Form factors of exclusive b→u transitions

We present the form factors of the B→π,ρ transitions induced by the b→u quark currents at all kinematically accessible q2. Our analysis is based on the spectral representations of the form factors within the constituent quark picture: we fix the soft meson wave functions and the constituent quark masses by fitting A1(q2) and T2(q2) to the lattice results at small recoils (17≲q2≲20 GeV2). We then calculate the B→π,ρ transition form factors down to q2=0. For the B→π case the region q2≲20 GeV2 however does not cover the whole kinematically accessible range. Due to the smallness of the pion mass the region of small recoils is close to the nearby B∗(5234) resonance. We develop a parametrization which includes the B∗ dominance of the form factors f+ and f− at small recoils and numerically reproduces the results of calculations at q2≲20 GeV2. We find Γ(B→πℓν)=8.0+0.8−0.2|Vub|2ps−1 and Γ(B→ρℓν)=15.8±2.3|Vub|2ps−1.