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

Abstract

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, $⟨0|\bar{s}(y)G_{\mu \nu }(x)b(0)|B(p)⟩$. Moreover, the dependence of this quantity on the variable $(x-y{)}^2$ is essential for a proper account of the ${\left({\Lambda }_{\mathrm{QCD}}{m}_b/m_c^2\right)}^n$ terms in the amplitudes of FCNC $B$-decays.

5 pages, minor clarifications added, version to appear in PLB