Precision calculations of $B\to K^{\ast }$ form factors from SCET sum rules beyond leading-power contributions

Abstract

We construct light-cone sum rules (LCSR) for the $B\to K^{\ast }$ form factors in the large recoil region using vacuum-to-$B$-meson correlation functions, and systematically calculate subleading-power corrections to these form factors at tree level, including next-to-leading power contributions from the hard-collinear propagator, the subleading effective current $\bar{q}\Gamma [i\text{slashed}{D}_{\perp }/(2m_b)]h_v$, and twist-five/six four-particle higher-twist effects. By incorporating the available leading-power results at $\mathcal{O}({\alpha }_s)$ and the corrections to higher-twist $B$-meson light-cone distribution amplitudes from our previous work, we improve the precision of theoretical predictions for $B\to K^{\ast }$ form factors and find that the subleading-power contributions amount to 30\% of the corresponding leading-power results. Employing the Bourrely-Caprini-Lellouch (BCL) parametrization, we determine the numerical results for $B\to K^{\ast }$ form factors across the full kinematic range through a combined fit of LCSR predictions in the large recoil region and lattice QCD results in the small recoil region. Using the newly obtained $B\to K^{\ast }$ form factors, we compute the branching fractions for the rare decays $B\to K^{\ast }{\nu }_{\ell }{\bar{\nu }}_{\ell }$ in the Standard Model, obtaining $\mathcal{B}\mathcal{R}({\bar{B}}^0\to {\bar{K}}^{\ast 0}{\nu }_{\ell }{\bar{\nu }}_{\ell })=8.09(96)\times 10^{-6}$ and $\mathcal{B}\mathcal{R}({\bar{B}}^{+}\to {\bar{K}}^{\ast +}{\nu }_{\ell }{\bar{\nu }}_{\ell })=9.95(1.05)\times 10^{-6}$. Additionally, we predict that the longitudinal $K^{\ast }$ polarization fraction is $F_L=0.44(4)$.

Comments: 32 pages, 9 figures