Radiative Semileptonic $\bar{B}$ Decays

We consider the form factors for the radiative semileptonic decays $\bar{B}(v) \rightarrow D^{(*)}(v') \ell {\bar ν}_\ell γ$ 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, $v^{(\prime)}\cdot k < Λ_\text{QCD}$.

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