No Naturalness or Fine-tuning Problems from No-Scale Supergravity

Abstract

We compute the electroweak fine-tuning in No-Scale Supergravity for a representative supersymmetric Grand Unification Theory (GUT) model, flipped $SU(5)$ with extra vector-like $flippons$, dubbed $\mathcal{F}$-$SU(5)$. We find that there is no problematic electroweak fine-tuning in No-Scale $\mathcal{F}$-$SU(5)$, due to an elegant proportional rescaling of the full mass spectrum with respect to just the unified gaugino mass $M_{1/2}$, as well as a dynamic equivalence enforced between $M_{1/2}$ and the supersymmetric Higgs mixing parameter $\mu$ at the heavy unification scale. We demonstrate both analytically and numerically that the No-Scale $\mathcal{F}$-$SU(5)$ fine-tuning parameter is consequently of unit order, ${\Delta }_{\mathrm{EENZ}}\simeq \mathcal{O}(1)$, at the electroweak scale.

Comments: 6 pages, 1 figure