FCNC transition $c\to u\gamma$ in $B_c\to B_u^*\gamma$ decay

TL;DR

This paper proposes using the decay $B_c\to B_u^*\gamma$ to probe the flavor-changing neutral current transition $c\to u\gamma$, estimating its branching ratio within the Standard Model and highlighting its potential to reveal new physics.

Contribution

It introduces the $B_c\to B_u^*\gamma$ decay as a sensitive probe for $c\to u\gamma$ transitions and provides the first estimate of its branching ratio within the Standard Model.

Findings

Standard Model predicts $Br(B_c\to B_u^*\gamma)\sim 10^{-8}$.

Decay contributions are comparable between short and long distances.

Detection above $10^{-8}$ branching ratio indicates possible new physics.

Abstract

We propose the $B_c\to B_u^*\gamma$ decay as the most suitable probe for the flavour changing neutral transition $c\to u\gamma$. We estimate the short and long distance contributions to this decay within the standard model and we find them to be comparable; this is in contrast to radiative decays of $D$ mesons, that are completely dominated by the long distance contributions. Since the $c\to u\gamma$ transition is very sensitive to the physics beyond the standard model, the standard model prediction $Br(B_c\to B_u^*\gamma)\sim 10^{-8}$ obtained here opens a new window for future experiments. The detection of $B_c\to B_u^*\gamma$ decay at branching ratio well above $10^{-8}$ would signal new physics.