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Constraints on B--->pi,K transition form factors from exclusive semileptonic D-meson decays

According to the heavy-quark flavour symmetry, the $B\to π, K$ transition form factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays $D \to π\ell ν$ and $D\to K \ell ν$, we perform a phenomenological study of $B \to π, K$ transition form factors based on this symmetry. Using BK, BZ and Series Expansion parameterizations of the form factor slope, we extrapolate $B \to π, K$ transition form factors from $q^{2}_{max}$ to $q^{2}=0$. It is found that, although being consistent with each other within error bars, the central values of our results for $B \to π, K$ form factors at $q^2=0$, $f_+^{B\to π, K}(0)$, are much smaller than predictions of the QCD light-cone sum rules, but are in good agreements with the ones extracted from hadronic B-meson decays within the SCET framework. Moreover, smaller form factors are also favored by the QCD factorization approach for hadronic B-meson decays.