$B\to \rho$ semileptonic decays and $|V_{ub}|$

Understand

We reevaluate the $B\to\rho\,l^+\nu_l$ decay width as a full $B\to\pi\pi\,l^+\nu_l$ four-particle decay, in which the two final pions are produced via an intermediate $\rho$ meson.

• The decay width can be written as a convolution of the $B\to\rho\,l^+\nu_l$ decay width, for an off-shell $\rho$, with the $\rho\to\pi\pi$ line shape.
• This allows to fully incorporate the effects of the finite $\rho$ meson width.
• As shown, consideration of the $\rho$ meson width effects increase the $|V_{ub}|$ value by some 8%, rendering it in better agreement with the determination based in the $B\to\pi$ decay.