Can The Supersymmetric Flavor Problem Decouple?

Abstract

It has been argued that the squarks and sleptons of the first and second generations can be relatively heavy without destabilizing the weak scale, thereby improving the situation with too-large flavor-changing neutral current (FCNC) and CP violating processes. In theories where the soft supersymmetry breaking parameters are generated at a high scale (such as the Planck scale), we show that such a mass spectrum tends to drive the scalar top mass squared $m_{\tilde{Q}_3}^2$ negative from two-loop renormalization group evolution. Even ignoring CP violation and allowing $O(λ) \sim .22$ alignment, the first two generation scalars must be heavier than 22 TeV to suppress FCNC. This in turn requires the boundary condition on $m_{\tilde{Q}_3} > 4 TeV$ to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale. Some of the models in the literature employing the anomalous U(1) in string theory are excluded by our analysis.

Figures (3)

• Figure 1: The minimum mass of the first- and second-generation scalars $\hbox{min}(\widetilde{m}_{1,2})$ to keep $(\Delta m_{K})_{\tilde{q},\tilde{g}}$$< (\Delta m_{K})_{obs}$ as a function of the gluino mass for four different cases: (I) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 1$, (II) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 0.22$, (III) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 0.05$, and (IV) $(\delta_{12}^{d})_{LL}=0.22$ and $(\delta_{12}^{d})_{RR} =0$. Including $O(1)$ CP violating phases makes the lower bound stronger by a factor of 13.
• Figure 2: Constraint on the mass ratio between the first- and second-generation scalars $\widetilde{m}_{1,2}$ and the third-generation scalars $m_{\tilde{f}}(0)$ from the requirement that none of the third-generation scalars acquire negative mass squared at the weak scale. The regions below the curves are excluded. Constraints are shown for the case $N_{5} = N_{10} = 2$. See the text for details of our conservative assumptions.
• Figure 3: The minimum boundary mass of the left-handed scalar top $\hbox{min}(m_{\tilde{Q}_3}(0))$ required to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale, while keeping the $\hbox{min}(\widetilde{m}_{1,2})$ within the constraints from Fig. \ref{['m1min']}. As in Fig. \ref{['m1min']}, four cases are considered: (I) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 1$, (II) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 0.22$, (III) $(\delta_{12}^{d})_{LL} = (\delta_{12}^{d})_{RR} = 0.05$, and (IV) $(\delta_{12}^{d})_{LL}=0.22$ and $(\delta_{12}^{d})_{RR} =0$. Two curves are shown for the last case. The upper curve is for $N_{5} = N_{10} = 2$ as in other cases, and the constraint is slightly weaker if $N_{5} = 0$.