Search for pair production of additional neutral scalars within the Inert Doublet Model in a final state with two electrons or two muons in proton-proton collisions at $\sqrt{s}$ = 13 TeV and 13.6 TeV

Using proton-proton collision data at 13 and 13.6 TeV collected by the CMS detector, this study performs the first dedicated search for pair-produced inert scalars in the Inert Doublet Model via a dilepton plus missing transverse momentum final state, finding no significant excess and setting 95% confidence level exclusion limits on the masses of the new neutral scalars.

The Gist

The Big Picture: Hunting for Invisible Ghosts

Imagine the universe is a giant, bustling city. We know almost everything about the people living there (the "Standard Model" of physics), but we also know there are "ghosts" (Dark Matter) that make up most of the city's mass. We can't see them, but we know they are there because they have weight and gravity.

The Inert Doublet Model (IDM) is a specific theory about what these ghosts might look like. It suggests that alongside our familiar particles, there is a hidden "shadow family" of particles. The lightest member of this shadow family, called H, is stable and invisible. It's a perfect candidate for a Dark Matter ghost.

This paper describes a massive experiment at CERN's Large Hadron Collider (LHC) where scientists tried to catch these ghosts in the act.

The Setup: A High-Speed Particle Smash

Think of the LHC as a giant, circular racetrack where protons (tiny subatomic particles) are zooming around at nearly the speed of light. The scientists smash two streams of these protons together head-on.

When they crash, the energy is so intense that it can create new, heavy particles. The scientists are looking for a specific event:

1. Two protons smash together.
2. They create a pair of new, heavy "shadow" particles (let's call them A and H).
3. Particle A is unstable and immediately decays (breaks apart) into a known particle (a Z boson) and another H.
4. The Z boson then decays into a pair of visible, charged particles: either two electrons or two muons (which are like heavy electrons).
5. The two H particles? They are the ghosts. They don't interact with the detector, so they just fly away, taking energy with them.

The Clue: Because the ghosts fly away unseen, the detector sees a pair of visible particles (the electrons/muons) that seem to be recoiling against nothing. This "missing energy" is the smoking gun that a ghost was there.

The Detective Work: Filtering the Noise

The problem is that the racetrack is messy. Every time protons smash, they create billions of "normal" events (Standard Model background) that look very similar to the ghost signal. It's like trying to find a specific rare coin in a pile of a billion other coins.

To find the needle in the haystack, the scientists used a three-step filter:

1. The Rough Filter (Pre-selection): They threw out any crash that didn't have exactly two electrons or two muons, or if there was too much "debris" (jets of other particles) flying around. They also looked for the specific "missing energy" signature.
2. The Smart Filter (The Neural Network): This is the paper's main innovation. Instead of just looking at one number (like "how much energy is missing?"), they used a Parameterised Neural Network (pNN).
   • Analogy: Imagine a security guard at a club. A normal guard checks your ID. A "smart" guard knows exactly what the VIPs look like for every possible VIP. This neural network was trained to recognize the specific "shape" of the signal for every possible mass of the ghost particle. It learned to say, "If the ghost weighs 70 GeV, look for this pattern. If it weighs 100 GeV, look for that pattern."
3. The Control Groups: To make sure they weren't tricked by the background noise, they set up "Control Regions." These are areas of the data where they know only normal background events should exist. They used these to calibrate their expectations, ensuring that if they saw something in the main area, it was real and not just a glitch in their math.

The Results: No Ghosts Found (Yet)

After analyzing data from 2016 to 2022 (a massive amount of information, equivalent to 172 "inverse femtobarns" of collisions), the scientists looked at the results.

• The Verdict: They found no significant excess of events. The number of "ghost-like" crashes they saw matched exactly what they expected from normal physics.
• The Exclusion Zone: Even though they didn't find the ghosts, they learned something valuable: The ghosts don't exist in the range we looked.
  • They ruled out the possibility that the "H" ghost has a mass between 60 and 180 GeV, depending on how heavy the "A" partner is.
  • Specifically, they can now say with 95% confidence that if these ghosts exist, they are either heavier than 108 GeV or have a different mass relationship than the ones they tested.

Why This Matters

This is the first dedicated search specifically designed to find these Inert Doublet Model particles using this specific method. Previous searches were like looking for a needle in a haystack while wearing blinders; this search used a specialized metal detector (the neural network) tuned specifically for that needle.

While they didn't find the Dark Matter, they have successfully narrowed the search area. They have told the universe: "If you are hiding a Dark Matter particle of this type, you are hiding it in a different mass range than we just checked." This forces theorists to update their maps and guides future experiments on where to look next.

In short: The scientists smashed particles, used a super-smart AI to look for invisible ghosts, found none, and successfully crossed off a huge section of the "Where to look" map.

Technical Summary

Technical Summary: Search for Pair Production of Additional Neutral Scalars within the Inert Doublet Model

Problem and Motivation
The Standard Model (SM) of particle physics fails to account for dark matter (DM), despite cosmological observations indicating its abundance. The Inert Doublet Model (IDM) is a well-motivated extension of the SM that introduces a second Higgs doublet protected by an unbroken $Z_2$ symmetry. This symmetry prevents the new scalars from coupling directly to fermions and ensures the stability of the lightest new scalar, $H$, making it a viable weakly interacting massive particle (WIMP) DM candidate. The IDM predicts four additional scalar bosons: two neutral ($H$ and $A$) and two charged ($H^\pm$). While phenomenological studies have explored IDM sensitivity at future colliders, no dedicated experimental search for IDM scalars using collider data had been performed prior to this work. Existing analyses were often insensitive to large portions of the IDM parameter space due to high thresholds on missing transverse momentum ($p_T^{miss}$) or loose constraints upon reinterpretation.

Methodology
This paper presents a search for the pair production of IDM scalars in proton-proton collisions at center-of-mass energies of $\sqrt{s} = 13$ TeV and 13.6 TeV, recorded by the CMS detector. The analysis utilizes an integrated luminosity of 138 fb$^{-1}$ (Run 2, 2016–2018) and 35 fb$^{-1}$ (Run 3, 2022).

• Signal Topology: The primary search channel targets the process $pp \to AH$, where the heavier scalar $A$ decays to $ZH$, and the stable $H$ particles escape detection. The final state consists of exactly two opposite-charge same-flavour (OCSF) leptons (electrons or muons) from the $Z$ boson decay, accompanied by significant missing transverse momentum ($p_T^{miss}$) from the two $H$ particles, and minimal hadronic activity. The analysis focuses on the dilepton invariant mass range $12 < m_{\ell\ell} < 80$ GeV to avoid low-mass resonances and the dominant $Z$-boson peak.
• Event Selection: Events undergo a preselection requiring two tight leptons, $p_T^{miss}$, and kinematic constraints on the dilepton system (e.g., $p_T^{\ell\ell} > 15$ GeV, $\Delta\phi(\vec{p}_T^{\ell\ell}, \vec{p}_T^{miss}) > 1$ rad). A veto is applied on events with additional loose leptons or $b$-tagged jets to suppress $t\bar{t}$ and $W$+jets backgrounds.
• Multivariate Analysis: To separate signal from the remaining SM backgrounds (dominated by $WW$, $t\bar{t}$, $ZZ$, and $WZ$), a parameterised neural network (pNN) is employed. The pNN takes the signal mass parameters ($m_H, m_A$) as inputs alongside 26 kinematic features (including transverse masses, stransverse masses $m_{T2}$, and jet-Z balance). This approach allows a single network to optimize discrimination across the entire parameter space ($m_H \in [60, 180]$ GeV, $m_A - m_H \in [20, 100]$ GeV) and facilitates interpolation between simulated mass points.
• Background Estimation: Background normalizations are constrained using data-driven control regions (CRs) enriched in specific processes:
  • ZZ CR: Four-lepton events with one dilepton pair acting as a neutrino proxy.
  • WW/$t\bar{t}$ CR: Events with opposite-charge different-flavour leptons, split by $b$-jet multiplicity.
  • WZ CR: Three-lepton events.
  • MisID CRs: Same-charge dilepton events to estimate backgrounds from jets misidentified as leptons.
    A simultaneous binned maximum likelihood fit is performed across the signal region (SR) and all CRs.

Key Contributions

• First Dedicated Search: This work constitutes the first dedicated search for IDM scalar pair production using LHC collision data.
• Parameterised Neural Network: The application of a pNN allows for a continuous scan of the IDM parameter space without requiring separate networks for each mass hypothesis, effectively handling the interpolation of signal shapes.
• Comprehensive Background Control: The analysis utilizes a robust set of control regions to constrain dominant backgrounds directly from data, reducing reliance on simulation-only predictions for normalizations.

Results
No significant excess of events over the SM background prediction was observed. The largest local excess corresponds to a $p$-value of approximately 1.5 standard deviations at $m_H = 110$ GeV and $m_A = 145$ GeV.

Exclusion limits at 95% confidence level (CL) were set on the production cross-section of the $AH$ pair as a function of $m_H$ and $m_A - m_H$:

• For a mass splitting of $m_A - m_H = 78$ GeV, the observed (expected) exclusion reaches $m_H = 108$ (106) GeV.
• At $m_H = 70$ GeV, the observed (expected) exclusion covers the range $m_A - m_H = 40\text{--}90$ (35–90) GeV.
• The limits are calculated assuming specific IDM parameters ($\lambda_2 = 1$, $\lambda_{345} = 10^{-6}$, $m_{H^\pm} = m_A + 50$ GeV), though the results are noted to be insensitive to variations in these parameters within their allowed ranges.

Significance
The paper claims that these results represent the first limits on the masses of the neutral scalars in the Inert Doublet Model obtained via a dedicated search using collision data. The derived exclusion contours significantly extend the constraints previously established by direct detection experiments, indirect DM searches, and reinterpretations of LEP data. By covering regions of parameter space not previously excluded, this analysis provides critical experimental input for the viability of the IDM as a dark matter model.