Radiative Semileptonic $\bar{B}$ Decays

TL;DR

This paper analyzes radiative semileptonic B decays using heavy quark symmetry, identifying only four new form factors at leading order and fixing one in terms of the Isgur-Wise function.

Contribution

It demonstrates the power of heavy quark symmetry in simplifying the form factors for these decays, reducing the number of unknowns significantly.

Findings

HQS reduces form factors to four at leading order.

One form factor is determined by the Isgur-Wise function.

Heavy quark symmetry applies when photon momentum is small.

Abstract

We consider the form factors for the radiative semileptonic decays $\bar{B}(v) \rightarrow D^{(*)}(v') \ell {\bar \nu}_\ell \gamma$ in the kinematic region where the photon momentum, $k$, is small enough that heavy quark symmetry (HQS) can be applied without the radiated photon changing the heavy quark velocity (i.e., $v^{(\prime)} \cdot k < m_{(b,c)}$). We find that HQS is remarkably powerful, leaving only four new undetermined form factors at leading order in $1/m_{(b,c)}$. In addition, one of them is fixed in terms of the leading order Isgur-Wise function in the kinematic region, $v^{(\prime)}\cdot k < \Lambda_\text{QCD}$.