Probing the structure of the $B$ meson with $B\to \ell \ell {\ell }^{\prime }\nu$

Abstract

We consider the decay $B\to \ell \ell {\ell }^{\prime }\nu$ in QCD factorization for the case of non-zero (but small) $q^2$, taking into account leading power contributions at NLL in $\mathcal{O}({\alpha }_s)$ and next-to-leading power corrections at $\mathcal{O}({\alpha }_s^0)$. We further incorporate soft contributions obtained from light-cone sum rules, extrapolated from the Euclidean to physical region using once-subtracted dispersion relations. We restrict ourselves to the case $\ell \ne {\ell }^{\prime }$ as otherwise the same sign $\ell$ and ${\ell }^{\prime }$ cannot be distinguished. We study the sensitivity of the results to the leading moment of the $B$-meson distribution amplitude and discuss the potential to extract this quantity at LHCb and the Belle II experiment.

Comments: 17 pages, 4 figures, 2 tables, version to be submitted to the journal