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We study the semileptonic $b\to u$ transition in the decay mode $B^-\to\pi^+\pi^-\ell^-\bar\nu_\ell$. We define $B\to \pi \pi$ form factors in thehelicity basis, and study their properties in various kinematic limits,including form factor relations in the heavy-mass and large-energy limits, thedecomposition into partial waves of the dipion system, and the resonantcontribution of vector and scalar mesons. We show how angular observables in$B^-\to \pi^+\pi^-\ell^-\bar\nu_\ell$ can be used to measure dipion formfactors or to perform null tests of the Standard Model.

Disentangling the Decay Observables in $B^- \to \pi^+\pi^-\ell^-\bar\nu_\ell$