{$SU(3)$} breaking in {$\bar{B}/D\rar Kl\bar \nu$} decays and value of {$V_{cd}/V_{cs}$}}

Abstract

We determine the $SU(3)$-breaking effects in the $\bar{B}/D \rar Kl\bar \nu$ decays from the ratio of the $\bar{B}/D\rar Kl\bar \nu$ over the $\bar{B}/D \rar \pi l\bar \nu$ semileptonic form factors using a {\it semi-analytic} expression based on QCD spectral sum rules. We obtain $f_+^{\bar{B}\rar K}(0)/f_+^{\bar{B} \rar \pi}(0)$ = $1.007\pm 0.020$ and $f_+^{D\rar K}(0)/f_+^{D \rar \pi}(0)$ = $1.102 \pm 0.007$, which combined with the present CLEO data, leads to $V_{cd}/V_{cs}$ = $ 0.323 \pm 0.058$ and then, to: $\vert V_{cs}\vert = 0.72\pm 0.10$. The prediction on the ratio of mixing angle is (surprisingly) much higher than the value $0.226 \pm 0.004$ derived from the unitarity constraint on the CKM matrix, while the corresponding value of $ V_{cs}$ is lower. These results can open a window for new physics, though a stringent conclusion needs data with much higher statistics (from e.g tau-charm factory) or/and alternative QCD-based estimates of the ratio of the semileptonic form factors.