Precision calculations of $B \to V$ form factors in QCD

Applying the vacuum-to-$B$-meson correlation functions with an interpolating current for the light vector meson we construct the light-cone sum rules (LCSR) for the "effective" form factors $ξ_{\parallel}(n \cdot p)$, $ξ_{\perp}(n \cdot p)$, $Ξ_{\parallel}(τ, n \cdot p)$ and $Ξ_{\perp}(τ, n \cdot p)$, defined by the corresponding hadronic matrix elements in soft-collinear effective theory (SCET), entering the leading-power factorization formulae for QCD form factors responsible for $B \to V \ell \bar ν_{\ell}$ and $B \to V \ell \bar \ell$ decays at large hadronic recoil at next-to-leading-order in QCD. The light-quark mass effect for the local SCET form factors $ξ_{\parallel}(n \cdot p)$ and $ξ_{\perp}(n \cdot p)$ is also computed from the LCSR method with the $B$-meson light-cone distribution amplitude $ϕ_B^{+}(ω, μ)$ at ${\cal O}(α_s)$. Furthermore, the subleading power corrections to $B \to V$ form factors from the higher-twist $B$-meson light-cone distribution amplitudes are also computed with the same method at tree level up to the twist-six accuracy. Having at our disposal the LCSR predictions for $B \to V$ form factors, we further perform new determinations of the CKM matrix element $|V_{ub}|$ from the semileptonic $B \to ρ\, \ell \, \bar ν_{\ell}$ and $B \to ω\, \ell \, \bar ν_{\ell}$ decays, and predict the normalized differential branching fractions and the $q^2$-binned $K^{\ast}$ longitudinal polarization fractions of the exclusive rare $B \to K^{\ast} \, ν_{\ell} \, \bar ν_{\ell}$ decays.

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