Revisiting nonfactorizable charm-loop effects in exclusive FCNC B-decays

We revisit the calculation of nonfactorizable corrections induced by charm-quark loops in exclusive FCNC B-decays. For the sake of clarity, we make use of a field theory with scalar particles: this allows us to focus on the conceptual issues and to avoid technical complications related to particle spins in QCD. We perform a straightforward calculation of the appropriate correlation function and show that it requires the knowledge of the full generic three-particle distribution amplitude with non-aligned arguments, $〈0\left|\overline{s}\right(y\left)G_{\mu \nu }\right(x\left)b\right(0\left)\right|B\left(p\right)〉$. Moreover, the dependence of this quantity on the variable ${(x-y)}^2$ is essential for a proper account of the ${({\Lambda }_{\mathrm{QCD}}{m}_b/m_c^2)}^n$ terms in the amplitudes of FCNC B-decays.