[Paper Review] Neutralino Proton Cross Sections For Dark Matter In SUGRA And D-BRANE Models

R. Arnowitt, Bhaskar Dutta+1 more|arXiv (Cornell University)|May 16, 2000

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper computes neutralino-proton spin-independent cross sections in mSUGRA, nonuniversal SUGRA, and D-brane models to assess detectability by direct dark matter experiments. It finds that nonuniversal models can achieve large cross sections at low tan β (≥4), while mSUGRA requires tan β ≥25, and CP-violating phases reduce cross sections by a factor of 2–3 with significant fine-tuning.

ABSTRACT

Neutralino proton cross sections are examined for models with R-parity invariance with universal soft breaking (mSUGRA) models, nonuniversal SUGRA models, and D-brane models. The region of parameter space where current dark matter detectors are sensitive, i.e. $1 imes 10^{-6}$ pb, is examined. For mSUGRA models, detectors are sampling parts of the parametr space for tan$β>\sim 25$. The nonuniversal models can achieve cross sections that are a factor of 10-100 bigger or smaller then the universal one and in the former case sample regions tan$β>\sim 4$. The D-brane models considered require tan$β>\sim 15$. The inclusion of CP violating phases reduces the cross section by a factor of $\sim$ 2-3 (but also requires considerable fine tuning at the GUT scale). The expected particle spectra at accelerators are examined and seen to differ for each model. Three new regions of possible coannihilation are noted.

Motivation & Objective

• To determine the portion of supersymmetry parameter space accessible to direct dark matter detectors with sensitivity down to 1×10⁻⁶ pb.
• To compare the spin-independent neutralino-proton cross sections across mSUGRA, nonuniversal SUGRA, and D-brane models.
• To assess the impact of CP-violating phases on cross sections and cosmological constraints.
• To identify new coannihilation channels that could affect relic density and detectability.

Proposed method

• Used full one-loop renormalization group equations (RGEs) from the GUT scale (2×10¹⁶ GeV) to the top quark mass (175 GeV), iterating for consistent mass spectra.
• Included L-R mixing in sfermion mass matrices, one-loop corrections to the Higgs and bottom quark masses, and QCD RGE corrections for accuracy.
• Applied leading-order and approximate next-to-leading-order corrections to the b→sγ decay rate.
• Imposed experimental constraints: m_χ±₁ > 94 GeV, m_h > 95 GeV, and B(B→Xₛγ) ∈ [1.8–4.5]×10⁻⁴.
• Used σ_πN = 65 MeV and σ₀ = 30 MeV for proton scattering cross section extraction, with quark mass ratio r = 24.4 ± 1.5.
• Evaluated relic density Ω_χ⁰₁h² within 0.02 to 0.25 to match cosmological observations.

Experimental results

Research questions

• RQ1 What range of SUSY parameters in mSUGRA, nonuniversal SUGRA, and D-brane models yields neutralino-proton cross sections detectable by current experiments (≥1×10⁻⁶ pb)?
• RQ2 How do CP-violating phases affect the spin-independent neutralino-proton cross section and what fine-tuning is required?
• RQ3 In which models can large cross sections be achieved at low tan β, and what are the associated Higgs and squark mass patterns?
• RQ4 What new coannihilation channels emerge in nonuniversal models that could alter relic density and cross section predictions?

Key findings

• In mSUGRA models, current detectors are sensitive only for tan β ≥ 25, with cross sections peaking for light neutralinos (m_χ⁰₁ ≤ 120 GeV) and moderate squark masses (m_d̃ ≈ 400–700 GeV).
• Nonuniversal SUGRA models can enhance or suppress cross sections by factors of 10–100; large cross sections are accessible at tan β ≥ 4, with heavier squarks (m_d̃ ≈ 600–1200 GeV) and lighter Higgs (m_h ≈ 100–110 GeV).
• D-brane models require tan β ≥ 15 for detectable cross sections, and CP-violating phases reduce σ_χ⁰₁−p by a factor of 2–3, demanding fine-tuning of the μ-phase at the GUT scale.
• Three new coannihilation regions are identified: χ̃±₁–χ̃⁰₁ degeneracy in mSUGRA at large tan β, τ̃_R–χ̃⁰₁ degeneracy in nonuniversal SUGRA with δ₅ < 0, and χ̃±₁–χ̃⁰₁ degeneracy in D-brane models for large Θ₁ (~0.8).
• The large cross sections in nonuniversal models at low tan β and high squark masses help reconcile detectable cross sections with low proton decay rates.
• Coannihilation effects are expected to suppress cross sections in regions of high m₀ and m₁/₂, but the paper focuses on maximum theoretical cross sections to assess detectability.