Direct-Transmission Models of Dynamical Supersymmetry Breaking

TL;DR

The paper constructs direct-transmission gauge-mediated SUSY-breaking models to realize $m_{3/2}\lesssim1$ keV within cosmological bounds. By engineering dynamical scale generation via an $SU(2)$ dynamics with four doublets and SP(4) flavor structure, and introducing multiplier singlets ($Z$-fields) that couple to messenger sectors, the authors derive realistic soft masses and gaugino masses through loop effects, despite leading-order suppressions. Among configurations with one, two, and three singlets, the three-singlet model most naturally yields the desired gravitino mass range and achieves MSSM mass scales $m_{\text{SUSY}}\sim10^2-10^3$ GeV with $Λ\sim10^5-10^6$ GeV, while also achieving gauge-coupling unification at $M_{\text{GUT}}\sim10^{16}$ GeV. The framework demonstrates cosmologically viable, direct-transmission SUSY breaking without requiring entropy production, and provides concrete mechanisms for the μ-term and CP-phase control in the GUT context.

Abstract

We systematically construct gauge-mediated supersymmetry(SUSY)-breaking models with direct transmission of SUSY-breaking effects to the standard-model sector. We obtain a natural model with the gravitino mass $m_{3/2}$ smaller than 1 keV as required from the standard cosmology. If all Yukawa coupling constants are of order one,the SUSY-breaking scale $m_{SUSY}$ transmitted into the standard-model sector is given by $m_{SUSY} \simeq 0.1 α_i/(4π) Λ$ where $Λ$ is the original dynamical SUSY-breaking scale. Imposing $m_{SUSY} \simeq (10^2-10^3)$ GeV, we get $Λ\simeq (10^5-10^6)$ GeV, which yields the gravitino mass $m_{3/2}\simeq (10^{-2}-1)$ keV.

Figures (5)

• Figure 1: Diagram contributing to the gaugino masses where the single soft SUSY-breaking mass $F^{(\psi)}$ is inserted. This contribution vanishes as shown in the Appendix.
• Figure 2: Diagram contributing to the gaugino masses where the three $F^{(\psi)}$'s are inserted.
• Figure 3: Typical two-loop diagram contributing to the sfermion masses.
• Figure 4: Typical diagram generating the effective Kähler potential which contributes to the soft SUSY-breaking masses of the messenger squarks and sleptons.
• Figure 5: Renormalization group flow of the coupling constants of SU(3)$_C$, SU(2)$_L$, U(1)$_Y$, and the strong SU(2) gauge groups. Here, the mass of messenger squarks and sleptons is taken to be $(10^5-10^6)~ {\rm GeV}$ and we assume that the gauge coupling constant $\tilde{\alpha}_2$ of the strong SU(2) becomes strong ($\tilde{\alpha}_2/\pi \simeq 1$) at the scale $\Lambda= (10^5-10^6)~ {\rm GeV}$.