  We provide improved Standard Model theory predictions for the exclusive rare
semimuonic processes $B\to K^{(*)}\mu^+\mu^-$ and $B_s\to\phi\mu^+\mu^-$. Our
results are based on a novel parametrization of the non-local form factors,
which manifestly respects a recently developed dispersive bound. We critically
compare our predictions to those obtained in the framework of QCD
factorization. Our predictions provide, for the first time, parametric
estimates of the systematic uncertainties due to non-local contributions.
Comparing our predictions within the Standard Model to available experimental
data, we find a large tension for $B\to K\mu^+\mu^-$. A simple
model-independent analysis of potential effects beyond the Standard Model
yields results compatible with other approaches, albeit with larger
uncertainties for the $B\to K^*\mu^+\mu^-$ and $B_s\to \phi\mu^+\mu^-$ decays.
Our approach yields systematically improvable predictions, and we look forward
to its application in further analyses beyond the Standard Model.
