B−→π−π0/ρ−ρ0to next-to-next-to-leading order in QCD factorization

Abstract

The approximate tree decays ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}/{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\rho}}^{0}$ may serve as benchmark channels for testing the various theoretical descriptions of the strong interaction dynamics in hadronic $B$ meson decays. The ratios of hadronic and differential semileptonic $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}/\ensuremath{\rho}\ensuremath{\ell}\ensuremath{\nu}$ decay rates at maximum recoil provide particularly clean probes of the QCD dynamics. We confront the recent next-to-next-to-leading order calculation in the QCD factorization framework with experimental data and find support for the factorization assumption. A detailed analysis of all tree-dominated $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}/\ensuremath{\pi}\ensuremath{\rho}/\ensuremath{\rho}\ensuremath{\rho}$ decay modes seems to favor somewhat enhanced color-suppressed amplitudes, which may be accommodated in QCD factorization by a small value of the first inverse moment of the $B$ meson light-cone distribution amplitude, ${\ensuremath{\lambda}}_{B}\ensuremath{\simeq}250\text{ }\text{ }\mathrm{MeV}$. Precise measurements of the semileptonic $B\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\ell}\ensuremath{\nu}$ spectrum could help to clarify this point.