Disentangling the Decay Observables in $B^- \to π^+π^-\ell^-\barν_\ell$

Abstract

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