Confronting Electroweak Fine-tuning with No-Scale Supergravity

TL;DR

This paper explores how No-Scale Supergravity boundary conditions applied to a flipped SU(5) GUT model with extra multiplets can naturally relate the Z-boson mass to gaugino mass, offering insights into the electroweak fine-tuning problem.

Contribution

It demonstrates a proportional relationship between model scales and gaugino mass, providing a potential mechanism to address electroweak fine-tuning within No-Scale ${ m F}$-$SU(5)$.

Findings

The Z-boson mass depends explicitly on the gaugino mass $M_{1/2}$.

The parameter $c$ tends toward 1, indicating a possible underlying Giudice-Masiero mechanism.

The model suggests a natural way to confront electroweak fine-tuning.

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 ${\cal F}$-$SU(5)$, 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 ${\cal F}$-$SU(5)$ model suggests one possible mechanism of confronting the electroweak fine tuning problem.