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Z Pole Observables in the MSSM

S. Heinemeyer, W. Hollik, A. M. Weber, G. Weiglein

TL;DR

The paper tackles precision predictions of $Z$-pole observables within the MSSM, explicitly incorporating complex parameters and their loop effects. It delivers the most complete calculation to date by combining full one-loop MSSM results with complex phases, all available MSSM two-loop corrections, and the full SM contributions, while also including higher-order Higgs-sector effects. A notable advance is the first full one-loop computation of $\Gamma(Z\to \tilde{\chi}^0_{1}\tilde{\chi}^0_{1})$. The analysis highlights how MSSM sectors and CP-violating phases influence $M_W$, $\sin^2\theta_{\text{eff}}$, and $\Gamma_Z$, assesses theoretical uncertainties, and discusses prospects for constraining SUSY parameters with current and future precision measurements (e.g., ILC/GigaZ).

Abstract

We present the currently most accurate prediction of Z pole observables such as sin^2 theta_eff, Gamma_Z, R_b, R_l, and sigma^0_had in the Minimal Supersymmetric Standard Model (MSSM). We take into account the complete one-loop results including the full complex phase dependence, all available MSSM two-loop corrections as well as the full SM results. We furthermore include higher-order corrections in the MSSM Higgs boson sector, entering via virtual Higgs boson contributions. For Gamma(Z -> neutralino{1} neutralino{1}) we present a full one-loop calculation. We analyse the impact of the different sectors of the MSSM with particular emphasis on the effects of the complex phases. The predictions for the Z boson observables and M_W are compared with the current experimental values. Furthermore we provide an estimate of the remaining higher-order uncertainties in the prediction of sin^2 theta_eff.

Z Pole Observables in the MSSM

TL;DR

The paper tackles precision predictions of -pole observables within the MSSM, explicitly incorporating complex parameters and their loop effects. It delivers the most complete calculation to date by combining full one-loop MSSM results with complex phases, all available MSSM two-loop corrections, and the full SM contributions, while also including higher-order Higgs-sector effects. A notable advance is the first full one-loop computation of . The analysis highlights how MSSM sectors and CP-violating phases influence , , and , assesses theoretical uncertainties, and discusses prospects for constraining SUSY parameters with current and future precision measurements (e.g., ILC/GigaZ).

Abstract

We present the currently most accurate prediction of Z pole observables such as sin^2 theta_eff, Gamma_Z, R_b, R_l, and sigma^0_had in the Minimal Supersymmetric Standard Model (MSSM). We take into account the complete one-loop results including the full complex phase dependence, all available MSSM two-loop corrections as well as the full SM results. We furthermore include higher-order corrections in the MSSM Higgs boson sector, entering via virtual Higgs boson contributions. For Gamma(Z -> neutralino{1} neutralino{1}) we present a full one-loop calculation. We analyse the impact of the different sectors of the MSSM with particular emphasis on the effects of the complex phases. The predictions for the Z boson observables and M_W are compared with the current experimental values. Furthermore we provide an estimate of the remaining higher-order uncertainties in the prediction of sin^2 theta_eff.

Paper Structure

This paper contains 11 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Notations and conventions
  3. Sfermions
  4. Gaugino sector
  5. Higgs bosons
  6. Description of the $Z$ boson resonance
  7. Effective coupling approach
  8. Remaining higher-order uncertainties for $\sin^2\theta_{\mathrm{eff}}$
  9. Conclusions
  10. Appendix
  11. One-loop vertex graphs for the process $Z\to f \bar{f}$

Figures (4)

  • Figure 1: MSSM parameter scan for $\sin^2\theta_{\mathrm{eff}}$ as a function of $m_{t}$ over the ranges given in eq. (\ref{['scaninput']}). Todays 68% C.L. ellipses as well as future precisions, drawn around todays central value, are indicated in the plot.
  • Figure 2: MSSM random parameter scan for $M_W$ as a function of $m_{t}$ over the ranges given in eq. (\ref{['scaninput']}). Todays 68% C.L. ellipses as well as future precisions, drawn around todays central value, are indicated in the plot.
  • Figure 3: MSSM random parameter scan over the ranges given in eq. (\ref{['scaninput']}). The top-quark mass is treated as an additional free parameter and is varied in the range $m_{t}=165 \textellipsis 175 \mathrm{GeV}$. Shown is the combination of $M_W$ and $\sin^2\theta_{\mathrm{eff}}$. Todays 68% C.L. ellipses as well as future precisions, drawn around todays central value, are indicated in the plot.
  • Figure :