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

TL;DR

This paper investigates non-factorizable charming-loop corrections in FCNC B decays, revealing significant differences from semileptonic form factor corrections due to distinct dominant configurations of the Bethe-Salpeter amplitude.

Contribution

It demonstrates that the charming-loop correction in FCNC B decays involves non-collinear configurations, contrasting with collinear configurations in semileptonic form factors.

Findings

Form factor correction dominated by collinear light-cone configuration.

FCNC amplitude dominated by non-collinear configuration.

Substantial differences between the two types of corrections.

Abstract

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., $z_\mu\ne u x_\mu$).