We construct light cone sum rules (LCSR) for the $B\to K^{*}$ 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 $\overline{q}\mathrm{\Gamma }[i{\cancel{D}}_{\perp }/(2m_b)]h_v$, 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 $B\to K^{*}$ form factors and find that the subleading-power contributions amount to 30% of the corresponding leading-power results. Employing the Bourrely-Caprini-Lellouch parametrization, we determine the numerical results for $B\to K^{*}$ 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 $B\to K^{*}$ form factors, we compute the branching fractions for the rare decays $B\to K^{*}{\nu }_{\ell }{\overline{\nu }}_{\ell }$ in the Standard Model, obtaining $\mathcal{B}\mathcal{R}({\overline{B}}^0\to {\overline{K}}^{*0}{\nu }_{\ell }{\overline{\nu }}_{\ell })=8.09(96)\times {10}^{-6}$ and $\mathcal{B}\mathcal{R}({\overline{B}}^{+}\to {\overline{K}}^{*+}{\nu }_{\ell }{\overline{\nu }}_{\ell })=9.95(1.05)\times {10}^{-6}$. Additionally, we predict that the longitudinal $K^{*}$ polarization fraction is $F_L=0.44(4)$.

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• Particle decays
• Particle phenomena