$|V_{ub}|$ and $B\to {\eta }^{{(}^{\prime })}$ Form Factors in Covariant Light Front Approach

Abstract

$B\to (\pi ,\eta ,{\eta }^{\prime })$ transition form factors are investigated in the covariant light-front approach. With theoretical uncertainties, we find that $B\to (\pi ,\eta ,{\eta }^{\prime })$ form factors at $q^2=0$ are $f_{+}^{(\pi ,\eta ,{\eta }^{\prime })}(0)=(0.245_{-0.001}^{+0.000}\pm 0.011,0.220\pm 0.009\pm 0.009,0.180\pm 0.008_{-0.007}^{+0.008})$ for vector current and $f_T^{(\pi ,\eta ,{\eta }^{\prime })}(0)=(0.239_{-0.003-0.018}^{+0.002+0.020},0.211\pm 0.009_{-0.015}^{+0.017},0.173\pm 0.007_{-0.013}^{+0.014})$ for tensor current, respectively. With the obtained $q^2$-dependent $f_{+}^{\pi }(q^2)$ and observed branching ratio (BR) for ${\bar{B}}_d\to {\pi }^{+}\ell {\bar{\nu }}_{\ell }$, the $V_{ub}$ is found as $|V_{ub}{|}_{LF}=(3.99\pm 0.13)\times 10^{-3}$. As a result, the predicted BRs for $\bar{B}\to (\eta ,{\eta }^{\prime })\ell {\bar{\nu }}_{\ell }$ decays with $\ell =e,\mu$ are given by $(0.49_{-0.04-0.07}^{+0.02+0.10},0.24_{-0.02-0.03}^{+0.01+0.04})\times 10^{-4}$, while the BRs for $D^{-}\to (\eta ,{\eta }^{\prime })\ell {\bar{\nu }}_{\ell }$ are $(11.1_{-0.6-0.9}^{+0.5+0.9},1.79_{-0.08-0.12}^{+0.07+0.12})\times 10^{-4}$. In addition, we also study the integrated lepton angular asymmetries for $\bar{B}\to (\pi ,\eta ,{\eta }^{\prime })\tau {\bar{\nu }}_{\tau }$:$(0.277_{-0.001-0.007}^{+0.001+0.005},0.290_{-0.000-0.003}^{+0.002+0.003},0.312_{-0.000-0.006}^{+0.004+0.005})$.

14 pages, 2 figures, final version to appear in PLB

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