Precise Prediction for M_W in the MSSM

TL;DR

This paper tackles the precise prediction of the W-boson mass M_W within the MSSM, addressing the need for MSSM-level accuracy to match current and future experimental precision. It combines the complete one-loop result in the complex MSSM with all known higher-order corrections from the SM and MSSM, producing the most comprehensive M_W prediction to date. The study finds that complex phases, especially in the stop sector, can shift M_W by tens of MeV, while overall SUSY effects remain significant for light to moderate superpartner masses but fade in the decoupling regime. The results provide a framework for constraining SUSY parameter space through electroweak precision tests and anticipate that future colliders like the ILC/GigaZ could probe these loop effects with even higher sensitivity.

Abstract

We present the currently most accurate evaluation of the W boson mass, M_W, in the Minimal Supersymmetric Standard Model (MSSM). The full complex phase dependence at the one-loop level, all available MSSM two-loop corrections as well as the full Standard Model result have been included. We analyse the impact of the different sectors of the MSSM at the one-loop level with a particular emphasis on the effect of the complex phases. We discuss the prediction for M_W based on all known higher-order contributions in representative MSSM scenarios. Furthermore we obtain an estimate of the remaining theoretical uncertainty from unknown higher-order corrections.

Figures (2)

• Figure 1: Prediction for $M_W$ as function of $m_{\tilde{t}_1}$, the mass of the lighter stop squark. The SUSY parameters are varied independently of each other in a random parameter scan as described in the text. The top-quark mass is fixed at its current experimental central value, $m_t=172.5 \mathrm{GeV}$.
• Figure 2: Prediction for $M_W$ in the MSSM and the SM as a function of $m_{t}$ in comparison with the present experimental results for $M_W$ and $m_{t}$ and the prospective accuracies (using the current central values) at the Tevatron / LHC and at the ILC. The allowed region in the MSSM, corresponding to the light-shaded (green) and dark-shaded (blue) bands, results from varying the SUSY parameters independently of each other in a random parameter scan. The allowed region in the SM, corresponding to the medium-shaded (red) and dark-shaded (blue) bands, results from varying the mass of the SM Higgs boson from $M_H=114 \mathrm{GeV}$ to $M_H=400 \mathrm{GeV}$. Values in the very light shaded region can only be obtained in the MSSM if at least one of the ratios $m_{\tilde{t}_2}/m_{\tilde{t}_1}$ or $m_{\tilde{b}_2}/m_{\tilde{b}_1}$ exceeds 2.5.