  We investigate the interference pattern of the charm-resonances
$\Psi(3370,4040,4160,4415)$ with the electroweak penguin operator $O_9$ in the
branching fraction of $B^+\to K^+\mu\mu$. For this purpose we extract the charm
vacuum polarisation via a standard dispersion relation from BESII-data on
$e^+e^-\to hadrons$. In the factorisation approximation (FA) the vacuum
polarisation describes the interference fully non-perturbatively. The observed
interference pattern by the LHCb collaboration is opposite in sign and and
significantly enhanced as compared to the FA. A change of the FA-result by a
factor of -2.5, which correspond to a 350%-corrections, results in a reasonable
agreement with the data. This raises the question on the size of
non-factorisable corrections which are colour enhanced but loop-suppressed. In
the parton picture it is found that the corrections are of relative size ~-0.5
when averaged over the open charm-region which is far below -3.5 needed to
explain the observed effect. We present combined fits to the BESII- and the
LHCb-data, testing for effects beyond the Standard Model (SM)-FA. We cannot
find any significant evidence of the parton estimate being too small due to
cancellations between the individual resonances. It seems difficult to
accommodate the LHCb-result in the standard treatment of the SM or QCD
respectively. In the SM the effect can be described in a $q^2$-dependent shift
of the Wilson coefficient combination $C^{eff}_9 + C^{' eff}_9$. We devise
strategies to investigate the microscopic structure in future measurements. We
show that the charm-resonance effects can accommodate the $B \to K^*
ll$-anomalies (e.g. $P_5'$). Hence our findings indicate that the
interpretation of the anomaly through a $Z'$-boson, mediating between $bs$ and
$ll$ fields, is disfavoured. More generally our results motivate investigations
into $b \to s\bar cc$-physics.
