Search for dark matter produced in association with a dark Higgs boson decaying into a bottom quark-antiquark pair in 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 study sets the most stringent limits to date on dark matter production associated with a dark Higgs boson decaying into a bottom quark-antiquark pair, excluding mediator masses up to 4.5 TeV for specific dark Higgs mass hypotheses.

The Gist

The Big Picture: Hunting the Invisible Ghost

Imagine the universe is a giant, crowded party. We know almost everyone at the party: the electrons, the protons, the quarks, and the Higgs boson (the "famous celebrity" of the particle world). But we also know that about 85% of the guests are invisible ghosts. We call this Dark Matter. We can't see them, but we know they are there because they are holding up the walls of the universe (gravity) and keeping galaxies from flying apart.

The problem? We've never actually seen a Dark Matter particle. We only know it exists because of its effects.

This paper is about a team of scientists (the CMS Collaboration at CERN) trying to catch these ghosts in the act. They aren't just looking for the ghosts; they are looking for the ghosts bringing a "plus-one."

The Theory: The Dark Higgs and the Mediator

The scientists have a specific theory about how these ghosts might interact with our visible world.

1. The Mediator (The Bouncer): Imagine Dark Matter and our normal world are two separate rooms at the party. They can't talk to each other directly. But there might be a "bouncer" (a particle called a Z' boson) who can walk between the rooms. If the bouncer gets hit hard enough, he might drop a message (a particle) into the Dark Matter room.
2. The Dark Higgs (The Plus-One): In this specific theory, when the bouncer (Z') interacts, he doesn't just drop a message; he also brings a "Dark Higgs boson" ($H_D$). Think of the Dark Higgs as a special, invisible gift box that the bouncer carries.
3. The Decay (The Unwrapping): The Dark Higgs is unstable. It doesn't stay dark for long. It quickly "unwraps" itself and turns into two visible particles: a bottom quark and an anti-bottom quark.

The Goal: The scientists want to see a collision where:

• Two invisible Dark Matter particles fly off in opposite directions (leaving a hole in the energy balance).
• A "Dark Higgs" is created, which immediately turns into a pair of bottom quarks (which look like a jet of particles in the detector).

The Experiment: The Cosmic Pinball Machine

To find this, they used the Large Hadron Collider (LHC). Imagine the LHC as a giant, circular pinball machine where they smash protons together at nearly the speed of light.

1. The Smash: They smashed protons together 138 trillion times (138 fb⁻¹ of data) over three years (2016–2018).
2. The Detector (CMS): The CMS detector is like a giant, high-speed 3D camera surrounding the collision point. It takes a snapshot of every particle flying out.
3. The Clues:
   • Missing Energy: Since Dark Matter is invisible, it won't hit the camera. But if you add up all the energy of the visible particles and it doesn't equal the energy of the incoming protons, the "missing" energy is the Dark Matter escaping. This is called Missing Transverse Momentum.
   • The Jet: They looked for a specific "jet" of particles (a spray of debris) that matches the mass of a bottom quark pair. This is the "unwrapped gift" from the Dark Higgs.

The Strategy: Filtering the Noise

The problem is that normal particle collisions happen all the time and create a lot of noise. It's like trying to hear a whisper in a stadium full of screaming fans.

• The Signal: A big gap in energy (Dark Matter) + a specific type of particle spray (Dark Higgs).
• The Background: Normal events where the camera makes a mistake, or where a known particle (like a Z boson) decays into invisible neutrinos, mimicking the missing energy.

The scientists built a sophisticated filter (a "Control Region" strategy). They looked at millions of events that looked like the background noise to understand exactly how the noise behaves. Then, they applied that knowledge to the "Signal Region" to see if there was anything left over that didn't fit the noise pattern.

The Results: The Ghosts Stay Hidden

After analyzing all the data, the scientists found nothing.

• No Excess: The number of events they saw with "Missing Energy + Bottom Quark Jets" was exactly what they expected from normal background noise. There were no extra "ghosts" showing up.
• The Exclusion: While they didn't find the Dark Matter, they did something very important: They drew a map of where it isn't.

Think of it like searching for a lost dog in a forest. You didn't find the dog, but you checked every bush in the north and the east. Now you know for sure the dog isn't in the north or east. You have to look in the south or west.

Specifically, they ruled out:

• If the "Mediator" (the bouncer) is lighter than 4.5 TeV (a very heavy mass) and the "Dark Higgs" is 50 GeV, that specific combination of particles does not exist.
• If the Dark Higgs is heavier (150 GeV), they ruled out mediators up to 2.5 TeV.

Why This Matters

Even though they didn't find the Dark Matter, this is a huge success.

1. It's the strictest test yet: They have set the tightest limits ever on this specific type of Dark Matter theory.
2. It narrows the search: Theorists can now throw away models that predict these specific particles. They have to come up with new ideas or look for heavier/lighter particles.
3. The hunt continues: The fact that the "ghosts" are hiding so well means they are either very heavy, very weakly interacting, or the theory needs to be tweaked.

In short: The scientists smashed protons together, looked for a specific invisible ghost bringing a visible gift, and found nothing. But by proving the ghost isn't there, they have narrowed down the search for the universe's biggest mystery.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics successfully describes known particles but fails to account for Dark Matter (DM), which constitutes approximately 85% of the universe's matter. While astrophysical observations confirm DM's existence, its particle nature remains unknown.

This paper investigates a specific theoretical framework where DM interacts with SM particles via a spin-1 gauge boson mediator ($Z'$) and a dark Higgs boson ($H_D$).

• The Model: The model assumes DM particles ($Z_\chi$, Majorana fermions) couple axially to the $Z'$, while the $Z'$ couples vector-like to SM quarks. A complex Higgs field in the dark sector breaks the gauge symmetry, generating the $Z'$ mass and a physical scalar $H_D$.
• The Annihilation Channel: If $H_D$ is light ($m_{H_D} < 160$ GeV), DM particles can annihilate into pairs of $H_D$ bosons. This channel helps reconcile the model with the observed cosmological DM relic abundance, alleviating tensions found in simpler "mono-X" models.
• The Signature: The search targets the associated production of DM and $H_D$ at the LHC. The $H_D$ decays into a bottom quark-antiquark pair ($b\bar{b}$), while the DM particles escape detection, resulting in large missing transverse momentum ($p_T^{miss}$). The experimental signature is a resonant $b\bar{b}$ pair (reconstructed as a large-radius jet) recoiling against large $p_T^{miss}$.

2. Methodology

Data and Detector

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS detector during 2016–2018.
• Integrated Luminosity: $138 \text{ fb}^{-1}$.
• Reconstruction: Events are reconstructed using the Particle-Flow (PF) algorithm. Jets are clustered using the anti-$k_T$ algorithm.
  • AK4 jets: Used for standard jet reconstruction and $b$-tagging.
  • AK15 jets: Large-radius jets ($R=1.5$) used to capture the hadronization of the boosted $H_D \to b\bar{b}$ system.

Event Selection

The analysis defines a Signal Region (SR) and multiple Control Regions (CRs) to constrain backgrounds.

• Signal Region (SR) Criteria:

  • Trigger: $p_T^{miss} > 120$ GeV and $H_T^{miss} > 120$ GeV.
  • Hadronic Recoil ($U$): $U > 250$ GeV (where $U$ is the magnitude of the vector sum of $p_T^{miss}$ and identified leptons; in this signal, $U \approx p_T^{miss}$).
  • Jet Requirements:
    • One leading AK15 jet with $p_T > 160$ GeV and $|\eta| < 2.4$.
    • Soft-drop mass ($m_{SD}$) of the AK15 jet in the range $[40, 300]$ GeV.
    • The jet must pass a DEEPAK15 deep neural network tagger requirement (optimized for $b\bar{b}$ origin) with a mass-decorrelated output to avoid biasing the mass spectrum.
  • Lepton/Veto: Events with isolated electrons, muons, or hadronic taus are vetoed to suppress $W/Z$+jets and $t\bar{t}$ backgrounds.
  • Quality Cuts: Veto on events with anomalous $p_T^{miss}$ due to detector malfunctions or pileup.

• Control Regions (CRs):

  • ZCR: Enriched in $Z(\to\nu\nu)$+jets by inverting the DEEPAK15 requirement.
  • WMPCR/WEPCR: Enriched in $W(\to\ell\nu)$+jets by requiring exactly one tight muon or electron (passing DEEPAK15).
  • WMFCR/WEFCR: $W$-enriched regions failing the DEEPAK15 requirement.
  • TTMCR/TTECR: $t\bar{t}$-enriched regions with single leptons and at least one extra $b$-tagged AK4 jet.

Background Estimation

A simultaneous maximum likelihood fit is performed across the SR and all CRs.

• Dominant Backgrounds: $Z(\to\nu\nu)$+jets, $W(\to\ell\nu)$+jets, and $t\bar{t}$.
• Method: The yields of dominant backgrounds in the SR are treated as free parameters, constrained by data in the CRs using transfer factors (ratios of simulated spectra between SR and CRs).
• Subdominant Backgrounds: $VV$, single top, $H \to b\bar{b}$, DY+jets, and QCD multijets are estimated directly from simulation with normalization uncertainties.

Systematic Uncertainties

Key uncertainties include:

• Experimental: Jet energy scale/resolution, $b$-tagging efficiency (DEEPJET), $H_D$ tagging efficiency (DEEPAK15), lepton identification, trigger efficiency, and pileup modeling.
• Theoretical: Parton distribution functions (NNPDF), higher-order QCD/EW corrections (NLO/NNLO), and modeling of the $p_T$ spectrum of vector bosons.
• Normalization: Large uncertainties (up to 100%) assigned to QCD multijet backgrounds due to misidentification.

3. Key Contributions

1. First CMS Search in this Mass Range: While previous ATLAS and CMS searches focused on heavy $H_D$ ($>160$ GeV) decaying to $WW$, this paper provides the first comprehensive CMS search for light dark Higgs bosons ($50 \le m_{H_D} \le 150$ GeV) decaying to $b\bar{b}$.
2. Advanced Tagging: Utilization of the mass-decorrelated DEEPAK15 tagger. This technique uses adversarial training to ensure the tagger's output score is uncorrelated with the jet mass, preserving the ability to search for a resonant peak in the $m_{SD}$ distribution without shaping the background.
3. Comprehensive Fit Strategy: A joint fit across multiple years (2016–2018) and regions (SR + CRs) allows for robust data-driven constraints on the dominant $Z$+jets and $W$+jets backgrounds, reducing reliance on pure simulation.

4. Results

• Observation: No significant excess of events was observed above the expected Standard Model background in the SR. The data is consistent with the background-only hypothesis.
• Exclusion Limits:
  • Upper limits on the signal strength ($\mu = \sigma/\sigma_{theory}$) were set at 95% Confidence Level (CL).
  • Mediator Mass ($m_{Z'}$) Exclusions:
    • For $m_{H_D} = 50$ GeV, mediator masses up to 4.5 TeV are excluded.
    • For $m_{H_D} = 150$ GeV, mediator masses up to 2.5 TeV are excluded.
  • These limits assume benchmark couplings: $g_{Z\chi} = 1.0$ (DM-mediator), $g_q = 0.25$ (quark-mediator), and a mixing angle $\theta_h = 0.01$.
• Comparison: The results are more stringent than previous ATLAS results for the same final state, excluding larger values of $m_{Z'}$ for the tested $m_{H_D}$ range.

5. Significance

This study represents a significant step in the search for simplified dark sector models at the LHC.

• Completing the Picture: By covering the low-mass region ($<160$ GeV) where $H_D \to b\bar{b}$ is dominant, this analysis complements existing searches for heavy dark Higgs bosons, providing a complete coverage of the parameter space for this specific model.
• Stringent Constraints: The exclusion of mediator masses up to 4.5 TeV places some of the most stringent limits to date on this specific dark sector scenario, significantly constraining the parameter space for models where DM annihilation proceeds via dark Higgs bosons.
• Methodological Benchmark: The successful application of mass-decorrelated deep learning taggers for resonant searches in the $b\bar{b}$ channel sets a precedent for future analyses targeting boosted heavy resonances in the presence of large missing energy.

In summary, while no new physics was discovered, the analysis successfully ruled out a wide range of theoretically motivated dark matter scenarios, pushing the boundaries of sensitivity for dark sector mediators at the energy frontier.