Phenomenological Constraints on Patterns of Supersymmetry Breaking

TL;DR

This work investigates how specific patterns of supersymmetry breaking, encoded as relations among high-scale soft parameters $A_0$ and $B_0$, constrain the electroweak parameter $\tan \beta$ in a CMSSM-like framework. By enforcing radiative electroweak symmetry breaking and applying LEP, $b \to s \gamma$, and WMAP-era relic-density constraints, the authors map allowed regions in $(m_{1/2}, m_0)$ space and extract $\tan \beta$ ranges for several patterns, notably the Polonyi model and no-scale scenarios. They find no funnel or focus-point solutions in these patterns; instead, viable regions are dominated by chi-$\tilde{\tau}_1$ coannihilation tails with tightly bounded $\tan \beta$ (e.g., $11 \lesssim \tan \beta \lesssim 20$ for the Polonyi case with $\mu > 0$). The results imply that an experimental measurement of $\tan \beta$ could serve as a discriminant among SUSY-breaking mechanisms, while highlighting the sensitivity of the allowed parameter space to the underlying high-scale relations among $A_0$, $B_0$, and $m_0$.

Abstract

Specific models of supersymmetry breaking predict relations between the trilinear and bilinear soft supersymmetry breaking parameters A_0 and B_0 at the input scale. In such models, the value of tan beta can be calculated as a function of the scalar masses m_0 and the gaugino masses m_{1/2}, which we assume to be universal. The experimental constraints on sparticle and Higgs masses, b to s gamma decay and the cold dark matter density Omega_{CDM} h^2 can then be used to constrain tan beta in such specific models of supersymmetry breaking. In the simplest Polonyi model with A_0 = (3 - sqrt{3})m_0 = B_0 + m_0, we find 11 < tan beta < 20 (tan beta ~ 4.15) for mu > 0 (mu < 0). We also discuss other models with A_0 = B_0 + m_0, finding that only the range -1.9 < A_0/m_0 < 2.5 is allowed for mu > 0, and the range 1.25 < A_0/m_0 < 4.8 for mu < 0. In these models, we find no solutions in the rapid-annihilation `funnels' or in the `focus-point' region. We also discuss the allowed range of tan beta in the no-scale model with A_0 = B_0 = 0. In all these models, most of the allowed regions are in the chi - stau_1 coannihilation `tail'.

Figures (4)

• Figure 1: Examples of $(m_{1/2}, m_0)$ planes with contours of $\tan \beta$ superposed, for $\mu > 0$ and (a) ${\hat{A}} = - 1.5, {\hat{B}} = {\hat{A}} -1$, (b) ${\hat{A}} = 0.75, {\hat{B}} = {\hat{A}} -1$, (c) the simplest Polonyi model with ${\hat{A}} = 3 - \sqrt{3}, {\hat{B}} = {\hat{A}} -1$ and (d) ${\hat{A}} = 2.0, {\hat{B}} = {\hat{A}} -1$. In each panel, we show the regions excluded by the LEP lower limits on MSSM particles, those ruled out by $b \to s \gamma$ decay bsg (medium green shading), and those excluded because the LSP would be charged (dark red shading). The region favoured by the WMAP range $\Omega_{CDM} h^2 = 0.1126^{+0.0081}_{-0.0091}$ has light turquoise shading. The region suggested by $g_\mu - 2$ is medium (pink) shaded.
• Figure 2: As in Fig. \ref{['fig:Polonyi']}, but now for $\mu < 0$ and the choices (a) ${\hat{A}} = 3 - \sqrt{3}, {\hat{B}} = {\hat{A}} -1$ and (b) ${\hat{A}} = 2, {\hat{B}} = {\hat{A}} -1$ and $\mu < 0$.
• Figure 3: The ranges of $\tan \beta$ allowed if ${\hat{B}} = {\hat{A}} - 1$ for $\mu > 0$ (solid lines) and $\mu < 0$ (dashed lines). The Polonyi model corresponds to ${\hat{A}} \simeq \pm 1.3$. Also shown as 'error bars' are the ranges of $\tan \beta$ allowed in the no-scale case ${\hat{A}} = {\hat{B}} = 0$ for $\mu > 0$ (upper) and $\mu < 0$ (lower).
• Figure 4: As in Fig. \ref{['fig:Polonyi']}, for the no-scale cases ${\hat{A}} = 0, {\hat{B}} = 0$ and (a) $\mu > 0$, (b) $\mu < 0$.