Sweet Spot Supersymmetry

TL;DR

Sweet Spot Supersymmetry identifies a sweet-spot region with gravitino mass around $m_{3/2} \sim O(1)\ \mathrm{GeV}$ in a Goldstino multiplet $S$–MSSM framework, resolving the flavor/CP, $\mu$, moduli, and proton-decay problems while enabling non-thermal gravitino dark matter from $S$ decays. The approach blends gauge- and gravity-mediated features, yielding a characteristic spectrum with a light Higgsino and a stau NLSP whose long lifetime yields distinctive collider signatures and opportunities for parameter extraction. The model is UV-supported with a cutoff near the GUT scale $\Lambda \sim M_{\rm GUT}$ and a simple three-parameter low-energy description $(\mu, M_{\rm mess}, \bar M)$ that can be tested via neutralino mass edges and heavy Higgs observables at the LHC. Collectively, these predictions offer a coherent path from high-scale SUSY breaking to concrete collider tests and cosmological consistency, enabling a robust confirmation or falsification of the scenario at current or near-future experiments.

Abstract

We find that there is no supersymmetric flavor/CP problem, mu-problem, cosmological moduli/gravitino problem or dimension four/five proton decay problem in a class of supersymmetric theories with O(1) GeV gravitino mass. The cosmic abundance of the non-thermally produced gravitinos naturally explains the dark matter component of the universe. A mild hierarchy between the mass scale of supersymmetric particles and electroweak scale is predicted, consistent with the null result of a search for the Higgs boson at the LEP-II experiments. A relation to the strong CP problem is addressed. We propose a parametrization of the model for the purpose of collider studies. The scalar tau lepton is the next to lightest supersymmetric particle in a theoretically favored region of the parameter space. The lifetime of the scalar tau is of O(1000) seconds with which it is regarded as a charged stable particle in collider experiments. We discuss characteristic signatures and a strategy for confirmation of this class of theories at the LHC experiments.

Figures (14)

• Figure 1: Schematic picture of mediation mechanisms. Different mechanism works for different values of gravitino masses. A sweet spot exists at $m_{3/2} \sim 1$ GeV where there is no phenomenological or cosmological problem.
• Figure 2: Phenomenologically required values of the Higgsino mass $\bar{\mu}$ (with an $O(1)$ ambiguity, see text), the Bino mass $m_{\tilde{B}}$ and the gravitino energy density $\Omega_{3/2} h^2$. These three quantities have different dependencies on parameters $m_{3/2}$ and $\Lambda$. The three bands meet around $m_{3/2} \sim 1$ GeV and $\Lambda \sim M_{\rm GUT}$. The quantity $\Omega_{3/2} h^2$ is defined in Eq. (\ref{['eq:omega']}). It represents the energy density of the non-thermally produced gravitinos through the decays of $S$ if $S \to hh$ is the dominant decay channel.
• Figure 3: Feynman diagrams to generate higher dimensional operators in a UV model.
• Figure 4: Structure of an example of the UV model Kitano:2006wm.
• Figure 5: Particles to describe the theory in each energy interval.