Search for a new resonance decaying to a Higgs boson and a scalar boson in events with two b jets and two Z bosons in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV, a search for new resonances decaying into Higgs boson pairs or a Higgs boson and a scalar boson in the bbZZ final state found no significant deviations from Standard Model predictions, resulting in the establishment of 95% confidence level upper limits on the production cross sections for these processes.

The Gist

The Mission: Hunting for a "Ghost" in the Machine

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smashers. It's like a giant, circular racetrack where we shoot protons (tiny bits of matter) at each other at nearly the speed of light. When they crash, they create a chaotic explosion of debris, much like smashing two watches together to see what gears fly out.

The CMS experiment is the giant camera and computer system watching these crashes. The goal of this specific paper is to look for a "Ghost."

In physics, we know about the Higgs boson (discovered in 2012). It's a known particle that gives other particles mass. But physicists suspect there might be heavier, unknown particles (let's call them X) that decay into Higgs bosons. Finding one would be like finding a new, heavier species of dinosaur that we only knew existed because we found its footprints.

The Setup: The "Double-Decker" Crash

The scientists are looking for a specific type of crash where a heavy, unknown particle X is created and then immediately splits apart. It has two possible ways to split:

1. HH Mode: It splits into two Higgs bosons.
2. HY Mode: It splits into one Higgs boson and a new, mysterious scalar particle Y.

Once these particles are created, they don't stay around long. They instantly decay (fall apart) into other things. The team is looking for a very specific "signature" left behind:

• Two "b-quarks": These are heavy particles that leave a trail of "jets" (sprays of particles) that look like a pair of heavy suitcases.
• Two Z bosons: These are like messengers. One of them decays into two leptons (electrons or muons), which are like bright, easy-to-spot flares. The other Z boson is tricky; it either decays into invisible neutrinos (ghosts that pass through walls) or into a pair of quarks (another jet).

So, the final scene the camera looks for is: Two bright flares + Two heavy suitcases + (either invisible ghosts or more suitcases).

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" is massive. The Standard Model (our current rulebook of physics) predicts that normal processes (like top quarks or Drell-Yan events) create this exact same signature all the time. It's like trying to find a specific rare coin in a pile of billions of identical-looking pennies.

To solve this, the CMS team used three clever strategies:

1. Sorting by "Speed" (The Boosted vs. Resolved)

If the heavy particle X is very massive, the particles it creates fly apart incredibly fast.

• Resolved: If X is lighter, the debris spreads out, and we can see the individual pieces clearly (like seeing two separate suitcases).
• Boosted: If X is super heavy, the debris is squished together into a single, giant blob (like two suitcases taped together).
  The team created different "bins" or categories to catch both slow-moving and super-fast particles.

2. The AI Detective (Machine Learning)

They didn't just look at the data; they trained a Machine Learning algorithm (a type of AI) to be a super-detective.

• They fed the AI millions of simulated crashes.
• They taught it to spot subtle differences between a "normal" crash and a "new physics" crash.
• The AI looks at things like the angle of the flares, the energy of the suitcases, and how spread out everything is. It gives every event a "score" on how suspicious it looks.

3. The "Control Group"

To make sure they aren't fooling themselves, they set up "Control Regions." These are areas of the data where they know no new physics exists. They use these to calibrate their background noise, ensuring that when they look at the "Signal Region" (where the ghost might be), they aren't just seeing static.

The Results: The Silence of the Ghost

After analyzing 138 "inverse femtobarns" of data (which is a fancy way of saying they looked at trillions of collisions from 2016 to 2018), the result was... nothing.

• No Ghost Found: The number of events they saw matched the Standard Model predictions perfectly. There were no "bumps" in the data that suggested a new particle X or Y was hiding there.
• Setting the Limits: Even though they didn't find the ghost, they learned something valuable. They can now say with 95% confidence: "If this ghost exists, it must be heavier than X, or it must be so rare that we would need a much bigger machine to see it."

They set strict "bounties" (upper limits) on how heavy or how common these particles could be. For example, if a heavy particle X exists, it can't be producing more than 1 "event" per trillion collisions at certain masses.

The Takeaway

Think of this paper as a report from a search team that scoured a massive forest for a specific rare bird. They used high-tech binoculars (detectors), AI to spot the bird's call (machine learning), and checked every tree (categorization).

They didn't find the bird. But by proving the bird isn't in the parts of the forest they searched, they have narrowed down the map. This tells other scientists: "Don't look here anymore; look somewhere else, or build a bigger net."

It's a "null result," but in science, knowing where the treasure isn't is just as important as finding it, because it helps us refine our map of the universe.

Technical Summary

1. Problem and Physics Motivation

The Standard Model (SM) of particle physics was completed with the discovery of the Higgs boson ($H$) in 2012. However, the SM does not explain phenomena such as dark matter, neutrino masses, or the hierarchy problem. Consequently, searches for physics Beyond the Standard Model (BSM) are critical.

This analysis targets two specific BSM scenarios involving a new heavy resonance $X$:

1. Resonant Di-Higgs Production ($X \to HH$): A search for a heavy scalar or radion decaying into two Higgs bosons. This is motivated by models with warped extra dimensions (e.g., Randall–Sundrum bulk models) which predict massive spin-0 radions and Kaluza–Klein graviton excitations with significant branching fractions to $HH$.
2. Resonant $HY$ Production ($X \to HY$): A search for a heavy scalar $X$ decaying into a SM Higgs boson and a new light scalar $Y$. This is motivated by the Next-to-Minimal Supersymmetric Standard Model (NMSSM), which introduces an additional singlet field to solve the $\mu$-problem, predicting a spectrum of spin-0 bosons where $X \to HY$ is a possible decay channel.

Decay Channel: The analysis focuses on the final state $bbZZ$, where:

• One Higgs boson (or the scalar $Y$) decays to a pair of bottom quarks ($b\bar{b}$).
• The other Higgs boson (or $Y$) decays to a pair of $Z$ bosons.
• One $Z$ boson decays leptonically ($Z \to \ell\ell$, where $\ell = e, \mu$).
• The other $Z$ boson decays either hadronically ($Z \to q\bar{q}$) or invisibly ($Z \to \nu\bar{\nu}$).

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS experiment during Run 2 (2016–2018), corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Simulation: Generated at Leading Order (LO) using MADGRAPH5_aMC@NLO for the hard process ($pp \to X \to HH$ or $HY$) and PYTHIA 8 for parton showering and hadronization.
• Background Simulation: Dominant backgrounds include Drell–Yan (DY) and top-quark pair ($t\bar{t}$) production, generated at Next-to-Leading Order (NLO) or NNLO. Other backgrounds (diboson, triboson, $t\bar{t}+V$) are also simulated.

Event Selection and Object Reconstruction

• Leptons: Events require exactly two tight, same-flavor, opposite-sign leptons ($ee$ or $\mu\mu$) with invariant mass $75 < m_{\ell\ell} < 105$ GeV (to suppress $WW$ background).
• Jets:
  • Resolved Topology: Uses small-radius jets (AK4, $R=0.4$) reconstructed with the CHS (Charged Hadron Subtraction) algorithm.
  • Boosted Topology: Uses large-radius jets (AK8, $R=0.8$) reconstructed with the PUPPI (PileUp Per Particle Identification) algorithm.
• b-tagging: AK4 jets are b-tagged using DeepJet (87% efficiency, 10% mistag rate).
• Higgs/Scalar Tagging: AK8 jets are tagged as $H \to b\bar{b}$ candidates using ParticleNet (PNET), a deep neural network. A mass-decorrelated (MD) version is used to ensure the selection does not distort the background mass shape.
• Missing Transverse Momentum ($p_T^{miss}$): Used to distinguish between channels with invisible $Z$ decays.

Event Categorization

To maximize sensitivity across a wide mass range ($260$ GeV to $4$ TeV for $HH$;$700$ GeV to $4$ TeV for $HY$), events are categorized into six Signal Regions (SRs) based on the decay topology (resolved vs. boosted) and the $Z$ boson decay mode:

1. $bbZ(qq)Z(\ell\ell)$ Channel (Visible $Z$):
   • qq0M: Resolved $H$ and $Z$ (4 AK4 jets, 2 b-tagged).
   • qqHM: Boosted $H$, resolved $Z$ (1 AK8 jet passing PNET, 2 AK4 jets).
   • qqZM: Resolved $H$, boosted $Z$ (1 AK8 jet failing PNET, 2 b-tagged AK4 jets).
   • qq2M: Boosted $H$ and $Z$ (2 AK8 jets, 1 passing PNET).
2. $bbZ(\nu\nu)Z(\ell\ell)$ Channel (Invisible $Z$):
   • $\nu\nu$1M: Boosted $H$ (1 AK8 jet passing PNET).
   • $\nu\nu$0M: Resolved $H$ (2 b-tagged AK4 jets).

Note: A strict $p_T^{miss} < 100$ GeV cut is applied to the $qq$ channel to ensure orthogonality with the $bbWW$ analysis, while the $\nu\nu$ channel requires $p_T^{miss} > 100$ GeV.

Background Estimation

• Drell-Yan (DY) and $t\bar{t}$: Normalization factors are extracted from data in dedicated Control Regions (CRs) (e.g., $DYCR1$, $DYCR2$, $TTCR$) by fitting the dilepton mass ($m_{\ell\ell}$) distribution.
• Non-prompt Leptons: Estimated using a "matrix method" based on sidebands with same-sign leptons or non-isolated leptons.
• Other Backgrounds: Normalized using theoretical cross-sections or latest measurements.

Signal Extraction

• Discriminants:
  • For fully resolved regions ($qq0M$, $\nu\nu0M$), a Boosted Decision Tree (BDT) is used. The BDT is trained on kinematic variables (e.g., $\Delta R(\ell, \ell)$, $H_T$, $\Delta R(\ell, b)$) and includes the resonance mass as a feature. A "mass-averaged" approach is used to avoid generating excessive background templates.
  • For boosted regions, the reconstructed resonance mass ($m_{rec}^X$ or $m_{rec}^{X'}$) is the primary discriminant.
• Statistical Analysis: A simultaneous binned profile likelihood fit is performed across all SRs and lepton channels using the COMBINE tool. Upper limits are set at 95% Confidence Level (CL) using the $CL_s$ method.

3. Key Contributions

1. Comprehensive Topology Coverage: Unlike previous searches that focused solely on resolved or boosted decays, this analysis simultaneously exploits four distinct topologies (resolved/boosted $H$ and $Z$) to cover the full mass spectrum of potential resonances.
2. Orthogonality to $bbWW$: The analysis implements a restrictive selection ($m_{\ell\ell} > 15$ GeV and specific $p_T^{miss}$ cuts) to clearly separate the $bbZZ$ signal from the $bbWW$ background, which shares the same final state in the invisible $Z$ channel. This allows for a cleaner definition of the signal process.
3. HY Search: This is a comprehensive search for the $X \to HY$ process in the $bbZZ$ channel, a channel previously less explored compared to $H \to \gamma\gamma$ or $H \to \tau\tau$.
4. Machine Learning Integration: The use of ParticleNet for boosted $H \to b\bar{b}$ tagging and a mass-averaged BDT strategy for signal extraction represents a state-of-the-art approach to handling high-mass resonances with complex decay topologies.

4. Results

• Observation: No significant deviations from the Standard Model predictions were observed in any of the signal regions. The data is consistent with background expectations.
• Limits on $pp \to X \to HH$:
  • Upper limits on the production cross section $\sigma(pp \to X \to HH)$ were set for resonance masses ($m_X$) from 260 GeV to 4 TeV.
  • The limits range from 400 pb at low mass ($m_X \approx 260$ GeV) down to 1 pb at high mass ($m_X \approx 4$ TeV).
  • These results are compared to the theoretical prediction for a bulk radion in the Randall–Sundrum model.
• Limits on $pp \to X \to HY \to bbZZ$:
  • Upper limits were set in the two-dimensional mass space ($m_X, m_Y$) for $m_X$ up to 4 TeV and $m_Y$ up to 2 TeV.
  • The observed limits on the cross section vary from approximately 5 fb to 500 fb, depending on the mass hypothesis.
  • The sensitivity is comparable to other complementary searches focusing on $H \to \gamma\gamma$ or $\tau\tau$.

5. Significance

This analysis significantly advances the search for BSM physics in the Higgs sector by:

• Expanding the Mass Reach: By utilizing boosted topologies and advanced machine learning, the analysis maintains sensitivity up to 4 TeV, a regime where traditional resolved analyses lose efficiency.
• Validating BSM Models: The results place stringent constraints on warped extra dimension models (radions) and NMSSM scenarios (heavy scalars decaying to $HY$).
• Methodological Benchmark: The successful application of mass-averaged BDTs and the rigorous separation of $bbZZ$ from $bbWW$ backgrounds provide a robust template for future high-luminosity LHC (HL-LHC) searches in complex multi-boson final states.

In conclusion, while no new resonance was discovered, the analysis sets the most stringent limits to date for the $bbZZ$ channel in the specified mass ranges, effectively probing the parameter space of several compelling BSM theories.