[Paper Review] Lightest Neutralino Mass in the MNSSM

S. Hesselbach, D.J. Miller+3 more|ArXiv.org|Oct 2, 2008

Nuclear physics research studies1 references13 citations

TL;DR

This paper establishes a theoretical upper bound on the lightest neutralino mass in the minimal non-minimal supersymmetric standard model (MNSSM), showing it is constrained to ≤80–85 GeV due to the interplay between the effective μ-term (μ_eff) and the singlet coupling λ. The authors derive an approximate analytical solution for the lightest neutralino mass using a simplified characteristic equation, validated numerically, and demonstrate it remains light even at high SUSY scales, distinguishing MNSSM from other SUSY models.

ABSTRACT

We argue that the allowed range of the mass of the lightest neutralino in the MNSSM is limited. We establish the theoretical upper bound on the lightest neutralino mass and obtain an approximate solution for this mass.

Motivation & Objective

• To determine the theoretical upper bound on the mass of the lightest neutralino in the MNSSM, a supersymmetric extension that solves the μ-problem without domain walls.
• To analyze the neutralino mass matrix structure in the MNSSM, particularly the role of the singlet superfield S and its vacuum expectation value in generating an effective μ-term.
• To derive an approximate analytical solution for the lightest neutralino mass that remains accurate across a wide range of parameter space.
• To compare the approximate solution with full numerical diagonalization and validate its accuracy.
• To establish that the lightest neutralino remains light (≤85 GeV) even in the limit of high SUSY breaking scales, contrasting with the MSSM.

Proposed method

• Construct the 5×5 neutralino mass matrix in the MNSSM using the superfield basis (B̃, W̃₃, H̃₀d, H̃₀u, S̃), incorporating M₁, M₂, μ_eff, λ, and tanβ.
• Transform the matrix to a basis where the bottom-right 2×2 block isolates the Higgsino–singlino sector, enabling analysis of the lightest neutralino mass via eigenvalues.
• Derive the characteristic equation for the neutralino mass eigenvalues, then simplify it by neglecting higher-order κ terms (κ³, κ⁴, κ⁵) under the assumption that m_χ₁⁰ ≪ other neutralino masses.
• Reduce the characteristic equation to a quadratic form: κ² - Bκ + C = 0, with B and C expressed in terms of μ_eff, ν = λv/√2, M₁, M₂, and M_Z.
• Use the quadratic formula to compute the lightest neutralino mass as the smaller root: |m_χ₁⁰| = min{½|B - √(B² - 4C)|, ½|B + √(B² - 4C)|}.
• Validate the approximate solution against full numerical diagonalization across varying μ_eff, M₂, tanβ, and λ, showing high accuracy.

Experimental results

Research questions

• RQ1 What is the theoretical upper bound on the mass of the lightest neutralino in the MNSSM, given the constraints on μ_eff and λ?
• RQ2 How does the lightest neutralino mass depend on μ_eff, M₂, and tanβ in the MNSSM?
• RQ3 Can a simplified analytical approximation accurately reproduce the lightest neutralino mass without full numerical diagonalization?
• RQ4 Does the lightest neutralino remain light even in the high-scale SUSY breaking limit, and what does this imply for its detection?
• RQ5 How does the mass of the lightest neutralino behave in the limit λ → 0, and what is its dependence on μ_eff and tanβ?

Key findings

• The lightest neutralino mass in the MNSSM is theoretically bounded above by 80–85 GeV, derived from constraints on μ_eff > 90–100 GeV and λ ≤ 0.7 at the Z-boson scale.
• The approximate analytical solution for the lightest neutralino mass, derived from a quadratic approximation of the characteristic equation, matches numerical results with high accuracy across the parameter space.
• When μ_eff ≫ M_Z and M₁, M₂ are large, the lightest neutralino mass scales as |m_χ₁⁰| ≈ |μ_eff ν² sin 2β| / (μ_eff² + ν²), showing inverse proportionality to μ_eff.
• The lightest neutralino mass vanishes in the limit λ → 0, scaling as λ², indicating it becomes predominantly singlino-like in this regime.
• For λ = 0.7 and M₂ = 200 GeV, the lightest neutralino mass decreases from ~85 GeV at μ_eff = 100 GeV to ~50 GeV at μ_eff = 500 GeV, consistent with the theoretical bound.
• The lightest neutralino remains predominantly singlino when m_χ₁⁰ ≪ M_Z, making it challenging to detect at future colliders due to its weak couplings.