  The hadronic vacuum polarization (HVP) contributions to the muon $g$$-$$2$
are the crucial quantity to resolve whether new physics is present or not in
the comparison between the Standard Model (SM) prediction and experimental
measurements at Fermilab. They are commonly and historically determined via
dispersion relations using a vast catalogue of experimentally measured,
low-energy $e^+e^-\to \,\rm{hadrons}$ cross section data as input. These
dispersive estimates result in a SM prediction that exhibits a muon $g$$-$$2$
discrepancy of more than $5\sigma$ when compared to experiment. However, recent
lattice QCD evaluations of the HVP and a new hadronic cross section measurement
from the CMD-3 experiment favor a no-new-physics scenario and, therefore,
exhibit a common tension with the previous $e^+e^-\to \,\rm{hadrons}$ data.
This study explores the current and future implications of these two scenarios
on other observables that are also sensitive to the HVP contributions in the
hope that they may provide independent tests of the current tensions observed
in the muon $g$$-$$2$.
