Supersymmetry and precision data after LEP2

TL;DR

This work analyzes one-loop supersymmetric corrections to precision observables after incorporating LEP2 $e^+e^-\to f\bar f$ cross sections, showing that LEP2 data largely remove earlier hints of SUSY and sometimes strengthen direct bounds. The authors formulate a heavy universal approximation in terms of the oblique parameters $\hat{S},\hat{T},W,Y$, and perform a full one-loop calculation across several SUSY scenarios (split SUSY, CMSSM, gauge mediation, and anomaly+radion mediation). They find that SUSY corrections to precision data are typically positive in $W$ and $Y$ and depend mainly on left-handed slepton/squark masses, as well as $M_2$ and $\mu$, with $\hat{S}$ often negative and stop effects entering the $\hat{T}$ channel. Overall, the inclusion of LEP2 data constrains the SUSY parameter space comparably to direct searches, guiding model-building and showing that regions with sparticles near current direct bounds are disfavored; the analysis provides robust, model-spanning insights into how precision data test supersymmetry via the oblique parameters.

Abstract

We study one loop supersymmetric corrections to precision observables. Adding LEP2 e ebar --> f fbar cross sections to the data-set removes previous hints for SUSY and the resulting constraints are in some cases stronger than direct bounds on sparticle masses. We consider specific models: split SUSY, CMSSM, gauge mediation, anomaly and radion mediation. Beyond performing a complete one-loop analysis, we also develop a simple approximation, based on the Shat, That, W, Y `universal' parameters. SUSY corrections give W,Y > 0 and mainly depend on the left-handed slepton and squark masses, on M_2 and on mu.

Figures (6)

• Figure 1: Corrections to $\varepsilon_1$ and to $\sigma(e\bar{e}\to \mu\bar{\mu},\sum_q q\bar{q})$ at CM energy $200\,{\rm GeV}$ generated when only the sparticle with the indicated mass is light. This allows to see the accuracy of the $\hat{S},\hat{T},W,Y$ approximation, which gives straight lines with the correct asymptotic behavior for $m_{\rm SUSY}\gg M_Z$.
• Figure 2: Upper row: definition of $\hat{S}$, $\hat{T}$, $W$ and $Y$ in terms of canonically normalized inverse propagators $\Pi$. Middle row: the corresponding dimension 6 operators. Lower row: one-loop Feynman graphs that contribute to $\hat{S}$, $\hat{T}$, $W$ and $Y$. Unspecified lines denote generic sparticles.
• Figure 3: Fig. \ref{['fig:SUSYM2']}a: $\chi^2-\chi^2_{\rm SM}$ in the case of light gauginos with $\tan\beta=10$, gaugino unification and $m_h=115\,{\rm GeV}$. The dashed line are our analytical approximation, while the continuous lines are the full numerical computation. The thick line is the result obtained including all data. The upper blue line shows the contribution of LEP2 only. The lower red line shows the result omitting LEP2, including only 'traditional' precision data. The shaded regions is excluded by direct LEP2 searches. Fig. \ref{['fig:SUSYM2']}b: analogous plot for the case of light higgsinos. We show only the full result.
• Figure 4: Fit of precision data with the sample sparticle spectrum of eq. (\ref{['eq:SUSYLIGHT']}). The label '$3\sigma$' means $\Delta\chi^2 = 3^2$ (i.e. SUSY is disfavoured) and the label '$-0.5\sigma$' means $\Delta\chi^2 = -0.5^2$ (i.e. SUSY is favoured).
• Figure 5: Fits of precision data. Regions shaded in red are disfavored at $1,2,3,\ldots\sigma$, as indicated on the iso-lines. Regions below the thick blue line are excluded by LEP2 direct searches. We performed a full one-loop analysis, including LEP2 precision data. We kept fixed $\tan\beta=10$, $A_0=0$, $\lambda_t(M_{\rm GUT})=0.6$, $\hbox{\rm sign}\,\mu=+1$, the gauge-mediation scale $M_{\rm GM} = 10^{10}\,{\rm GeV}$.