[Paper Review] Pseudo-Dirac Dark Matter Leaves a Trace

Andrea De Simone, Verónica Sanz+1 more|DSpace@MIT (Massachusetts Institute of Technology)|Apr 9, 2010

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper proposes pseudo-Dirac Dark Matter (pDDM) as a viable dark matter candidate that leaves a detectable displaced vertex signal at colliders due to a small mass splitting between two nearly degenerate states. The model enables direct measurement of the dark matter mass and splitting via decay length and invariant mass reconstruction, offering a unique, testable collider signature beyond missing energy alone.

ABSTRACT

Pseudo-Dirac Dark Matter is a viable type of dark matter which originates from a new Dirac fermion whose two Weyl states get slightly split in mass by a small Majorana term. The decay of the heavier to the lighter state naturally occurs over a detectable length scale. Thus, whenever pseudo-Dirac Dark Matter is produced in a collider, it leaves a clear trace: a visible displaced vertex in association with missing energy. Moreover, pseudo-Dirac Dark Matter behaves Dirac-like for relic abundance and Majorana-like in direct detection experiments: it has efficient s-wave annihilations but it lacks of dangerous vector interactions with the quarks in the nuclei. We provide a general treatment using an effective field theory approach, then specializing to the supersymmetric situation of a pseudo-Dirac Bino. The dark matter mass and the mass splitting can be extracted from measurements of the decay length and the invariant mass of the products, even in presence of missing energy.

Motivation & Objective

• To propose a dark matter model that produces observable collider signals through displaced vertices, overcoming the indirect inference of dark matter via missing energy.
• To demonstrate that a small mass splitting in a pseudo-Dirac fermion system naturally leads to a detectable decay length within collider detector ranges.
• To show that pDDM achieves correct relic abundance via s-wave coannihilations while avoiding dangerous vector interactions in direct detection.
• To provide a framework for measuring the dark matter mass and splitting using displaced vertex and di-lepton edge observables.
• To connect cosmological dark matter abundance to measurable collider parameters through a predictive relation.

Proposed method

• Formulate a pseudo-Dirac fermion model with a Dirac mass at the electroweak scale and a small Majorana mass splitting, preserving an approximate U(1) symmetry.
• Use an effective field theory approach to describe interactions between the pDDM state and the Standard Model via dimension-6 operators suppressed by a scale Λ.
• Derive the decay length of the heavier state into the lighter dark matter state, showing it scales as L₀ ∝ (Δm)⁻⁵ for fixed DM mass.
• Compute the relic abundance using s-wave coannihilation between the two nearly degenerate states, ensuring agreement with ΩDMh² ≈ 0.11.
• Analyze direct detection cross sections, showing suppression of vector-like interactions with quarks due to momentum transfer being much smaller than the mass splitting.
• Construct a collider analysis strategy using displaced vertex reconstruction and di-lepton invariant mass edge to extract Δm and m₁.

Experimental results

Research questions

• RQ1 Can a pseudo-Dirac dark matter model produce a displaced vertex signal at colliders that is both detectable and measurable?
• RQ2 How does the mass splitting Δm between the two pDDM states determine the decay length, and can this be measured at current or future colliders?
• RQ3 To what extent does pDDM evade direct detection constraints while maintaining a correct relic abundance?
• RQ4 Can the combination of displaced vertex and di-lepton edge measurements allow for independent determination of the dark matter mass and splitting?
• RQ5 What is the connection between the observed dark matter relic density and the measurable parameters of the pDDM sector at colliders?

Key findings

• The decay length of the heavier pDDM state is predicted to be in the range of a few centimeters to tens of centimeters, making it detectable in collider experiments.
• The decay length scales as L₀ ≈ 30 cm × (ΩDMh²/0.11) × (m₁/100 GeV)² × (1 GeV/Δm)⁵ × exp(–24Δm/m₁), linking cosmology to collider observables.
• The di-lepton invariant mass edge from the decay of the heavier state provides a direct measurement of the mass splitting Δm.
• The model achieves correct relic abundance via s-wave coannihilations between the two nearly degenerate states, even with a small mass splitting.
• Vector-like interactions with quarks are suppressed in direct detection due to momentum transfer being much smaller than Δm, making pDDM compatible with current experimental limits.
• In the supersymmetric realization, the pDDM scenario predicts a slepton mass of mℓ̃R ≈ 202 GeV × (ΩDMh²/0.11)¹/⁴ × (m₁/100 GeV)¹/² × exp(–6Δm/m₁), linking collider and cosmological parameters.