Disentangling the decay observables inB−→π+π−ℓ−ν¯ℓ

Abstract

We study the semileptonic $b\ensuremath{\rightarrow}u$ transition in the decay mode ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$. We define $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ 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 ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ can be used to measure dipion form factors or to perform null tests of the Standard Model.