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We consider the decay $B\to\ell\ell\ell^{\prime}\nu$, taking into account theleading $1/m_b$ and $q^2$ corrections calculated in the QCD factorizationframework as well as the soft corrections calculated employing dispersionrelations and quark-hadron duality. We extend the existing results for theradiative decay $B\to\gamma\ell\nu$ to the case of non-zero (but small) $q^2$,the invariant mass squared of the dilepton pair $\ell^+\ell^-$. This restrictsus to the case $\ell\neq\ell'$ as otherwise the same sign $\ell$ and $\ell'$cannot be distinguished. We further study the sensitivity of the results to theleading moment of the $B$-meson distribution amplitude and discuss thepotential to extract this quantity at LHCb and the Belle II experiment.

Probing the structure of the $B$ meson with $B\to\ell\ell\ell'\nu$