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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 difference between $B \to \rho \ell \bar \nu_\ell$ and $B \to \omega \ell \bar \nu_\ell$ from a recent Belle measurement of the $m_{\pi\pi}$ spectrum of $B \to \pi^+ \pi^- \ell \bar \nu_\ell$. In addition, we investigate different ways of modelling the $S$-wave component within an $m_{\pi\pi}$ window ranging from $2 m_\pi$ to $1.02 \, \mathrm{GeV}$. We also determine the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element of $|V_{ub}|_{\rho-\omega} = ( 3.03^{+0.49}_{-0.44}) \times 10^{-3}$, which takes into account the $\rho-\omega$ interference.
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