Highly boosted dielectron identification in proton-proton collisions at $\sqrt{s}$ = 13 TeV

This paper presents a new technique using two multivariate models to identify highly boosted dielectrons that merge into a single electromagnetic calorimeter cluster in 13 TeV proton-proton collisions, achieving 80% and 60% efficiencies for cases with two and one reconstructed tracks, respectively, alongside a dedicated energy correction method.

The Gist

Imagine you are a detective trying to solve a crime at a massive, high-speed train station (the Large Hadron Collider). Your job is to spot specific pairs of suspects (electrons) who are running so fast and are so close together that they look like a single, blurry blob to your cameras.

This paper from the CMS experiment at CERN is about teaching the station's cameras and computers how to recognize these "blurred pairs" so they don't miss them.

Here is the breakdown of the story, using simple analogies:

1. The Problem: The "Super-Blurry" Blob

In the world of particle physics, scientists smash protons together to create new particles. Sometimes, these new particles decay into two electrons ($e^+e^-$).

• Normal Situation: Usually, these two electrons fly apart. Your camera sees two distinct dots. Easy to identify.
• The Problem: Sometimes, the parent particle is moving incredibly fast (it's "boosted"). This squishes the two electrons together so tightly that they land on the detector's camera sensor almost on top of each other.
• The Result: Instead of seeing two dots, the camera sees one big, merged blob. Standard software looks at this blob and thinks, "That's just one electron," or gets confused and ignores it. If we ignore it, we might miss a brand-new type of physics (like a hidden "dark boson").

2. The Solution: Two New Detective Tools

The team developed a new "ID system" with two different strategies, depending on how the blob looks:

Strategy A: The "Two-Track" Detective

When to use it: The blob is tight, but we can still see two tiny trails (tracks) leading into it, like two footprints merging into a single puddle.

• The Analogy: Imagine seeing a puddle on the sidewalk. You can't see the people who made it, but you see two distinct footprints leading right up to it.
• The Tool: They built a smart computer model (a "Boosted Decision Tree") that looks at the geometry. It asks: "Do these two footprints line up perfectly with this one puddle?" If yes, it's a merged pair!
• Success Rate: This works about 80% of the time.

Strategy B: The "One-Track" Detective

When to use it: The electrons are moving so fast that the camera only catches one of the footprints. The other one is invisible or lost in the noise.

• The Analogy: You see a puddle and only one footprint. But, the puddle is huge—way bigger than a single person could make. Your brain says, "Wait, one person didn't make this. There must be a second person right next to them, even if I can't see their foot."
• The Tool: This model compares the size of the energy "puddle" to the speed of the single "footprint." If the puddle is too big for the single track, it flags it as a merged pair.
• Success Rate: This works about 60% of the time.

3. How They Taught the Detectives (Training)

You can't just tell a computer "look for blobs." You have to show it examples.

• For the Two-Track model: They used J/$\psi$ mesons (a type of particle that decays into electron pairs). These are like "practice dummies" that naturally produce the exact kind of merged blobs they are looking for. They checked if their new system could find them.
• For the One-Track model: They used Z bosons that emit a photon (light), which then turns into an electron pair. Sometimes, the detector only sees one track from this pair. This was the perfect "test case" to teach the system how to spot a hidden partner.

4. Fixing the Ruler (Energy Correction)

There was one more problem. When the electrons merge, the detector's "ruler" for measuring energy gets a little bit confused. It might say the blob weighs 100 units when it's actually 105.

• The Fix: They used a specific decay chain involving a Kaon (a type of particle) and a J/$\psi$ to create a known "resonance" (a very specific, predictable energy signature). By comparing what they knew the energy should be versus what the detector measured, they created a correction formula. It's like calibrating a scale: "Okay, when the scale says 100, we know it's actually 103. Let's adjust the math."

5. Why Does This Matter?

Think of the Standard Model of physics as a completed puzzle. But scientists suspect there are hidden pieces (New Physics) that are light and fast.

• If these new particles exist, they would decay into these super-fast, merged electron pairs.
• Without this new technique, those pairs would look like background noise or just single electrons, and the new physics would remain invisible.
• The Result: This new ID system acts like a high-powered magnifying glass. It allows scientists to look at the "blurry" parts of the data and say, "Aha! That's not just noise; that's a hidden particle!"

In summary: The CMS team built a smarter way to spot two electrons that are running so fast they look like one. They taught their computers to recognize the "footprints" of these pairs, even when the evidence is messy, opening the door to discovering new, hidden particles in the universe.

Technical Summary

1. Problem Statement

In Beyond the Standard Model (BSM) scenarios, light bosons produced in the decay of heavy resonances can be highly boosted. When these light bosons decay into dielectron pairs ($e^+e^-$), the resulting electrons are often extremely collimated.

• Merging Issue: If the angular separation ($\Delta R$) between the two electrons is smaller than the calorimeter granularity or the Molière radius of the lead tungstate crystals (approx. 22 mm), the standard CMS reconstruction algorithms fail to resolve them as two distinct objects. Instead, they form a single merged cluster in the Electromagnetic Calorimeter (ECAL).
• Track Loss: At very high Lorentz boosts ($\gamma_L > 200$), the two electron tracks may share hits in the inner silicon tracker. The standard "trajectory cleaner" algorithm, designed to remove duplicate tracks, often removes one of the tracks, leaving only a single reconstructed track associated with the merged cluster.
• Consequence: Standard electron identification (ID) techniques, optimized for isolated prompt electrons, have poor efficiency for these merged dielectrons (eME), leading to a significant loss of sensitivity in searches for new physics in the electron channel.

2. Methodology

The paper presents a novel identification technique for merged electrons (eME) utilizing two distinct multivariate models based on Boosted Decision Trees (BDT), tailored to the specific reconstruction topology of the event.

A. Reconstruction and Clustering Modifications

• Cluster Definition: For the "two-track" case, the standard supercluster (SC) is insufficient. The authors define a $U_{5\times5}$ cluster, which is the union of two $5\times5$ matrices of ECAL crystals centered around the two electron tracks. This captures the full energy deposit of the merged pair.
• Track Association:
  • Primary Track: Reconstructed using the Gaussian Sum Filter (GSF) algorithm.
  • Secondary Track: A secondary track is searched for within $\Delta R < 0.4$ of the primary track. Strict quality criteria (e.g., $p_T > 10$ GeV, hit requirements, vertex fit probability) are applied to distinguish true secondary electrons from background (e.g., photon conversions).
• New Matching Variables: Standard geometric matching ($\Delta \eta, \Delta \phi$) is suboptimal for merged clusters because the cluster center of gravity (CoG) is shifted. New variables were devised:
  • $\Delta u, \Delta v$: Angular separations perpendicular and parallel to the line connecting the tracks.
  • $\alpha_{track}, \alpha_{5\times5}$: Angles relative to the $\phi$ axis.
  • $cov_{5\times5}^{i\eta i\eta}$: Log-weighted variance of crystal distances.

B. The Two Multivariate Models

1. Two-Track Model:
   • Input: Geometrical compatibility between the $U_{5\times5}$ cluster CoG and the two reconstructed tracks.
   • Training Signal: Simulated $X \to YY \to 4e$ events (where $Y$ is a light boson).
   • Training Background: Isolated electrons from $W$, Drell-Yan, and $t\bar{t}$ processes.
2. Single-Track Model:
   • Input: Primarily the ratio of the merged cluster energy to the single track momentum ($E/p$), along with cluster shape variables.
   • Training Signal: Simulated highly boosted $X \to YY \to 4e$ events where one track is lost.
   • Training Background: Same as above.

C. Efficiency Measurement and Calibration

• Two-Track Efficiency: Measured using boosted $J/\psi \to e^+e^-$ decays from the "B Parking" dataset. The $J/\psi$ mass peak is used to count signal candidates passing/failing the ID.
• Single-Track Efficiency: Measured using $Z \to \mu^+\mu^-\gamma$ events where the photon converts into a collimated $e^+e^-$ pair (single-leg conversion). This mimics the single-track topology.
• Energy Correction: A dedicated correction is developed for the $U_{5\times5}$ cluster energy using $B^\pm \to J/\psi K^\pm \to e^+e^- K^\pm$ decays. The invariant mass of the $U_{5\times5}$ cluster and the kaon is used to derive scale ($\alpha$) and smearing ($\beta$) correction parameters to match data to simulation.

3. Key Results

• Identification Efficiency:
  • Two-Track Model: Achieves an overall efficiency of ~80% for boosted $J/\psi$ candidates ($\gamma_L > 20$). The efficiency is validated as a function of transverse energy ($E_T^{5\times5}$) and transverse decay length ($L_{xy}$).
  • Single-Track Model: Achieves an efficiency of ~60% for single-track candidates. This model is crucial for extreme boosts ($\gamma_L > 200$) where track merging occurs.
• Performance vs. Separation:
  • For $\Delta R \approx 0.01$ (approx. 1–2 Molière radii), the standard reconstruction resolves only 5–40% of pairs. The new eME ID significantly recovers these events.
  • The total dielectron efficiency (standard + eME ID) is maintained across a wide range of $\Delta R$.
• Energy Scale and Resolution:
  • The energy correction derived from $B^\pm \to J/\psi K^\pm$ aligns the data and simulation.
  • Correction parameters: Scale factor $\alpha = 1.003 \pm 0.003$; Smearing factor $\beta = 0.02 \pm 0.01$.
  • The systematic uncertainty on the scale factor is approximately 6% for the two-track model and up to 40% for the single-track model (dominated by topology differences).

4. Significance and Impact

• Enhanced BSM Sensitivity: This technique significantly improves the sensitivity of the CMS experiment to BSM models predicting light bosons decaying to electrons, specifically in the high-Lorentz-boost phase space ($\gamma_L > 20$) where previous analyses were blind.
• Background Reduction: By specifically identifying merged clusters, the method reduces backgrounds from isolated single electrons that might otherwise mimic the signal.
• Methodological Advancement: The paper demonstrates a robust framework for handling "merged" objects in high-granularity calorimeters, utilizing image-like cluster variables and specialized track-cluster matching that goes beyond standard isolation criteria.
• Data/MC Agreement: The use of control regions ($J/\psi$ and $Z \to \mu\mu\gamma$) ensures that the efficiency and energy corrections are grounded in real data, minimizing reliance on simulation for the final physics results.

In summary, this work provides a critical tool for the CMS collaboration to explore the "dark sector" and other BSM phenomena in the electron channel, recovering signal events that would otherwise be lost due to the limitations of standard reconstruction algorithms in highly boosted regimes.