[Paper Review] Precision Observables in the MSSM: Leading Electroweak Two-loop Corrections

S. Heinemeyer, G. Weiglein|ArXiv.org|Feb 26, 2001

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper calculates the leading electroweak two-loop corrections to the ρ-parameter in the Minimal Supersymmetric Standard Model (MSSM) at O(G_F²m_t⁴), deriving a compact analytical expression dependent on the CP-odd Higgs mass M_A and top quark mass m_t. The corrections are shown to exceed the leading O(αα_s) QCD corrections in the MSSM for M_SUSY ≥ 500 GeV and exhibit decoupling in the M_A → ∞ limit, confirming consistency with the Standard Model.

ABSTRACT

The leading electroweak MSSM two-loop corrections to the $ρ$-parameter are calculated. They are obtained by evaluating the two-loop self-energies of the Z and the W boson at O(Gf^2 m_t^4) in the limit of heavy scalar quarks. A very compact expression is derived, depending on the ratio of the CP-odd Higgs boson mass, M_A, and the top quark mass, m_t. Expressions for the limiting cases M_A >> m_t and M_A << m_t are also given. The decoupling of the non-SM contribution in the limit M_A -> oo is verified at the two-loop level. The numerical effect of the leading electroweak MSSM two-loop corrections is analyzed in comparison with the leading corrections of O(Gf^2 m_t^4) in the SM and with the O(alpha alpha_s) corrections in the MSSM.

Motivation & Objective

• To compute the leading electroweak two-loop corrections to the ρ-parameter in the MSSM at O(G_F²m_t⁴) in the heavy squark limit.
• To derive a compact analytical expression for the correction depending only on M_A and m_t.
• To verify the decoupling of MSSM contributions in the M_A → ∞ limit at the two-loop level.
• To compare the numerical impact of these corrections with the leading O(α²) SM result (M_H^SM = 0) and O(αα_s) MSSM corrections from the top-squark sector.
• To assess the phenomenological relevance of these corrections for precision electroweak observables like M_W and sin²θ_eff.

Proposed method

• Evaluates two-loop self-energies of the Z and W bosons at zero momentum transfer in the limit of heavy scalar quarks.
• Uses the effective Higgs sector of the MSSM with only the two Higgs doublets active, neglecting other SUSY particles.
• Derives a compact analytical formula for Δρ at O(G_F²m_t⁴), parameterized by M_A and m_t.
• Applies the decoupling limit M_A → ∞ to verify consistency with the Standard Model result.
• Performs numerical comparisons with the O(α²) SM correction (M_H^SM = 0) and O(αα_s) MSSM corrections from top-squark loops.
• Uses approximate relations δM_W ≈ (M_W / 2) * (c_W² / (c_W² - s_W²)) * Δρ and δsin²θ_eff ≈ - (c_W²s_W² / (c_W² - s_W²)) * Δρ to estimate shifts in precision observables.

Experimental results

Research questions

• RQ1 What is the analytical form of the leading O(G_F²m_t⁴) two-loop correction to Δρ in the MSSM under the heavy squark approximation?
• RQ2 How do the two-loop corrections behave in the limits M_A ≫ m_t and M_A ≪ m_t?
• RQ3 Does the MSSM result correctly reproduce the Standard Model result in the M_A → ∞ decoupling limit?
• RQ4 How do the O(G_F²m_t⁴) corrections compare numerically with the leading O(α²) SM correction (M_H^SM = 0) and the O(αα_s) MSSM corrections?
• RQ5 What is the numerical impact of these corrections on the W boson mass and the effective weak mixing angle?

Key findings

• A compact analytical expression for the O(G_F²m_t⁴) two-loop correction to Δρ is derived, depending only on M_A and m_t.
• The correction exceeds the leading O(αα_s) MSSM correction from the top-squark sector for M_SUSY ≥ 500 GeV.
• For small tanβ and moderate M_A (~300 GeV), the new correction is approximately twice as large as the O(α²) SM result with M_H^SM = 0.
• The correction on δM_W ranges from -1.5 MeV to -2.0 MeV for small tanβ, and remains approximately constant at -1.25 MeV for tanβ = 40.
• The correction on δsin²θ_eff is at most 1 × 10⁻⁵, with a similar tanβ dependence as δM_W.
• The decoupling limit M_A → ∞ is confirmed at the two-loop level, with the MSSM result approaching the SM result for M_H^SM = 0.