Search for a new heavy scalar resonance decaying into the Higgs boson and a new scalar particle in the $\mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}}$ final state using proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS detector, this paper presents a search for a heavy scalar resonance decaying into a Higgs boson and a new scalar particle in the four-bottom-quark final state, finding no significant evidence for new physics beyond the background expectation while setting upper limits on production cross sections within the next-to-minimal supersymmetric standard model scenario.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It takes two beams of protons and smashes them together at nearly the speed of light, creating a chaotic explosion of new particles. For decades, scientists have been looking for the "Standard Model" particles (the known rules of the universe), and they found the famous Higgs boson in 2012. But they suspect there's a whole "underground" world of new, heavier particles hiding in the debris that we haven't seen yet.

This paper is a report from the CMS experiment, a giant detector at the LHC, describing a specific "treasure hunt" they conducted.

The Mission: Hunting for a Heavy Parent and a New Child

The scientists were looking for a specific scenario: a heavy, new particle (let's call it X) that is so heavy it doesn't last long. When it decays (breaks apart), it splits into two things:

1. The known Higgs boson (the particle discovered in 2012).
2. A brand new, lighter particle (let's call it Y).

Both of these "children" then immediately break apart again, specifically into pairs of bottom quarks (heavy particles that turn into jets of debris). So, the final signature the scientists were looking for was four bottom quarks (or "bbbb") flying out of the collision.

The Analogy: Imagine a heavy, mysterious suitcase (Particle X) falling from a plane. When it hits the ground, it bursts open to reveal a famous, recognizable watch (the Higgs) and a strange, new gadget (Particle Y). Both the watch and the gadget then immediately shatter into four specific types of metal shards (the bottom quarks). The scientists are trying to find the four shards and prove they came from that specific suitcase.

The Search Strategy: Finding a Needle in a Haystack

The problem is that the LHC produces billions of collisions, and most of them are just "noise" (background events) that look like four bottom quarks but didn't come from a new heavy particle. It's like trying to find a specific four-leaf clover in a field of billions of three-leaf clovers.

To solve this, the team used a clever two-step filter:

1. The "Three-Leaf" Control Group: They first looked at events where they found three bottom quarks and one "almost" bottom quark. This group is mostly just noise. They used a smart computer algorithm (a Boosted Decision Tree, or BDT) to learn exactly what this noise looks like.
2. The "Four-Leaf" Signal Group: Then, they looked at the events with four bottom quarks. They used the lessons learned from the "three-leaf" group to predict what the noise should look like in the "four-leaf" group.

If the actual data in the "four-leaf" group matched the prediction perfectly, it meant there was no new particle. If the data showed a huge spike or "bump" that the noise couldn't explain, that would be the discovery of Particle X.

The Results: A Near Miss, But No New Treasure

The scientists analyzed data collected over three years (2016–2018), representing 138 "inverse femtobarns" of collisions (a fancy unit meaning a massive amount of data).

• The Verdict: The data matched the "noise" prediction almost perfectly. They did not find a new heavy particle.
• The "Almost": There was one spot in the data where the numbers were slightly higher than expected. It looked like a small hill rather than a mountain. Statistically, this was a "3.47 sigma" fluctuation. In the world of particle physics, this is like flipping a coin and getting heads 3.5 times in a row more often than chance would predict. It's interesting, but not enough to claim a discovery (which requires a "5 sigma" or a 1-in-3.5-million chance of being a fluke).
• The Limits: Because they didn't find the particle, they set a "fence." They can now say with 95% confidence that if this heavy particle does exist, it cannot be within the mass ranges they searched (from 400 GeV to 1.6 TeV for the heavy particle, and 60 GeV to 1.4 TeV for the new light particle). They have effectively ruled out those specific "neighborhoods" of the particle world.

Why This Matters

Even though they didn't find the new particle, this is a successful mission. By ruling out these mass ranges, they are helping theorists (the people who write the math) narrow down where to look next.

The paper specifically mentions that their results help constrain a theory called the Next-to-Minimal Supersymmetric Standard Model (NMSSM). Think of this theory as a map with many possible paths. This experiment has closed off several paths on the map, telling scientists, "Don't look here; the treasure isn't in this neighborhood."

Summary

• Goal: Find a heavy new particle that decays into a Higgs boson and a new light particle, both turning into four bottom quarks.
• Method: Used a massive dataset and a smart computer trick to distinguish between background noise and a potential signal.
• Outcome: No new particle was found. The data looks exactly like what we expect from known physics.
• Significance: They have set strict limits on where this new particle cannot be, helping to refine our understanding of the universe's fundamental building blocks.

Technical Summary

1. Problem Statement and Physics Motivation

The Standard Model (SM) of particle physics was confirmed by the discovery of the Higgs boson ($H$), but it does not explain phenomena such as dark matter or the hierarchy problem. Many Beyond the Standard Model (BSM) theories, including the Next-to-Minimal Supersymmetric Standard Model (NMSSM), predict an extended scalar sector with additional heavy scalar ($X$) and light scalar ($Y$) particles.

The specific process investigated is the production of a heavy resonance $X$ which decays into the SM Higgs boson ($H$) and a new scalar particle ($Y$):
$$pp \to X \to YH$$
Both $Y$ and $H$ subsequently decay into bottom quark-antiquark pairs ($b\bar{b}$), resulting in a four-bottom-quark ($bbbb$) final state. This channel is particularly challenging due to the overwhelming QCD multijet background but offers high branching fractions in specific BSM scenarios (up to 50% in NMSSM).

The analysis aims to:

• Search for resonances $X$ with masses ($m_X$) from 400 GeV to 1.6 TeV.
• Search for scalars $Y$ with masses ($m_Y$) from 60 GeV to 1.4 TeV.
• Interpret results within the NMSSM framework.

2. Methodology

Data Sample

• Experiment: CMS detector at the LHC.
• Collision Energy: $\sqrt{s} = 13$ TeV.
• Integrated Luminosity: 138 fb$^{-1}$ collected during Run 2 (2016–2018).

Event Reconstruction and Selection

• Trigger: A combination of Level-1 (L1) and High-Level Trigger (HLT) algorithms requiring multiple jets and $b$-tagged jets. Offline selection thresholds were set at 90% of the HLT turn-on efficiency.
• Jet Reconstruction: Particle-Flow (PF) candidates clustered using the anti-$k_T$ algorithm ($R=0.4$). Jets are required to have $|\eta| < 2.4$ (2016) or $2.5$ (2017–2018).
• $b$-tagging: The DEEPJET algorithm is used.
  • Signal Region (4b): Events with four jets passing the medium $b$-tagging working point.
  • Background Control Region (3b): Events with three jets passing the medium point and one passing the loose but failing the medium point.
• Candidate Reconstruction:
  • The four highest $b$-tagged jets are paired.
  • The pair with an invariant mass ($m_{reco}$) closest to 125 GeV is assigned as the Higgs candidate ($H$).
  • The remaining pair is assigned as the $Y$ candidate.
  • The $X$ candidate mass ($m_X^{reco}$) is the invariant mass of all four jets.
  • Kinematic Constraint: The $b$-jet momenta are adjusted to enforce $m_H = 125$ GeV to improve resolution.

Analysis Regions

Events are categorized based on the reconstructed Higgs mass ($m_H^{reco}$):

• Signal Region (SR): $|m_H^{reco} - 125| < 20$ GeV.
• Validation Region (VR): $20 < |m_H^{reco} - 125| < 30$ GeV.
• Control Region (CR): $30 < |m_H^{reco} - 125| < 60$ GeV.

Background Modeling

The dominant background is QCD multijet (90%) and $t\bar{t}$ (10%).

• Data-Driven Approach: The background in the Signal Region (4b) is estimated using the Control Region (3b) data.
• Reweighting: A Boosted Decision Tree (BDT) is trained to reweight the 3b sample to match the kinematic distributions (e.g., $m_X^{reco}$, $m_Y^{reco}$, jet $p_T$, $\Delta R$) of the 4b sample.
• Validation: The model is validated in the VR and a statistically independent sample (assuming $m_H = 205$ GeV) to ensure no bias from potential signal contamination in the 3b sample.

Statistical Analysis

• A 2D binned maximum likelihood fit is performed in the $(m_X^{reco}, m_Y^{reco})$ plane.
• Systematic uncertainties (trigger, $b$-tagging, jet energy scale, luminosity, PDF, etc.) are included as nuisance parameters.
• Limits: 95% Confidence Level (CL) upper limits on $\sigma(pp \to X) \times \mathcal{B}(X \to YH \to bbbb)$ are set using the asymptotic $CL_s$ method.

3. Key Contributions

1. Model-Independent Search: The analysis covers a broad mass range ($m_X$: 400–1600 GeV, $m_Y$: 60–1400 GeV) without assuming a specific BSM model, making it sensitive to various theoretical scenarios.
2. Advanced Background Estimation: The use of a BDT-based reweighting technique to model the 4b background from the 3b data sample allows for a robust, data-driven estimation that accounts for complex kinematic correlations.
3. Kinematic Optimization: The specific mass windowing and kinematic constraints (enforcing $m_H=125$ GeV) significantly improve the signal-to-background ratio in the $bbbb$ channel, which is notoriously difficult due to QCD backgrounds.
4. NMSSM Interpretation: The results are directly interpreted to constrain the parameter space of the NMSSM, specifically the region where a heavy scalar decays into a Higgs and a singlet scalar.

4. Results

• Observation: The observed data are in good agreement with the background-only hypothesis. No significant localized excess was found across the entire search range.
• Largest Excess: A local excess with a significance of 3.47 standard deviations (global significance 2.44$\sigma$) was observed for the mass hypothesis $m_X = 600$ GeV and $m_Y = 400$ GeV. This is consistent with a statistical fluctuation given the "look-elsewhere effect."
• Exclusion Limits:
  • Upper limits on the production cross-section times branching fraction ($\sigma\mathcal{B}$) were set for all tested mass hypotheses.
  • For $m_X \le 1000$ GeV, the expected limits are 30% more stringent on average than previous CMS combinations of other channels.
  • For $m_X > 1000$ GeV, the improvement is 84% on average.
  • The results exclude specific regions of the NMSSM parameter space that were previously unconstrained.
• Comparison: The results are compatible with previous CMS limits on $HH \to bbbb$ and are competitive with recent ATLAS results, though ATLAS shows slightly more stringent limits in the specific $HH$ channel for some mass points.

5. Significance

This paper represents a significant advancement in the search for BSM physics in the $bbbb$ final state. By utilizing the full Run 2 dataset and a sophisticated data-driven background modeling technique, CMS has set the most stringent limits to date for a heavy scalar decaying into a Higgs and a new scalar in this channel.

The lack of discovery, combined with the improved exclusion limits, places strong constraints on the NMSSM and other models predicting extended Higgs sectors. The methodology developed here, particularly the BDT reweighting of control samples, serves as a template for future high-multiplicity jet analyses at the LHC. The results effectively close off a large portion of the phase space for light singlet scalars produced in association with the Higgs boson.