Confronting Electroweak Fine-tuning with No-Scale Supergravity

Abstract

Applying No-Scale Supergravity boundary conditions at a heavy unification scale to the Flipped $SU(5)$ grand unified theory with extra TeV-scale vector-like multiplets, $i.e.$ No-Scale $\mathcal{F}$-$SU(5)$, we express the $Z$-boson mass $M_Z$ as an explicit function of the boundary gaugino mass $M_{1/2}$, $M_Z^2=M_Z^2(M_{1/2}^2)$, with implicit dependence upon a dimensionless ratio $c$ of the supersymmetric Higgs mixing parameter $\mu$ and $M_{1/2}$. Setting the top Yukawa coupling consistent with $m_t=174.3$ GeV at $M_Z=91.2$ GeV, the value of $c$ naturally tends toward $c\simeq 1$, which indirectly suggests underlying action of the Giudice-Masiero mechanism. Proportional dependence of all model scales upon the unified gaugino mass $M_{1/2}$ in the No-Scale $\mathcal{F}$-$SU(5)$ model suggests one possible mechanism of confronting the electroweak fine tuning problem.

Physics Letters B version; 8 Pages, 7 Figures, 1 Table

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