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

Abstract

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 ${\xi }_{\parallel }(n\cdot p)$, ${\xi }_{\perp }(n\cdot p)$, ${\Xi }_{\parallel }(\tau ,n\cdot p)$ and ${\Xi }_{\perp }(\tau ,n\cdot p)$, 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 $B\to V\ell {\bar{\nu }}_{\ell }$ 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 ${\xi }_{\parallel }(n\cdot p)$ and ${\xi }_{\perp }(n\cdot p)$ is also computed from the LCSR method with the $B$-meson light-cone distribution amplitude ${\varphi }_B^{+}(\omega ,\mu )$ at $\mathcal{O}({\alpha }_s)$. 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 $B\to \rho \ell {\bar{\nu }}_{\ell }$ and $B\to \omega \ell {\bar{\nu }}_{\ell }$ decays, and predict the normalized differential branching fractions and the $q^2$-binned $K^{\ast }$ longitudinal polarization fractions of the exclusive rare $B\to K^{\ast }{\nu }_{\ell }{\bar{\nu }}_{\ell }$ decays.

arXiv comment76 pages, 15 figures

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