[Paper Review] Testing the MSSM with the Mass of the W Boson

S. Heinemeyer, W. Hollik+3 more|arXiv (Cornell University)|Nov 29, 2006

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the most precise theoretical prediction of the W boson mass (MW) in the Minimal Supersymmetric Standard Model (MSSM), incorporating full one-loop corrections with complex phase dependencies, all available two-loop MSSM corrections, and the full Standard Model result. It reveals that phases in the third-generation squark sector can induce shifts in MW exceeding 20 MeV, with stronger effects at low sfermion masses and large |μ|, and finds a slight preference for the MSSM over the SM given current experimental MW and mt measurements.

ABSTRACT

We review the currently most accurate evaluation of the W boson mass, M_W, in the Minimal Supersymmetric Standard Model (MSSM). It consists of a full one-loop calculation, including the complex phase dependence, all available MSSM two-loop corrections as well as the full Standard Model result. We analyse the impact of the phases in the scalar quark sector on M_W and compare the prediction for M_W based on all known higher-order contributions with the experimental results.

Motivation & Objective

• To provide the most accurate theoretical prediction of the W boson mass (MW) in the MSSM, including all known higher-order quantum corrections.
• To investigate the impact of complex phases in the scalar quark sector—specifically φAt + φμ and φAb + φμ—on MW within the MSSM.
• To compare the MSSM prediction for MW, incorporating all known higher-order contributions, with current experimental data to test the model's viability.
• To assess the sensitivity of MW to variations in SUSY parameters such as sfermion mass, |μ|, and tanβ, particularly in relation to phase-dependent effects.

Proposed method

• A full one-loop calculation of Δr in the MSSM, including complex phase dependence in the squark sector, using the full Standard Model result as a baseline.
• Incorporation of all available two-loop MSSM corrections to Δr, ensuring high theoretical precision in MW prediction.
• Use of the FeynHiggs2.2 program to determine Higgs sector parameters, including μ and tanβ, consistently with MSSM constraints.
• Numerical scanning over a broad range of MSSM parameters, including M~f, |μ|, tanβ, and trilinear couplings, while applying LEP Higgs and SUSY mass bounds.
• Calculation of δMW via δMW = - (MW_ref / 2) * (sw² / (cw² - sw²)) * Δr^SUSY, where Δr^SUSY is the one-loop SUSY contribution to Δr.
• Generation of contour plots and parameter scans to visualize the dependence of MW on complex phases and key SUSY parameters.

Experimental results

Research questions

• RQ1 How do complex phases in the third-generation squark sector affect the predicted value of the W boson mass in the MSSM?
• RQ2 What is the maximum phase-induced shift in MW that can be achieved under realistic MSSM parameter choices?
• RQ3 How does the inclusion of two-loop corrections and complex phases alter the MSSM prediction for MW compared to previous approximations?
• RQ4 Does the current experimental measurement of MW and mt favor the MSSM over the Standard Model, given the full theoretical uncertainty?
• RQ5 What constraints do phase-dependent effects place on the allowed parameter space of the MSSM, particularly in relation to sfermion mixing and |μ|?

Key findings

• Complex phases in the squark sector—specifically φAt + φμ and φAb + φμ—can induce shifts in MW exceeding 20 MeV in scenarios with low sfermion masses (M~f = 500 GeV) and large |μ| (900 GeV).
• The phase dependence of MW is strongly suppressed in high tanβ scenarios (e.g., tanβ = 30), where phase-induced shifts are less than 0.5 MeV, even for large |μ|.
• For tanβ = 5 and M~f = 500 GeV, the maximum phase-induced shift in MW reaches approximately 20 MeV, indicating a significant sensitivity to CP-violating phases in the squark sector.
• The MSSM prediction for MW, including all known higher-order corrections, shows a slight preference over the SM when compared to current experimental data (MW = 80.392 ± 0.029 GeV, mt = 171.4 ± 2.1 GeV).
• The overlap region between SM and MSSM MW predictions is relatively small, with the MSSM allowing for larger MW values in certain parameter regions, particularly when sfermion mixing is strong (e.g., m~t2/m~t1 > 2.5).
• The study confirms that the phases of X~t and X~b (via At and Ab) do not contribute to Δr at one-loop order, but their combined phases with μ do affect MW through mass and mixing angle shifts.