Role of $\rho -\omega$ interference in semileptonic $B\to {\pi }^{+}{\pi }^{-}\ell {\bar{\nu }}_{\ell }$ decays

Abstract

It is long known that interference effects play an important role in understanding the shape of the ${\pi }^{+}{\pi }^{-}$ spectrum of resonances near the threshold. In this manuscript we investigate the role of the $\rho -\omega$ interference in the study of semileptonic $B\to {\pi }^{+}{\pi }^{-}\ell {\bar{\nu }}_{\ell }$ decays. We determine for the first time the strong phase between $B\to {\rho }^0\ell {\bar{\nu }}_{\ell }$ and $B\to \omega \ell {\bar{\nu }}_{\ell }$ from a recent Belle measurement of the $m_{\pi \pi }$ spectrum of $B\to {\pi }^{+}{\pi }^{-}\ell {\bar{\nu }}_{\ell }$. We find ${\varphi }_{\rho -\omega }=\left(-46_{-67}^{+155}\right)°$ and extract the branching fraction of $\mathcal{B}(B\to {\rho }^0\ell {\bar{\nu }}_{\ell })=\left(1.41_{-0.38}^{+0.49}\right)\times 10^{-4}$. In addition, we set a limit on the $S$-wave component within a mass window ranging from $2m_{\pi }$ to $1.02\mathrm{GeV}$ of $0.51\times 10^{-4}\mathrm{at}90\%\mathrm{CL}$. We also determine the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element of $|V_{ub}{|}_{\rho -\omega }=\left(3.03_{-0.44}^{+0.49}\right)\times 10^{-3}$, which takes into account the $\rho -\omega$ interference.

Comments: 13 pages, 16 figures