Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$

Abstract

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 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 $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$ can be used to measure dipion form factors or to perform null tests of the Standard Model.

Comments: 11 pages, 2 figures; v2 as published: references added, conclusions remain unchanged