Search for new physics in triple boson production in proton-proton collisions at $\sqrt{s}$ = 13 TeV using the effective field theory approach

This paper presents a search for new physics in proton-proton collisions at 13 TeV via triple boson production using the effective field theory approach, where no excess over Standard Model expectations was observed, leading to stringent 95% confidence level bounds on dimension-6 and -8 Wilson coefficients.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "smash-up" machine. Scientists fire protons (tiny particles) at each other at nearly the speed of light to see what happens when they collide. Usually, these collisions produce a predictable spray of debris, much like smashing two watches together and getting gears and springs. This is the "Standard Model," our current rulebook for how the universe works.

But sometimes, scientists suspect there might be hidden rules or new, heavier particles we haven't seen yet. These hypothetical particles are too heavy to be created directly, but they might leave subtle "footprints" or distortions in the debris of the smash-ups.

This paper is a report from the CMS experiment (one of the big detectors at the LHC) looking for those footprints in a very specific, rare type of collision: Triple Boson Production.

The "Rare Triple Play"

In the Standard Model, it is possible for a single collision to produce three massive force-carrying particles at once (called W or Z bosons). Think of this as a "rare triple play" in baseball. It happens, but it's incredibly uncommon.

The scientists focused on a specific scenario: The "Boosted" Regime.
Imagine a car driving so fast that its parts start to blur together. In these collisions, the three bosons are moving so fast (they have high "transverse momentum") that they are "Lorentz-boosted." When they decay (break apart), their pieces get squashed together into a single, giant, messy clump of energy, rather than flying apart in different directions.

The Detective Work: Finding the "V-Tagged" Jets

When these fast-moving bosons break apart hadronically (into quarks), they don't look like individual particles anymore. Instead, they form a single, large "jet" of particles.

• The Analogy: Imagine a firework that explodes. Usually, you see distinct sparks. But if the firework is moving incredibly fast, the sparks smear into a single, long streak.
• The Tool: The scientists used a sophisticated AI tool called PARTICLENET to look inside these giant streaks (jets). They were looking for a specific internal pattern (substructure) that proves the streak came from a W or Z boson. If the pattern matched, they gave the jet a "V-tag" (like a VIP pass).

The Search Strategy: Sorting the Trash

The team collected data from 2016 to 2018 (138 "inverse femtobarns" of data—a massive amount of collision records). They sorted the events into different "bins" based on what they saw:

• Zero Lepton Channels: No electrons or muons (just the messy jets).
• One or Two Lepton Channels: Some clean particles (electrons/muons) mixed with the messy jets.
• Tau Channels: Special heavy particles called taus that decay into hadrons.

They looked for an excess of events in the "high energy" bins. If new physics existed, they expected to see more "rare triple plays" than the Standard Model predicted, especially in the highest energy categories.

The "Effective Field Theory" (EFT) Lens

Since they didn't find a specific new particle, they used a mathematical framework called Effective Field Theory (EFT).

• The Metaphor: Imagine you are trying to figure out if a new, invisible wind is blowing. You can't see the wind, but you can measure how much the trees sway. EFT is like a set of equations that says, "If there were a new wind, the trees would sway in this specific pattern."
• They tested 32 different "patterns" (called Wilson coefficients) that could indicate new physics. They checked if the data fit the "Standard Model wind" or if it matched any of the "New Physics wind" patterns.

The Results: No New Wind Found

After crunching the numbers and comparing the data to the predictions:

1. No Excess: The number of "rare triple plays" they found matched the Standard Model predictions perfectly. There were no surprises.
2. Setting Limits: Even though they didn't find new physics, they set very strict boundaries. They can now say with 95% confidence that if new physics does exist, it cannot be stronger than certain limits.
   • For example, they constrained a specific mathematical value (related to how W bosons interact) to be between -0.13 and 0.12. If the value were outside this tiny range, they would have seen it.

The "Clipping" Safety Net

One tricky part of this analysis is that if new physics exists, it might only show up at energies so high that our current math (EFT) breaks down. To handle this, they used a "clipping" procedure.

• The Analogy: Imagine trying to predict the weather. If you only look at the data from a sunny day, your model works. But if a hurricane hits, your model might fail. So, they "clipped" the data, ignoring the most extreme, high-energy events to ensure their math remained valid. They found that even with this safety net, the data still looked like the Standard Model.

Summary

In simple terms, the CMS team took a massive amount of data from proton collisions, used AI to identify rare, high-speed particle clusters, and looked for signs of new physics. They found nothing new. The universe, in this specific high-energy regime, behaves exactly as our current rulebook (the Standard Model) predicts. However, by not finding anything, they have tightened the screws on where new physics could be hiding, ruling out many possibilities and telling future scientists exactly where not to look.

Technical Summary

Technical Summary: Search for New Physics in Triple Boson Production at $\sqrt{s} = 13$ TeV

Problem and Motivation
The Standard Model (SM) predicts the production of three massive gauge bosons ($VVV$, where $V$ is a $W$ or $Z$ boson) in proton-proton collisions. While rare, this process is sensitive to triple and quartic gauge couplings, making it a critical probe of the electroweak sector. New physics (NP) at mass scales significantly above 1 TeV could modify these couplings, leading to deviations in kinematic distributions. The sensitivity to such effects is maximized in the Lorentz-boosted regime, where all three vector bosons possess high transverse momentum ($p_T > 200$ GeV). In this regime, SM backgrounds are minimal, allowing for a sensitive search for deviations. This analysis formulates the search within the framework of the Standard Model Effective Field Theory (SMEFT), utilizing mass dimension-6 and dimension-8 operators to parameterize potential NP effects.

Methodology
The analysis utilizes a dataset of proton-proton collisions at a center-of-mass energy of 13 TeV, recorded by the CMS detector during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.

• Event Selection and Reconstruction: The search targets final states with high transverse momentum. A key feature is the identification of "V-tagged jets"—large-radius jets ($R=0.8$) with $p_T > 200$ GeV and substructure consistent with the hadronic decay of a boosted $W$ or $Z$ boson. These are reconstructed using the PARTICLENET algorithm, which provides a score for jet origin, and the soft-drop mass ($m_{SD}$) is required to be consistent with the $W/Z$ mass range ($40 < m_{SD} < 150$ GeV).
• Analysis Channels: Events are categorized into 37 distinct signal regions (SRs) based on the multiplicity of charged leptons (electrons, muons, and hadronically decaying $\tau$ leptons, $\tau_h$) and V-tagged jets. Channels include:
  • Zero-lepton (all hadronic) with 2 or 3 V-tagged jets.
  • One-lepton with 2 V-tagged jets.
  • Opposite-sign dilepton (1 or 2 V-tagged jets), further subdivided by lepton flavor and invariant mass relative to the $Z$ boson.
  • Same-sign dilepton (1 V-tagged jet).
  • Channels involving $\tau_h$ candidates.
• Background Estimation: Backgrounds are estimated using a combination of Monte Carlo (MC) simulations and data-driven methods. Control regions (CRs) enriched in specific backgrounds (e.g., $t\bar{t}$, $W$+jets, $Z$+jets) are defined to derive correction factors. For the dominant QCD multijet background in the zero-lepton channel, an ABCD method utilizing sidebands of the soft-drop mass and PARTICLENET scores is employed.
• Statistical Framework: The analysis employs a simultaneous maximum-likelihood fit to the observed event yields in bins of a discriminating kinematic variable, $S_T$ (the scalar sum of transverse momenta of reconstructed objects), which correlates with the triboson invariant mass ($m_{VVV}$). The fit incorporates nuisance parameters for systematic uncertainties (e.g., jet energy scale, luminosity, PDFs, and theoretical cross-section variations). The signal is parameterized as a function of Wilson coefficients ($c_i$) for dim-6 and dim-8 operators, following the dependence $\sigma(c) = \sigma_{SM} + c\sigma_{lin} + c^2\sigma_{quad}$.

Key Contributions

• Comprehensive Channel Coverage: The analysis defines and combines 37 signal regions across diverse final states, including fully hadronic, semi-leptonic, and fully leptonic decays, as well as channels with hadronic $\tau$ decays.
• Advanced Jet Tagging: The application of the PARTICLENET algorithm for V-tagging in the boosted regime allows for efficient selection of hadronic $W/Z$ decays while suppressing QCD multijet backgrounds.
• EFT Interpretation: The results are interpreted in the SMEFT framework, setting constraints on 12 dim-6 and 20 dim-8 Wilson coefficients. The analysis addresses unitarity violations at high energies by implementing a "clipping" procedure, which systematically removes events above a certain $m_{VVV}$ threshold to ensure the validity of the EFT expansion.
• Template Fitting: A novel template fit is introduced to infer the $m_{VVV}$ distribution from the observed $S_T$ distribution, allowing for a model-independent check of the shape of the distribution in the presence of potential excesses.

Results

• Observation: No significant excess of events over the SM expectations is observed in any of the signal regions. The observed event yields are consistent with SM predictions across all bins of the discriminating variables.
• Constraints on Wilson Coefficients:
  • Dim-6 Operators: The most stringent 95% confidence level (CL) bounds are placed on the Wilson coefficients $c_W$ and $c_{Hq3}$. The observed bounds are $-0.13 < c_W/\Lambda^2 < 0.12$ TeV$^{-2}$ and $-0.24 < c_{Hq3}/\Lambda^2 < 0.21$ TeV$^{-2}$. These limits are derived both when other coefficients are fixed to zero and when they are profiled (allowed to vary).
  • Dim-8 Operators: Bounds are set for 20 dim-8 operators, with the tightest constraints on $f_{T,0}/\Lambda^4$ ($[-0.57, 0.63]$ TeV$^{-4}$).
  • Multi-parameter Fits: Two-dimensional fits for pairs of Wilson coefficients show no significant "flat directions" (degeneracies), though correlations exist (e.g., between $c_W$ and $c_{H\ell3}$).
• SM VVV Production: The analysis retains sensitivity to the SM $VVV$ production process itself. A fit for the SM signal strength parameter $\mu_{SM}$ yields a value of $1.74^{+1.07}_{-0.98}$, which is consistent with the SM prediction of unity, though with large uncertainties.

Significance
This paper presents the most comprehensive search for new physics in triple boson production to date, specifically targeting the high-$p_T$ boosted regime where SMEFT effects are expected to be most prominent. By combining multiple final states and utilizing advanced machine-learning techniques for jet substructure, the analysis achieves competitive constraints on Wilson coefficients, particularly for operators affecting gauge boson self-interactions and gauge-fermion interactions. The results provide robust limits on NP scales up to several TeV and validate the SM description of electroweak processes in a regime previously unexplored with such precision. The paper emphasizes that the absence of deviations supports the SM, while the derived bounds significantly constrain the parameter space for various EFT operators.