Dynamical Soft Terms with Unbroken Supersymmetry

TL;DR

Dimopoulos, Dvali, Rattazzi, and Giudice develop a framework for dynamical soft terms where SUSY is broken on a metastable plateau rather than in the true vacuum, stabilized by Coleman-Weinberg effects along a charged flat direction with $W_{eff}=\lambda_2\Lambda^2 X$ and a plateau potential $V_{eff}\sim \lambda_2^2\Lambda^4/Z_R$. The SUSY-breaking is gauge-mediated to the MSSM, with a messenger scale $X$ set by RG-driven localization of the Kähler metric, allowing $X$ to range from $10^8$ to $M_{Pl}$ while maintaining calculability. They present explicit models (e.g., $SU(2)^3$, $SU(6)\times SU(6)$, and $SU(5)^3$) illustrating viable regions for $X$ and discussing the implications for sparticle spectra and novel boundary conditions, such as $A$-terms, as well as cosmological constraints. Nucleosynthesis bounds require the messenger scale to be below about $10^{11}$ GeV for safe NLSP decays, which sharply constrains high-scale realizations, though the framework remains a compelling route to flavor-safe gauge mediation with rich phenomenology.

Abstract

We construct a class of simple and calculable theories for the supersymmetry breaking soft terms. They are based on quantum modified moduli spaces. These theories do not break supersymmetry in their ground state; instead we postulate that we live in a supersymmetry breaking plateau of false vacua. We demonstrate that tunneling from the plateau to the supersymmetric ground state is highly supressed. At one loop, the plateau develops a local minimum which can be anywhere between $10^8$ GeV and the grand unification scale. The value of this minimum is the mass of the messengers of supersymmetry breaking. Primordial element abundances indicate that the messengers' mass is smaller than $10^{12}$ GeV.

Figures (4)

• Figure 1: An idealized flat potential with $V(\phi>\Lambda)=U_0\sim \Lambda^4$ and $V(0)=0$.
• Figure 2: The region of parameters where the $SU(2)\times SU(2)\times SU(2)$ model can have a local supersymmetry-breaking vacuum at $\langle X\rangle =10^{10}$ GeV.
• Figure 3: The region of parameters where the $SU(6)\times SU(6)$ model can have a local supersymmetry-breaking vacuum at $\langle X\rangle =10^{10}$ GeV.
• Figure 4: The regions in the $N$--$M$ parameter space where the neutralino ($\chi^0$) or the right-handed stau (${\tilde{\tau}}$) are the next-to-lightest supersymmetric particle (NLSP). Above the upper curve the gauge coupling constants become non-perturbative before the GUT scale.