[Paper Review] Sensitivities to the SUSY Scale from Electroweak Precision Observables

John Ellis, S. Heinemeyer+2 more|arXiv (Cornell University)|Aug 16, 2005

Particle physics theoretical and experimental studies1 references16 citations

TL;DR

This paper investigates indirect sensitivities to the supersymmetry (SUSY) scale using electroweak precision observables within the constrained minimal supersymmetric standard model (CMSSM). Using a χ² analysis that incorporates WMAP dark matter constraints, it shows that future International Linear Collider (ILC) measurements will significantly improve sensitivity to the universal gaugino mass m₁/₂, enabling indirect detection of SUSY even beyond the direct reach of the LHC or ILC, with constraints tightening to ±10% at 95% C.L. for m₁/₂ ≈ 300 GeV.

ABSTRACT

Precision measurements, now and at a future linear electron-positron collider (ILC), can provide indirect information about the possible scale of supersymmetry. Performing a chi^2 analysis, we illustrate the present-day and possible future ILC sensitivities within the constrained minimal supersymmetric extension of the Standard Model (CMSSM), varying the parameters so as to obtain the cold dark matter density allowed by WMAP and other cosmological data. The current data are in very good agreement with the CMSSM prediction for tan beta = 10, with a clear preference for relatively small values of the universal gaugino mass, m_{1/2} \sim 300 GeV. In this case, there would be good prospects for observing supersymmetry directly at both the LHC and the ILC, and some chance already at the Tevatron collider. For tan beta = 50, the quality of the fit is worse, and somewhat larger m_{1/2} values are favoured. With the prospective ILC accuracies the sensitivity to indirect effects of supersymmetry greatly improves. This may provide indirect access to supersymmetry even at scales beyond the direct reach of the LHC or the ILC.

Motivation & Objective

• To assess current and future indirect sensitivity to the supersymmetry scale using precision electroweak observables.
• To evaluate the impact of WMAP-constrained dark matter density on the parameter space of the CMSSM.
• To project the sensitivity of future International Linear Collider (ILC) measurements to the universal gaugino mass m₁/₂ and trilinear parameter A₀.
• To test the consistency of indirect SUSY signals with direct detection prospects at the LHC and ILC.
• To explore whether indirect precision data can constrain SUSY scales beyond the direct reach of future colliders.

Proposed method

• A χ² analysis is performed on key electroweak observables: M_W, sin²θ_eff, (g-2)_μ, BR(b→sγ), M_h, and BR(h→bb)/BR(h→WW*).
• The analysis is conducted within the constrained MSSM (CMSSM), with parameters m₁/₂, m₀, A₀, and tanβ, and the WMAP-allowed dark matter density is enforced as a constraint.
• Present-day experimental data and future ILC projected accuracies are used to assess sensitivity to m₁/₂ and A₀ in the (m₁/₂, A₀) plane.
• Theoretical uncertainties from higher-order corrections are estimated and included in the ILC sensitivity projections.
• Best-fit points are identified for both current data and hypothetical future ILC data, with confidence level regions (68% and 90%) computed.
• The comparison of indirect constraints from precision data with direct detection reach tests the validity of the CMSSM framework at loop level.

Experimental results

Research questions

• RQ1 How sensitive are current electroweak precision measurements to the supersymmetry scale in the CMSSM framework?
• RQ2 What is the expected improvement in sensitivity to m₁/₂ and A₀ from future ILC measurements compared to present data?
• RQ3 Can indirect precision data constrain m₁/₂ values beyond the direct discovery reach of the LHC or ILC?
• RQ4 How does the quality of the fit to precision observables depend on tanβ, and what are the implications for m₁/₂ constraints?
• RQ5 To what extent can indirect constraints on m₁/₂ remain viable for m₁/₂ > 1.5 TeV, even when direct signals are unobservable?

Key findings

• For tanβ = 10, current data yield a 68% confidence level upper bound of approximately 450 GeV on m₁/₂, increasing to 600 GeV at 90% C.L., with best fit at m₁/₂ ≈ 300 GeV and negative A₀.
• For tanβ = 50, the fit quality is worse, and the upper bound on m₁/₂ increases to nearly 1 TeV at 68% C.L., with best fit at m₁/₂ ≈ 500 GeV.
• Future ILC precision would reduce the allowed (m₁/₂, A₀) region to very small areas, enabling constraints on m₁/₂ within ±10% at 95% C.L. for m₁/₂ ≈ 300 GeV.
• Even for m₁/₂ values up to 1 TeV—beyond the ILC’s direct reach—ILC precision data could still establish an upper bound on m₁/₂ within the WMAP-allowed region.
• For m₁/₂ > 1.5 TeV, indirect effects become too small to resolve even with ILC-level accuracies, limiting the reach of indirect constraints.
• The comparison of indirect precision data with direct detection results would provide a stringent test of the CMSSM framework; discrepancies could signal physics beyond the CMSSM.