactly two OS leptons with $p_T > 35$ GeV (electrons) or $p_T > 30$ GeV (muons) and $|\eta| < 2.5$ (electrons) or $2.4$ (muons). Jets must have $p_T > 30$ GeV and $|\eta| < 2.5$. To suppress low-mass Drell–Yan (DY) backgrounds, the invariant mass of the lepton pair ($m_{\ell\ell}$) is required to be less than 60 GeV.
• Signal Reconstruction: The primary discriminating variable is the reconstructed invariant mass of the $T$ candidate ($m_{tH}$). The top quark is reconstructed from a $b$-tagged jet and a $W$ boson candidate (formed from two jets with invariant mass near the world-average $W$ mass). The Higgs boson is reconstructed from the two leptons and the missing transverse momentum. Due to the presence of two neutrinos in the $H \to WW \to \ell\ell'\nu\nu$ decay, a partial reconstruction is employed. Assuming the neutrino pair is collinear with the lepton pair, the longitudinal momentum of the neutrinos is estimated, and the invariant mass of the neutrino pair is approximated using the mean value from simulated signal events ($\langle m_{\nu\nu} \rangle = 30$ GeV).
• Background Estimation: The dominant backgrounds are top quark pair ($t\bar{t}$) production and DY production. The background shape in the signal region is estimated directly from observed data using a parameterized function (an exponential of a second-order polynomial in the logarithm of $m_{tH}$). This approach minimizes dependence on Monte Carlo (MC) simulations for normalization. The selection includes a dynamic threshold on the scalar sum of transverse momenta ($S_T$) of the top and Higgs candidates, defined as a function of $m_{tH}$ to maintain a smoothly falling background shape.
• Statistical Analysis: A binned maximum likelihood fit is performed on the $m_{tH}$ distribution across twelve categories (three lepton flavor combinations $\times$ four data-taking periods). Systematic uncertainties, including those related to jet energy scale/resolution, $b$-tagging, luminosity, and background parameterization, are treated as nuisance parameters.

Key Contributions

• First Search in OS Dilepton Channel: This work presents the first search for single $T$ production in the $T \to tH$ channel utilizing opposite-sign dilepton final states at the LHC. Previous CMS analyses in this channel focused on fully hadronic top decays or Higgs decays to diphotons or $b$-quark pairs.
• Partial Reconstruction Technique: The analysis implements a specific kinematic reconstruction method for the $H \to WW \to \ell\ell\nu\nu$ decay mode, allowing the use of the $m_{tH}$ variable despite the unobserved neutrinos.
• Model-Independent Limits: Given the dependence of the single production cross-section on couplings to SM quarks and electroweak bosons, the results are presented as upper limits on the product of the production cross-section and the branching fraction, $\sigma(pp \to T)\mathcal{B}(T \to tH)$, rather than on the mass alone.

Results
No significant excess of events over the expected SM background was observed in the data across the tested $T$ mass range of 600 to 1200 GeV. Consequently, 95% confidence level (CL) upper limits were set on $\sigma(pp \to T)\mathcal{B}(T \to tH)$.

• The observed limits range from 2.0 pb at a $T$ mass of 600 GeV to 0.1 pb at 1000 GeV.
• The limits are consistent with the expected limits within uncertainty bands.
• The electron-muon ($e\mu$) channel provided the strongest constraints due to its high branching fraction and the absence of the DY background.
• The analysis assumes a narrow-width approximation for the $T$ resonance and a width-to-mass ratio ($\Gamma_T/M_T$) of 5%.

Significance
The paper claims that this search complements previous searches for single $T$ VLQ production by extending the analysis to the OS dilepton final state. By probing the $T \to tH$ decay mode in this specific topology, the analysis covers a previously unexplored region of the parameter space for vector-like quark searches at the LHC. The results provide constraints on the product of the production cross-section and branching fraction for $T$ masses between 600 and 1200 GeV, contributing to the broader effort to test the Standard Model and search for new physics phenomena.