Search for heavy resonances decaying into four-lepton final states via light bosons 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 a search for heavy resonances decaying into four leptons via light intermediate bosons, employing novel techniques to identify collimated dilepton pairs and setting upper limits on the production cross section in the previously unexplored dilepton mass range of 0.4–15 GeV without observing any significant excess over background predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "particle smasher." It fires two beams of protons (tiny subatomic particles) at each other at nearly the speed of light. When they crash, it's like two cars colliding at 100 mph, but instead of just crumpling metal, the energy creates a shower of new, exotic particles that didn't exist a split second before.

Physicists are constantly looking for "heavy" particles that shouldn't exist according to our current rulebook (the Standard Model). Finding one would be like finding a new color or a new musical note—it would rewrite the laws of physics.

The Big Idea: The "Heavy Parent" and the "Light Children"

This paper is about a specific search for a heavy, invisible parent particle (let's call it X) that decays into two lighter particles (let's call them Y). These two light particles then immediately split apart into pairs of electrons or muons (types of leptons, which are like heavy cousins of electrons).

So, the chain reaction looks like this:
Heavy X $\rightarrow$ Light Y + Light Y $\rightarrow$ 4 Leptons (electrons or muons).

The Problem:
Usually, when a heavy particle decays, its children fly apart in different directions, making them easy to spot. But in this scenario, the "Light Y" particles are very light, and the "Heavy X" is very heavy. This creates a situation where the "Light Y" particles are moving so fast (they are Lorentz boosted) that their children (the electron pairs) are squished together, flying in almost the exact same direction.

The Analogy:
Imagine a firework rocket (the Heavy X) exploding in the sky.

• Normal Explosion: The sparks fly out in a wide circle. You can easily see four distinct sparks.
• This Scenario: The rocket is moving so fast that when it explodes, the sparks are squished into a single, tight beam. To a camera (the detector), it looks like one giant spark instead of two separate ones. Or, if the sparks are muons, one might be so hidden behind the other that the camera only sees three sparks instead of four.

If the scientists used their standard "rules" for spotting particles, they would miss these events entirely because they would think, "Hey, we only see one spark here, that's not our signal!"

The New Tools: "Merged" and "Missing"

To catch these sneaky particles, the CMS team (the group of scientists who built the detector) invented two new tricks:

1. The "Merged Electron" (eME) Trick:
   When two electrons fly so close together that they look like one blob, the detector usually gets confused. The team developed a new algorithm that acts like a high-resolution microscope. Instead of trying to separate the blob, they look for specific "fingerprints" (like the shape of the energy deposit) that say, "Hey, this isn't one big electron; this is actually two tiny ones hugging each other!"

2. The "Missing Muon" (µMM) Trick:
   Sometimes, two muons fly so close that the detector's tracking system gets tangled and only records one of them. It's like trying to count two people walking in a single-file line through a narrow door, but the counter only clicks once.
   The team realized: "If we see a muon and a 'ghost' (missing momentum) pointing in the same direction, that 'ghost' is probably the second muon hiding behind the first." They used the missing momentum vector as a shadow to infer the presence of the hidden particle.

The Search and the Results

The scientists looked at 138 "years" of data (technically, 138 inverse femtobarns of collision data) from 2016 to 2018. They scanned for these heavy parents (X) with masses between 250 and 2000 GeV, and their light children (Y) with masses as low as 0.4 GeV.

The Outcome:

• No New Particles Found: Unfortunately, they didn't find any evidence of this heavy parent particle. The data matched the predictions of the Standard Model perfectly.
• Setting Limits: Even though they didn't find a "new particle," they didn't fail. They set a speed limit for where these particles could exist. They said, "If this particle exists, it cannot be this heavy or decay this often, because we would have seen it."
• The "Almost" Moment: They did see a tiny blip (a fluctuation) in the data that looked slightly interesting (about 2.4 standard deviations), but in the world of particle physics, you need a 5-sigma signal (a 1 in 3.5 million chance of being a fluke) to claim a discovery. This blip was likely just a random statistical wobble.

Why This Matters

Even though they didn't find the "Holy Grail" particle, this paper is a victory for innovation.

• Exploring the Unknown: They looked in a part of the universe (very light intermediate particles) that previous experiments ignored because the particles were too "squished" to see.
• Better Tools: They proved that with clever software and new ways of thinking about "missing" data, we can see things that were previously invisible.

In Summary:
The CMS team built a better net to catch fish that swim in a tight school. They cast the net wide over a massive ocean of data. They didn't catch the specific "monster fish" they were hunting, but they proved their new net works and mapped out exactly where the monster fish isn't, narrowing down the search for the next time.

Technical Summary

1. Problem Statement and Motivation

The search addresses a specific gap in the exploration of Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC).

• Theoretical Context: Many BSM theories (e.g., Two-Higgs-Doublet Models, models with extended $U(1)$ gauge symmetries, or dark sector models) predict a heavy neutral boson ($X$) decaying into two intermediate bosons ($Y$), which subsequently decay into lepton pairs ($X \to YY \to 4\ell$).
• The Challenge: Previous searches focused on intermediate boson masses ($m_Y$) greater than 15 GeV. However, if $X$ is significantly heavier than the Standard Model Higgs boson, the intermediate $Y$ bosons can be highly Lorentz-boosted.
• The Detection Gap: For light $Y$ bosons ($m_Y \lesssim 10$ GeV), the resulting lepton pairs (dileptons) become highly collimated. In standard reconstruction algorithms, these pairs often merge into a single object or fail reconstruction entirely, causing such events to be missed by traditional triggers and selection criteria. This paper aims to probe the previously unexplored phase space of $0.4 < m_Y < 15$ GeV.

2. Methodology

Data and Simulation:

• Dataset: Proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS experiment during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Generation: Monte Carlo (MC) simulations using PYTHIA 8.240 for signal hypotheses $X \to YY \to 4\ell$ and $X \to ZY \to 4\ell$.
  • Mass ranges: $m_X \in [250, 2000]$ GeV and $m_Y \in [0.4, 100]$ GeV.
  • Narrow-width approximation assumed ($\Gamma/m = 10^{-4}$).
• Background Estimation:
  • Irreducible: $ZZ \to 4\ell$ and $WZ \to 3\ell\nu$ simulated with POWHEG and MADGRAPH5_aMC@NLO.
  • Non-prompt/Misidentified: Estimated using data-driven methods (fake factors) derived from Control Regions (CRs) enriched in Drell-Yan, $t\bar{t}$, and $W$+jets events.

Novel Reconstruction Techniques:
To recover the signal efficiency for highly collimated leptons, the analysis introduces two specialized identification (ID) techniques:

1. Merged Electrons (eME):
   • Problem: When two electrons are within $\Delta R < 0.1$, the clustering algorithm may merge them into a single supercluster (SC).
   • Solution: A dedicated eME ID using Boosted Decision Trees (BDT) for two-track and single-track scenarios.
   • Variables: Uses the angular separation between the energy-weighted cluster position and the line connecting the two extrapolated electron trajectories on the ECAL surface.
   • Performance: Achieves ~80% efficiency for two-track eME and ~70% for single-track eME with ~10% background rejection.
2. Missing Muons ($\mu$MM):
   • Problem: Highly collinear dimuons ($\Delta R < 0.1$) can cause track reconstruction failures in the silicon tracker, leading to one muon being "lost."
   • Solution: Infers the presence of a missing muon using the missing transverse momentum vector ($\vec{p}_T^{miss}$).
   • Criteria: Requires $\vec{p}_T^{miss}$ to point close to the remaining muon in azimuth ($\Delta \phi < 0.3$) and satisfy a transverse mass cut ($m_T > 250$ GeV).

Signal Regions (SRs):
The analysis defines multiple SRs based on lepton flavor and object type (Resolved vs. Merged):

• Resolved: 4 resolved leptons ($4e, 2e2\mu, 4\mu$).
• Merged: Combinations involving eME and $\mu$MM (e.g., $2e + \text{eME}$, $e\text{ME} + 2\mu$, $3\mu + \mu\text{MM}$).
• Kinematic Cuts: Merged channels require visible invariant mass $> 50$ GeV and specific $\vec{p}_T^{miss}$ ratios.

3. Key Contributions

• First LHC Probe of Low-Mass Intermediate Bosons: This is the first LHC result searching for heavy resonances decaying into four leptons via intermediate bosons with masses in the range $0.4 < m_Y < 15$ GeV.
• Advanced Reconstruction Algorithms: The development and validation of the eME (merged electron) and $\mu$MM (missing muon) techniques significantly extend the sensitivity of the CMS detector to highly boosted, collimated final states.
• Model-Independent Search: The search is performed without assuming a specific BSM model, covering a wide range of $m_X$ and $m_Y$ masses.

4. Results

• Observation: No significant excess of data over the Standard Model background predictions was observed across any of the signal regions.
• Significance:
  • The highest local significance observed was 2.4$\sigma$ (global significance 1.8$\sigma$) at $m_X = 550$ GeV and $m_Y = 0.8$ GeV in the $X \to ZY \to 4\ell$ channel (specifically the $2\mu\text{eME}$ SR).
  • This fluctuation is consistent with a background fluctuation.
• Limits:
  • Upper limits (95% Confidence Level) were set on the production cross-section times branching fraction, $\sigma(pp \to X) \times \mathcal{B}(X \to 4\ell)$.
  • Limits cover the full explored phase space: $m_X > 250$ GeV and $m_Y > 0.4$ GeV.
  • Exclusive limits for $Y \to ee$ and $Y \to \mu\mu$ decay modes were also provided.

5. Significance

This paper represents a critical advancement in the search for BSM physics by addressing the "blind spot" created by highly boosted light bosons.

• Methodological Impact: The successful implementation of merged-object reconstruction techniques (eME and $\mu$MM) provides a blueprint for future searches involving light, boosted particles, which are common in dark sector and hidden valley models.
• Physics Impact: By excluding a significant portion of the parameter space for heavy resonances decaying via light intermediate bosons, the results constrain various BSM scenarios, including extended Higgs sectors and models with kinetic mixing.
• Future Outlook: The techniques developed here are essential for the High-Luminosity LHC (HL-LHC) era, where higher boost factors will make the reconstruction of such collimated final states even more challenging and necessary.