Evaluation of CKM matrix elements from exclusive $P_{\ell 4}$ decays

Abstract

We consider the exclusive $P_{\ell 4}$ decays, $P\to (P_1{P}_2{)}_V\ell {\nu }_{\ell }$, where the subindex $V$ means that the invariant mass of the pseudoscalar pair is taken within a small window around the mass of the vector meson $V$. Pole contributions beyond the dominant $P\to V(\to P_1{P}_2)\ell {\nu }_{\ell }$ amplitude of $P_{\ell 4}$ decays are identified, which, in turn, affects the determination of the CKM matrix elements $|V_{q{q}^{\prime }}|$. We evaluate the effects of those contributions in the extraction of bottom and charm quark mixings. An application to $B\to (\pi \pi {)}_{\rho }\ell {\nu }_{\ell }$ data from Belle collaboration, shows an increase in the extracted value of $|V_{ub}|$ in better agreement with determinations based on $B\to \pi \ell {\nu }_{\ell }$ decays. The effect of the $\rho$ and $D^{\ast }$ pole contributions in the determination of $|V_{cd}|$ from the decay $D\to \pi \pi {\ell }^{-}{\bar{\nu }}_{\ell }$, has been also investigated.

Comments: A few comments added. Final text to match version accepted for publication