Non-factorizable charming loops in FCNC B decays vs B-decay semileptonic form factors

We compare a non-factorizable charming-loop correction to an exclusive FCNC $B$-decay given in terms of the 3-particle Bethe-Salpeter amplitude (3BS) of the $B$-meson, $\langle 0|\bar q(x)G_{\mu\nu}(z)b(0)|B(p)\rangle$, with the corresponding correction to the $B$-meson semileptonic form factor. In spite of certain similarities, these two corrections are shown to have substantial differences: The form factor correction is dominated by the collinear light-cone configuration of 3BS: $z_\mu= u x_\mu$, $0 < u < 1$, $x^2=0$. In contrast, the FCNC amplitude is dominated by a different configuration with non-collinear arguments: $x^2=0$, $z^2=0$, but $(x-z)^2\ne 0$ (i.e., $z_\mu\ne u x_\mu$).