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

Abstract

We determine the $SU(3)$-breaking effects in the $\bar{B}/D\text{rar}Kl\bar{\nu }$ decays from the ratio of the $\bar{B}/D\text{rar}Kl\bar{\nu }$ over the $\bar{B}/D\text{rar}\pi l\bar{\nu }$ semileptonic form factors using a {\it semi-analytic} expression based on QCD spectral sum rules. We obtain $f_{+}^{\bar{B}\text{rar}K}(0)/f_{+}^{\bar{B}\text{rar}\pi }(0)$ = $1.007\pm 0.020$ and $f_{+}^{D\text{rar}K}(0)/f_{+}^{D\text{rar}\pi }(0)$ = $1.102\pm 0.007$, which combined with the present CLEO data, leads to $V_{cd}/V_{cs}$ = $0.323\pm 0.058$ and then, to: $|V_{cs}|=0.72\pm 0.10$. 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.

Comments: 8 pages in latex file + 3 figures in PS-files available on requests. CERN-TH 7309/94 (1994) (to appear as Phys. Lett. B)