Nonfactorizable charming loops in exclusive FCNC $B$ decays

Abstract

We compare (i) nonfactorizable charm-quark loops in exclusive FCNC B-decays and (ii) three-particle contributions to the amplitude of semileptonic B-decay. Both amplitudes are given in the heavy-quark limit, $m_b\to\infty$, by a convolution of a hard kernel and a three-particle wave function of the $B$-meson, $\langle 0|\bar q(x)G_{\mu\nu}(z) b(0)|B(p)\rangle$. An essential difference between the two amplitudes is that the amplitude of semileptonic $B$-decay involves this 3-particle wave function in a collinear light-cone configuration, whereas the amplitude of nonfactorizable charm in FCNC $B$-decays involves this 3-particle wave function in a double collinear light-cone configuration.