Probing the flavour structure of dimension-6 EFT operators in multilepton final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, this study presents the first simultaneous disentanglement of the flavour structure of dimension-6 EFT operators by probing quark-Z interactions across different generations in multilepton final states, confirming Standard Model consistency and setting limits on Wilson coefficients for both light and heavy quarks.

The Gist

Imagine the universe as a giant, incredibly complex machine. For decades, physicists have had a "user manual" for this machine called the Standard Model. It explains how tiny particles like electrons and quarks interact to build everything we see. But, like any manual, we know it's incomplete. It doesn't explain gravity, dark matter, or why the universe exists at all.

Physicists suspect there are "hidden features" or "secret upgrades" to this machine that are too heavy or too fast to be seen directly. This is where the Large Hadron Collider (LHC) at CERN comes in. It smashes protons together at nearly the speed of light to see if we can spot any glitches or weird behavior that hints at these hidden features.

The Detective Work: "Effective Field Theory"

Since we can't build a machine powerful enough to see the "secret upgrades" directly, the scientists in this paper use a clever detective trick called Effective Field Theory (EFT).

Think of it like this: Imagine you are trying to figure out what's inside a sealed, heavy box without opening it. You can't see inside, but you can shake it, weigh it, and listen to the sounds it makes.

• The Box: The Standard Model (what we already know).
• The Shaking: The high-energy collisions at the LHC.
• The Sounds: Tiny deviations in how particles behave.

EFT is the mathematical framework that translates those "sounds" (deviations) into clues about what might be inside the box. Instead of guessing specific new particles, they look for general "tweaks" to the rules of the game. These tweaks are called operators, and they have "knobs" (called Wilson Coefficients) that physicists turn to see how much the rules change.

The Specific Mystery: "Flavor" and the Z-Boson

In this specific study, the CMS collaboration (one of the big teams at the LHC) focused on a very specific interaction: How the Z-boson (a force-carrying particle) talks to different types of quarks.

Quarks come in "flavors," just like ice cream. There are light flavors (up and down quarks, which make up protons and neutrons) and heavy flavors (top and bottom quarks).

• The Old Way: Previous studies mostly looked at how the Z-boson talks to the heavy "top" quarks. It was like only listening to the bass notes of a song.
• The New Way: This paper is the first to listen to the whole orchestra. They simultaneously checked how the Z-boson interacts with light quarks (the common ones) and heavy quarks (the rare ones).

They did this by looking at three specific "scenes" in the particle collision data:

1. Top-Top-Z: A pair of heavy top quarks created alongside a Z-boson.
2. W-Z: A W-boson and a Z-boson created together.
3. Z-Z: Two Z-bosons created together.

By comparing these three scenes, they could tell if the Z-boson was treating the light quarks differently than the heavy ones. If the "knobs" (Wilson coefficients) were turned, it would mean the Z-boson has a secret preference for certain flavors, which would break the Standard Model.

The Search for "Leptons"

How did they find these rare events? They looked for multilepton final states.

• Leptons are particles like electrons and muons. They are the "clean" particles that leave clear tracks in the detector, unlike the messy spray of debris from quarks.
• The team looked for events with at least three of these clean leptons. It's like looking for a specific, rare pattern of footprints in the snow. If you see three perfect footprints, you know something specific happened, and you can ignore the messy footprints of the crowd.

The Results: The Machine is Still Running Smoothly

After analyzing a massive amount of data (138 "inverse femtobarns"—which is a fancy way of saying they looked at trillions of collisions from 2016 to 2018), here is what they found:

The Z-boson is behaving exactly as the Standard Model predicts.

• No Secret Flavors: The Z-boson treats light quarks and heavy quarks exactly the same way it's supposed to.
• No New Physics (Yet): The "knobs" they tried to turn were all found to be at zero. There is no evidence of new physics hiding in these specific interactions.

Why This Matters

You might think, "If they found nothing, why write a paper?"

1. Ruling Out Options: In science, knowing what isn't there is just as important as knowing what is. By proving that the Z-boson doesn't have secret flavor preferences, they have ruled out many theories about what new physics might look like.
2. Setting the Stage: They have tightened the constraints. If new physics does exist, it must be even more subtle or at even higher energies than we thought.
3. The "Flavor" Breakthrough: This is the first time they successfully disentangled the light and heavy quark interactions simultaneously. It's like finally being able to hear the violins and the cellos separately in a symphony, rather than just hearing the whole noise. This sets a new standard for how future experiments will look for new physics.

The Bottom Line

The CMS team acted like master mechanics checking the engine of the universe. They looked for a specific type of rattle (flavor-changing interactions) in the engine's rhythm. They listened to the engine running at full speed (13 TeV collisions) and found that, for now, the engine is humming along perfectly according to the original blueprint.

While they didn't find the "secret upgrade" they were hoping for, they proved that the blueprint is incredibly robust, and they've given future detectives a much sharper set of tools to keep looking. The search for the "new physics" continues, but the path is now clearer.

Technical Summary

1. Problem Statement

The Standard Model (SM) of particle physics is known to be incomplete, yet direct searches for Beyond-the-Standard-Model (BSM) physics at the Large Hadron Collider (LHC) have not yet yielded definitive evidence. BSM physics may exist at energy scales ($\Lambda$) too high to be directly produced but could manifest as deviations in precision measurements.

Effective Field Theory (EFT) provides a framework to describe these effects via higher-dimensional operators. While previous CMS analyses have probed EFT operators involving top and bottom quarks, a critical gap remained: the flavour structure of these operators was not fully disentangled. Specifically, it was unclear how couplings to light quark generations (1st and 2nd) differed from those to heavy quark generations (3rd) in processes involving $Z$ bosons. Furthermore, many analyses treated processes like $t\bar{t}Z$, $WZ$, and $ZZ$ in isolation, potentially missing correlations between EFT effects that act as backgrounds to one another.

2. Methodology

Data and Simulation:

• Dataset: Proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Target Processes: The analysis focuses on the associated production of a top-quark pair and a $Z$ boson ($t\bar{t}Z$), as well as diboson processes ($WZ$ and $ZZ$).
• Final States: Events are selected with at least three leptons (electrons or muons), ensuring high purity for $Z$ boson reconstruction.
• Simulation: Signal processes ($t\bar{t}Z$, $WZ$, $ZZ$) are simulated at Next-to-Leading Order (NLO) in QCD. EFT effects are modeled using a reweighting technique based on the Warsaw basis, calculating matrix elements at leading order with up to one additional parton.

Event Selection and Regions:
The analysis defines three Signal Regions (SRs) and two Control Regions (CRs) based on lepton multiplicity and kinematic requirements:

1. SR$_{t\bar{t}Z}$: Requires exactly 3 tight leptons, at least one $b$-tagged jet, and at least 3 jets. This region is sensitive to 3rd-generation couplings (via $Z$ radiation from top quarks) and 1st/2nd-generation couplings (via initial-state radiation).
2. SR$_{WZ}$: Requires exactly 3 tight leptons, no $b$-tagged jets, and high missing transverse momentum ($p_T^{miss} > 60$ GeV). This suppresses $t\bar{t}Z$ and enhances sensitivity to light-quark couplings.
3. SR$_{ZZ}$: Requires 4 tight leptons and two $Z$ candidates. This is a very pure sample for constraining light-quark couplings.
4. CRs: Defined to estimate "non-prompt" (fake) lepton backgrounds using data-driven methods (transfer factors derived from misidentification rates).

Statistical Analysis:

• Observable: The transverse momentum ($p_T$) distribution of the reconstructed $Z$ boson candidate is the primary observable, as EFT effects typically enhance high-$p_T$ tails.
• Fit: A simultaneous profiled maximum likelihood fit is performed across all three SRs.
• Parameters of Interest: The analysis extracts limits on dimension-6 Wilson Coefficients (WCs) in the Warsaw basis, specifically:
  • $c^{(-)}_{\phi q}$ and $c^{(3)}_{\phi q}$ (Left-handed quark doublets).
  • $c_{\phi u}$ and $c_{\phi d}$ (Right-handed up and down quarks).
  • $c_W$ and $c_{\tilde{W}}$ (Triple gauge boson couplings).
• Flavour Decomposition: The WCs are split into light-quark ($11+22$) and heavy-quark ($33$) components to disentangle flavour dependencies.

3. Key Contributions

1. First Simultaneous Flavour Disentanglement: This is the first analysis to simultaneously probe and disentangle the flavour structure of dimension-6 EFT operators involving $Z$-quark couplings for both light (1st/2nd) and heavy (3rd) quark generations.
2. Global Process Combination: By simultaneously fitting $t\bar{t}Z$, $WZ$, and $ZZ$ processes, the analysis correctly accounts for correlations between EFT effects that act as backgrounds to each other. This avoids the biases inherent in analyzing these processes in isolation.
3. Comprehensive Systematic Treatment: The analysis includes a rigorous treatment of systematic uncertainties (experimental and theoretical), including non-prompt lepton backgrounds estimated via data-driven methods, ensuring the reliability of the extracted limits.
4. Operator Basis: The study focuses on operators modifying electroweak vector couplings ($O^{(1)}_{\phi q}, O^{(3)}_{\phi q}, O_{\phi u}, O_{\phi d}$) and triple gauge couplings ($O_W, O_{\tilde{W}}$), providing a direct mapping to physical $Z$ and $W$ boson couplings.

4. Results

• Consistency with SM: The data are found to be consistent with the Standard Model predictions within uncertainties. No significant deviations were observed in the $p_T$ distributions of the $Z$ boson.
• Wilson Coefficient Limits:
  • Limits were set on all considered Wilson coefficients for both light and heavy quark generations.
  • Flavour Correlations: The analysis successfully constrained the light-quark couplings ($c^{(-)}_{\phi q(11+22)}$, etc.) and heavy-quark couplings ($c^{(-)}_{\phi q(33)}$, etc.) simultaneously.
  • Degeneracies: Some correlations were observed (e.g., between $c^{(33)}_{\phi u}$ and $c^{(-)(33)}_{\phi q}$), which were handled by profiling the likelihood.
  • Triple Gauge Couplings: The coefficients $c_W$ and $c_{\tilde{W}}$ were measured close to zero, consistent with SM expectations.
• Energy Scale Limits: The results were translated into lower limits on the new physics energy scale $\Lambda$. For a Wilson coefficient of $c_i = 1$, the limits on $\Lambda$ generally range from a few TeV to over 10 TeV, depending on the specific operator and flavour combination.
• Cross-Section Measurements: The production cross-sections for $t\bar{t}Z$, $WZ$, and $ZZ$ were extracted (with all WCs set to zero) and found to be compatible with SM predictions and dedicated measurements.

5. Significance

• Enhanced EFT Interpretation: This work moves beyond "process-by-process" EFT interpretations. By combining channels, it provides a more robust and global view of potential BSM physics, preserving correlations that are crucial for future global fits.
• Flavour Physics Sensitivity: It demonstrates the LHC's capability to probe flavour-dependent new physics in the electroweak sector, specifically distinguishing between couplings to light and heavy quarks in $Z$ boson interactions. This is relevant for understanding anomalies in $b \to s \ell^+ \ell^-$ transitions.
• Benchmark for Future Analyses: The methodology of simultaneous fitting across multiple multilepton channels serves as a template for future high-luminosity LHC analyses aiming to constrain the flavour structure of the SMEFT.
• No New Physics Found (Yet): The results reinforce the robustness of the Standard Model up to the probed energy scales, placing stringent constraints on models predicting flavour-violating or flavour-universal deviations in electroweak couplings.

In conclusion, this analysis represents a significant step forward in the precision testing of the Standard Model's flavour structure using EFT, leveraging the full power of the CMS multilepton dataset to constrain new physics scenarios that couple differently to quark generations.