Resolving the $(g-2)_{\mu}$ Discrepancy with $\cal{F}$-$SU$(5) Intersecting D-branes

A discrepancy between the measured anomalous magnetic moment of the muon $(g - 2)_{\mu}$ and computed Standard Model value now stands at a combined $4.2\sigma$ following experiments at Brookhaven National Lab (BNL) and the Fermi National Accelerator Laboratory (FNAL). A solution to the disagreement is uncovered in flipped $SU(5)$ with additional TeV-Scale vector-like $\bf 10 + \overline{10}$ multiplets and charged singlet derived from local F-Theory, collectively referred to as $\cal{F}$-$SU(5)$. Here we engage general No-Scale supersymmetry (SUSY) breaking in $\cal{F}$-$SU(5)$ D-brane model building to alleviate the $(g - 2)_{\mu}$ tension between the Standard Model and observations. A robust $\Delta a_{\mu}$(SUSY) is realized via mixing of $M_5$ and $M_{1X}$ at the secondary $SU(5) \times U(1)_X$ unification scale in $\cal{F}$-$SU(5)$ emanating from $SU(5)$ breaking and $U(1)_X$ flux effects. Calculations unveil $\Delta a_{\mu}({\rm SUSY}) = 19.0 - 22.3 \times 10^{-10}$ for gluino masses of $M(\widetilde{g}) = 2.25 - 2.56$ TeV and higgsino dark matter, aptly residing within the BNL+FNAL $1\sigma$ mean. This $(g - 2)_{\mu}$ favorable region of the model space also generates the correct light Higgs boson mass and branching ratios of companion rare decay processes, and is further consistent with all LHC Run 2 constraints. Finally, we examine the heavy SUSY Higgs boson in light of recent LHC searches for an extended Higgs sector.