Search for dark matter production in association with bottom quarks and a lepton pair in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data, the CMS collaboration performed a first-of-its-kind search for dark matter production associated with bottom quarks and a lepton pair within a 2HDM+a framework, finding no evidence of new physics and setting stringent upper limits on the production cross-sections of heavy Higgs bosons and pseudoscalar mediators.

The Gist

The Big Picture: Hunting the Invisible Ghost

Imagine the universe is filled with a mysterious, invisible substance called Dark Matter. We know it's there because it has gravity (it holds galaxies together), but we've never seen it, touched it, or caught it. It's like a ghost that walks through walls but leaves a shadow.

Scientists at CERN (the European Organization for Nuclear Research) have been trying to catch this ghost by smashing particles together at nearly the speed of light. This paper describes a specific "fishing expedition" using the CMS detector, a massive, high-tech camera the size of a cathedral, to look for a very specific type of ghostly interaction.

The Setup: The Cosmic Pinball Machine

The scientists used the Large Hadron Collider (LHC) to smash protons together. Think of this as a cosmic pinball machine. When the balls (protons) hit each other, they shatter into a shower of new particles.

Usually, when these particles fly out, they hit the walls of the detector and leave a trail. But Dark Matter is a "ghost." It doesn't hit the walls; it just flies right through the detector and disappears into the universe.

How do you know a ghost was there?
You look for Missing Momentum. Imagine you are watching a game of billiards. If you hit the cue ball, and it smashes into a cluster of balls, you expect all the energy to be accounted for. But if one ball suddenly vanishes, the remaining balls will recoil in a weird direction to balance the equation. In the particle world, if the visible particles (like electrons or muons) recoil with a lot of "missing" energy, it suggests something invisible (Dark Matter) flew away.

The Specific Hunt: The "Bottom Quark" Connection

In the past, scientists looked for Dark Matter appearing alone or with simple particles. This paper focuses on a more complex, "exotic" scenario based on a theory called 2HDM+a (Two Higgs Doublet Model plus a pseudoscalar).

Here is the story the scientists are looking for:

1. The Heavy Higgs (H): A heavy, new particle is created.
2. The Bottom Quark Pair: This heavy particle is produced alongside a pair of "bottom quarks" (heavy cousins of the particles that make up protons). Think of these as the "bouncers" at the club; their presence is a specific signature of this theory.
3. The Decay: The heavy particle (H) splits apart.
   • One part becomes a Z boson, which immediately decays into a pair of visible leptons (electrons or muons). These are the "flashy lights" we can see.
   • The other part becomes a pseudoscalar (a), which acts as a "bridge" or "mediator."
4. The Ghost Exit: This bridge (a) then decays into two Dark Matter particles (χ). These two ghosts fly away, taking their energy with them, leaving the detector with a huge amount of Missing Transverse Momentum.

The Analogy: Imagine a magician (the Heavy Higgs) appears on stage. He is flanked by two heavy guards (the bottom quarks). He pulls a rabbit out of a hat (the Z boson/leptons), which is visible. But then, he pulls out a bag of invisible sand (Dark Matter) that vanishes instantly. The stage shakes (Missing Momentum) because the sand took energy with it. The scientists are looking for that specific combination: Guards + Visible Rabbit + Invisible Sand.

The Search: Filtering the Noise

The problem is that the universe is messy. Many other processes can look like this "ghost" event by accident.

• Sometimes, a particle flies out of the detector without being seen (like a neutrino), creating fake missing energy.
• Sometimes, the detector misreads a particle's speed.

To find the signal, the scientists used a Machine Learning "Filter" (a neural network).

• They fed the computer thousands of simulated examples of what the "Ghost Signal" looks like versus what "Background Noise" looks like.
• The computer learned to spot subtle patterns in the angles, speeds, and energies of the particles.
• It gave every event a "score." High scores meant "This looks like a Ghost!" Low scores meant "This is just background noise."

The Results: The Ghost Remains Elusive

After analyzing 138 "femtobarns" of data (which is a massive amount of particle collision data, equivalent to 13 years of the LHC running at full speed), the scientists looked at the results.

The Verdict: They found zero evidence of Dark Matter being produced in this specific way.

• The number of "Ghost-like" events they saw matched exactly what they expected from standard physics (background noise).
• The "Missing Momentum" they saw was just the usual background static, not a new particle.

What Does This Mean? (The "Exclusion Zone")

Even though they didn't find the ghost, the search wasn't a failure. It's like searching a dark room with a flashlight. You didn't find the cat, but you proved the cat isn't hiding in the corner you just scanned.

The paper draws a map of the "Dark Matter Universe" and says:

• "We have checked the area where the Heavy Higgs has a mass between 400 and 2000 GeV."
• "We have checked the area where the 'bridge' particle has specific masses."
• "If Dark Matter exists with these specific properties, it would have been brighter than our background noise. Since we didn't see it, we can rule out those specific possibilities."

They set strict limits (upper limits) on how likely it is for this specific type of Dark Matter to exist. If it does exist, it must be much rarer or have different properties than the ones they tested.

Summary

This paper is a high-tech "search and destroy" mission for a specific theory of Dark Matter.

1. The Theory: Dark Matter is made via a heavy particle that also produces bottom quarks and a visible Z boson.
2. The Method: Smash protons, look for bottom quarks + visible electrons/muons + missing energy, and use AI to filter out the noise.
3. The Outcome: No Dark Matter found.
4. The Takeaway: We have successfully crossed off a large chunk of the "Dark Matter map," telling future scientists, "Don't look here; the ghost isn't hiding in this specific room."

Technical Summary

Technical Summary: Search for Dark Matter Production in Association with Bottom Quarks and a Lepton Pair

Problem and Motivation
The nature of dark matter (DM) remains unknown, with Weakly Interacting Massive Particles (WIMPs) being a leading hypothesis. While direct and indirect detection methods are active, collider searches offer a complementary approach by producing DM particles in controlled environments. A specific motivation for this analysis arises from the Fermi-LAT observation of a gamma-ray excess in the Galactic Center, which could be interpreted as DM annihilating into bottom quark-antiquark ($b\bar{b}$) pairs. This interpretation suggests the existence of a pseudoscalar mediator connecting the Standard Model (SM) and the dark sector, potentially leading to spin-dependent interactions that evade current direct detection limits.

Theoretical frameworks such as the Two Higgs Doublet Model plus a pseudoscalar (2HDM+a) provide a gauge-invariant mechanism for such a mediator. In this model, a heavy neutral Higgs boson ($H$) can be produced in association with a $b\bar{b}$ pair and decay into a $Z$ boson and a pseudoscalar mediator ($a$). The $Z$ boson decays leptonically ($Z \to \ell\bar{\ell}$), while the pseudoscalar decays into a pair of DM particles ($a \to \chi\bar{\chi}$), resulting in a final state characterized by a $b\bar{b}$ pair, a lepton pair, and significant missing transverse momentum ($p^{\text{miss}}_T$). This paper presents the first dedicated LHC search for this specific signature.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$ (2016–2018).

• Event Reconstruction and Selection: Events are selected requiring exactly two opposite-sign, same-flavor leptons (electrons or muons) with an invariant mass near the $Z$ boson mass ($m_Z$), at least one $b$-tagged jet, and $p^{\text{miss}}_T > 65$ GeV. To suppress the dominant $t\bar{t}$ background, an analytical reconstruction method is employed to identify and reject events consistent with dileptonic $t\bar{t}$ decays.
• Multivariate Analysis: A Multi-Layer Perceptron (MLP) neural network is trained to discriminate between signal and background. The input variables include kinematic properties of the leptons, the dilepton system, and $p^{\text{miss}}_T$, specifically the transverse mass ($m_T^{\ell\ell, p^{\text{miss}}_T}$) and the $m_{T2}$ variable. Jet kinematics are excluded from the MLP inputs to avoid propagating modeling uncertainties. The MLP output is transformed into an "MLP4" score, which is used to define 17 search bins in the Signal Region (SR).
• Background Estimation: Backgrounds from SM processes (Drell-Yan, $t\bar{t}$, single top, $WZ$, and $ZZ$) are estimated using a combination of simulation and data-driven methods. Control Regions (CRs) enriched in specific background processes (DY, $t\bar{t}$, $WZ$, $ZZ$) are defined to constrain normalization factors via a simultaneous maximum likelihood fit. Corrections for theoretical uncertainties (e.g., NNLO QCD corrections for $t\bar{t}$ and $WZ$) and experimental effects (e.g., jet energy scale, $p^{\text{miss}}_T$ resolution) are applied.
• Statistical Interpretation: A binned maximum likelihood fit is performed across the CRs and the 17 SR bins. Upper limits on the signal cross-section are set using the $CL_s$ method.

Key Contributions

• Novel Search Channel: This work constitutes the first dedicated experimental search at the LHC for the associated production of a heavy Higgs boson with a $b\bar{b}$ pair, followed by the decay chain $H \to Za \to (\ell\bar{\ell})(\chi\bar{\chi})$.
• Model-Specific Constraints: The analysis translates observed limits into constraints on the parameter space of the 2HDM+a benchmark model, specifically probing the masses of the heavy scalar ($m_H$) and pseudoscalar ($m_a$), the ratio of vacuum expectation values ($\tan \beta$), and the mixing angle ($\sin \theta$).
• Cosmological Correlation: The derived constraints are compared against regions of parameter space favored by cosmological predictions for the DM relic density, assuming thermal freeze-out.

Results

• Observation: The observed data are consistent with the SM background expectations. No significant excess of events is found. The maximum local significance for an excess is below 0.7 standard deviations, occurring for a signal hypothesis with $m_H = 2000$ GeV and $m_a = 400$ GeV.
• Exclusion Limits: 95% confidence level (CL) upper limits are set on the product of the production cross-section and branching fractions ($\sigma \mathcal{B}$). The limits range from approximately $10^{-2}$ pb for $m_H = 400$ GeV to $10^{-3}$ pb for $m_H = 2000$ GeV.
• Parameter Space Constraints: In the 2HDM+a context, the analysis excludes heavy scalar masses up to 900 GeV for small pseudoscalar masses. For $\tan \beta \sim 25$, masses of the heavy scalar up to $\sim 1.1$ TeV are excluded. The analysis demonstrates sensitivity to intermediate values of $\sin \theta$ (around 0.1–0.35) and large $\tan \beta$ values, regions that are often difficult to probe with other search channels.
• Background Modeling: The fit reveals that the normalizations for $WZ$ and $ZZ$ backgrounds require significant upward adjustments (101% and 113%, respectively) compared to theoretical predictions, attributed to the specific phase space requirements (large $p^{\text{miss}}_T$ and $b$-jets) and known limitations in diboson modeling with additional heavy flavor.

Significance
The paper claims significance primarily through the exploration of a previously untested signature that connects the Galactic Center gamma-ray excess to collider physics. By targeting the 2HDM+a model, the analysis probes regions of parameter space characterized by large $\tan \beta$ and specific mixing angles that are favored by cosmological relic density calculations but remain inaccessible to searches for DM production in association with other final states (e.g., mono-jet or mono-Z without $b$-tags). The results provide the first experimental constraints on this specific production mechanism, effectively ruling out significant portions of the parameter space preferred by the DM interpretation of the Galactic Center excess for the benchmark scenarios considered.