Distinguishing Higgs portal and neutralino dark matter via vector boson fusion

This paper demonstrates that vector boson fusion processes at the LHC can distinguish between Higgs portal and neutralino dark matter scenarios with over $5\sigma$ confidence by exploiting characteristic differences in jet transverse momentum and kinematic variables like $\Delta\eta$ and $\Delta\phi$.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle smasher. Scientists are trying to solve a cosmic mystery: Dark Matter. We know it's there because it holds galaxies together, but we've never seen it. The big question is: What exactly is it made of?

This paper acts like a detective's guidebook for the future. It proposes a way to tell two very different "suspects" apart if we catch them at the collider. The two suspects are:

1. The "Higgs Portal" Dark Matter: A particle that only talks to the rest of the universe through the Higgs boson (the particle that gives things mass).
2. The "Neutralino" Dark Matter: A particle that comes from a theory called Supersymmetry, where every known particle has a heavier, invisible "twin."

The Crime Scene: Vector Boson Fusion (VBF)

To catch these invisible particles, the scientists look for a specific event called Vector Boson Fusion (VBF).

Think of two protons (the particles in the collider) as two people throwing a ball (a weak force carrier) at each other. Instead of hitting each other directly, they throw these balls, which crash together and create a pair of invisible Dark Matter particles.

• The Clue: Because the "balls" were thrown, the two people (the protons) recoil and shoot two jets of debris (particles) forward.
• The Mystery: The Dark Matter flies away unseen, leaving behind a "missing energy" gap. The scientists see the two jets and the missing energy, but they don't know which type of Dark Matter was created.

The Detective's Tool: How the Jets Dance

The paper argues that the two suspects leave different "footprints" in how those two jets fly away. It's all about the polarization of the force carriers, which is a fancy way of describing how the "balls" spin or vibrate.

• The Higgs Portal Suspect: This suspect prefers to use "longitudinal" balls (imagine a ball vibrating back and forth along its path). When these collide, the resulting jets are softer (less energetic) and tend to fly more straight ahead.
• The Neutralino Suspect: This suspect prefers "transverse" balls (imagine a ball spinning wildly side-to-side). When these collide, the resulting jets are harder (more energetic) and fly out at wider angles.

The Analogy:
Imagine two different types of fireworks exploding in the sky.

• The Higgs Portal explosion sends sparks drifting gently downward in a tight, soft cluster.
• The Neutralino explosion sends sparks shooting out violently and widely.
  Even if you can't see the firework itself (the Dark Matter), the pattern of the sparks (the jets) tells you exactly which type of firework it was.

The Investigation: Measuring the Angles

The researchers looked at specific measurements to prove this difference:

1. The Gap (∆η): How far apart the two jets are in the sky. The Higgs Portal jets are usually closer together in a specific way compared to the Neutralino jets.
2. The Twist (∆ϕ): The angle between the jets. The paper found that for Higgs Portal events, the jets tend to line up in a specific way that is the opposite of how Neutralino jets line up.

The Verdict: Can We Tell Them Apart?

To be sure, the scientists used a statistical tool called the Kolmogorov–Smirnov test (think of it as a super-precise ruler) combined with a method called Linear Discriminant Analysis (a way to combine all the clues into one big score).

They simulated billions of collisions at the future "High-Luminosity" version of the LHC (which will be much more powerful than today's).

• The Result: They found that they could distinguish between the Higgs Portal and Neutralino suspects with extreme confidence (more than 99.99% certainty, or "5 sigma").
• The Nuance: They could also tell the difference between the two types of Neutralinos (Wino vs. Higgsino), though it was a bit harder. Interestingly, they found it was very difficult to tell the difference between the two types of Higgs Portal suspects (scalar vs. fermionic), as they look almost identical.

The Bottom Line

This paper doesn't claim to have found Dark Matter yet. Instead, it proves a principle: If we do find Dark Matter at the LHC in the future, we won't just know that we found it; we will be able to tell what kind it is by looking at the angle and energy of the debris jets flying around it. It's like being able to identify a thief not just by the fact that a window was broken, but by the specific pattern of the shattered glass on the floor.

Technical Summary

Technical Summary: Distinguishing Higgs Portal and Neutralino Dark Matter via Vector Boson Fusion

Problem Statement
While the Standard Model (SM) successfully describes known elementary particles, it lacks a viable candidate for dark matter (DM), a fact firmly established by astrophysical and cosmological observations. Numerous extensions to the SM propose new particles to account for the observed DM relic abundance. A critical challenge in particle physics is not merely detecting DM but distinguishing between competing theoretical frameworks. This paper addresses the feasibility of differentiating between Higgs portal DM (HPDM) and neutralino DM (specifically wino- and higgsino-like scenarios) using collider signatures at the Large Hadron Collider (LHC). The authors focus on the Vector Boson Fusion (VBF) channel leading to a di-jet plus missing transverse energy ($2j + \not{E}_T$) final state, a process characterized by lower backgrounds compared to other DM search channels.

Methodology
The study employs a proof-of-principle approach to analyze VBF production mechanisms at the High-Luminosity LHC (HL-LHC) with a center-of-mass energy of $\sqrt{s} = 14$ TeV and an integrated luminosity of $3 \text{ ab}^{-1}$.

1. Theoretical Frameworks:

   • Higgs Portal DM (HPDM): The authors consider both fermionic (HPF-DM) and scalar (HPS-DM) DM candidates. In these models, DM interacts with the SM exclusively via the Higgs boson. For fermionic DM, a singlet scalar mediator is introduced. The analysis utilizes specific benchmark points (e.g., $m_\chi = 130$ GeV, $m_{h_2} = 275$ GeV) consistent with LHC constraints on Higgs signal strengths.
   • Neutralino DM: Based on the Minimal Supersymmetric SM (MSSM), the study examines scenarios with a compressed electroweakino spectrum where the lightest neutralino ($\chi^0_1$) is the DM candidate. Two benchmarks are analyzed: a bino-wino mixture (Wino-DM) and a higgsino-like state (Higgsino-DM). In these compressed scenarios, chargino decays yield soft visible particles that fail reconstruction, effectively resulting in the same $2j + \not{E}_T$ final state.

2. Simulation and Analysis:

   • Event generation was performed using MadGraph5 aMC@NLO, followed by parton showering and hadronization with Pythia8, and fast detector simulation using Delphes.
   • The analysis applies kinematic cuts optimized for Higgs-to-invisible decay searches (e.g., $p_{Tj} > 80/40$ GeV, $M_{jj} > 2500$ GeV, $|\Delta\eta_{jj}| > 4.0$).
   • Kinematic Discrimination: The authors investigate the polarization of weak bosons in VBF. They posit that HPDM is dominated by longitudinally polarized ($W_L$) boson scattering, leading to softer, more forward jets, whereas neutralino DM (particularly wino-like) is dominated by transversely polarized ($W_T$) scattering, yielding harder jets.
   • Statistical Tests: To quantify the distinguishability between scenarios, the authors employ Linear Discriminant Analysis (LDA) to construct an optimal variable ($LD_1$) from a set of kinematic observables ($p_{Tj}$, $M_{jj}$, $\Delta\eta$, $\Delta\phi$, $\not{E}_T$, etc.). This single variable is then subjected to a Kolmogorov–Smirnov (KS) test to determine the confidence level (C.L.) of separation between hypotheses.

Key Contributions and Results

• Kinematic Features: The study confirms that the polarization structure of the exchanged vector bosons significantly shapes the transverse momentum distributions of the tagged jets. HPDM jets are found to be less energetic in the transverse direction compared to neutralino DM jets.
• Angular Variables: Significant differences are observed in the angular separations of the forward jets. Specifically, the azimuthal separation ($\Delta\phi_{jj}$) peaks near zero for HPDM but near $\pi/2$ for SUSY scenarios. An asymmetry variable $A_{\Delta\phi}$ is constructed, showing negative values for HPDM and positive values for neutralino DM.
• Statistical Significance:
  • Signal Yields: After applying VBF cuts, the expected signal significances ($S/\sqrt{B}$) for the individual scenarios range from $\sim 1\sigma$ (Higgsino-DM) to $\sim 5.7\sigma$ (HPS-DM).
  • Discrimination Power: The KS test results demonstrate that HPDM signals (both scalar and fermionic) can be distinguished from neutralino DM signals (Wino-DM) with a confidence level exceeding 99.99% (corresponding to $>5\sigma$).
  • Sub-discrimination: While HPDM and neutralino DM are clearly separable, the distinction between scalar and fermionic HPDM is weaker (84% C.L.), and the separation between wino- and higgsino-like neutralinos is moderate (90% C.L.).
• Variable Importance: The analysis identifies $\Delta\eta_{jj}$ as the dominant variable for separating HPDM from neutralino DM, while $\Delta\phi_{j\not{E}_T}$ is most significant for distinguishing between wino- and higgsino-like neutralinos.

Significance and Claims
The paper claims to establish the viability of collider-based discrimination between different dark matter models using VBF observables. It serves as a proof of principle that the polarization structure of weak bosons, combined with specific angular observables like $\Delta\eta$ and $\Delta\phi$, provides a robust framework for distinguishing Higgs portal DM from neutralino DM. The authors emphasize that while their benchmark points are chosen to demonstrate this discriminating power rather than to strictly reproduce the observed relic density, the results suggest that the HL-LHC could effectively probe the nature of the DM candidate and the underlying theoretical framework if such signals are observed. The study concludes that VBF processes offer a powerful and complementary probe to mono-jet searches for characterizing the properties of dark matter.