On the smallness of charm loop effects in $B\to K^{(*)} \ell\ell$ at low $q^2$: light meson Distribution Amplitude analysis

The non-local effects originating from the charm quark loops at dilepton invariant masses smaller than the charmonium threshold in $B\to K \ell\ell$ are evaluated with light meson distribution amplitudes. The revised estimates with B-meson distribution amplitude within a Light Cone Sum Rule approach yielded results about three orders smaller than the original computation. In view of the importance of these non-factorizable soft gluon effects, both conceptually and phenomenologically, an independent evaluation is necessary. It is found that to twist-4 accuracy, these soft gluon effects vanish when evaluated employing the kaon distribution amplitude. Similar results hold for $B\to K^* \ell\ell$ to the leading twist. This eliminates one of the major sources of potential uncertainty which usually makes it difficult for a clear case of new physics, should the data show deviations from the standard model.