B→ρsemileptonic decays and|Vub|

Abstract

We reevaluate the $B\ensuremath{\rightarrow}\ensuremath{\rho}{l}^{+}{\ensuremath{\nu}}_{l}$ decay width as a full $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}{l}^{+}{\ensuremath{\nu}}_{l}$ four-particle decay, in which the two final pions are produced via an intermediate $\ensuremath{\rho}$ meson. The decay width can be written as a convolution of the $B\ensuremath{\rightarrow}\ensuremath{\rho}{l}^{+}{\ensuremath{\nu}}_{l}$ decay width, for an off-shell $\ensuremath{\rho}$, with the $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ line shape. This allows us to fully incorporate the effects of the finite $\ensuremath{\rho}$ meson width and a better comparison with actual experiments. We use an Omn\`es representation to provide the dependence of the $B\ensuremath{\rightarrow}\ensuremath{\rho}$ semileptonic form factors on ${q}^{2}$. The Omn\`es subtraction constants and the overall normalization parameter $|{V}_{ub}|$ are fitted to light cone sum rules and lattice QCD theoretical form-factor calculations, in the low and high ${q}^{2}$ regions, respectively, together to the CLEO, BABAR, and Belle experimental partial branching fraction distributions. The extracted value from this global fit is $|{V}_{ub}|=(3.40\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$, in agreement with $|{V}_{ub}|$ extracted using all other inputs in Cabibbo--Kobayashi--Maskawa fits and the exclusive semileptonic $B\ensuremath{\rightarrow}\ensuremath{\pi}$ channel, but showing a clear disagreement with $|{V}_{ub}|$ extracted from inclusive semileptonic $b\ensuremath{\rightarrow}u$ decays. As estimated by [U.-G. Mei\ss{}ner and W. Wang, J. High Energy Phys. 01 (2014) 107], taking into account the $\ensuremath{\rho}$ meson width effects and the actual acceptance of the experiments is essential to render the $|{V}_{ub}|$ determinations from exclusive $B\ensuremath{\rightarrow}\ensuremath{\pi}$ and $B\ensuremath{\rightarrow}\ensuremath{\rho}$ decays totally compatible.