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

$B\to (\pi, \eta, \eta')$ transition form factors are investigated in the covariant light-front approach. With theoretical uncertainties, we find that $B\to (\pi, \eta, \eta')$ form factors at $q^2=0$ are $f^{(\pi, \eta, \eta')}_{+}(0)=(0.245^{+0.000}_{-0.001}\pm 0.011, 0.220 \pm 0.009\pm0.009, 0.180\pm 0.008^{+0.008}_{-0.007})$ for vector current and $f^{(\pi, \eta, \eta')}_{T}(0)=(0.239^{+0.002+0.020}_{-0.003-0.018}, 0.211\pm 0.009^{+0.017}_{-0.015}, 0.173\pm 0.007^{+0.014}_{-0.013})$ 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 $\bar B\to (\eta, \eta') \ell \bar\nu_{\ell}$ decays with $\ell=e,\mu$ are given by $(0.49^{+0.02+0.10}_{-0.04- 0.07}, 0.24^{+0.01+0.04}_{-0.02-0.03})\times 10^{-4}$, while the BRs for $D^-\to (\eta,\eta')\ell\bar\nu_{\ell}$ are $(11.1^{+0.5+0.9}_{-0.6-0.9}, 1.79^{+0.07+0.12}_{-0.08-0.12})\times 10^{-4}$. In addition, we also study the integrated lepton angular asymmetries for $\bar B\to (\pi,\eta,\eta')\tau \bar\nu_{\tau}$:$(0.277^{+0.001+0.005}_{-0.001-0.007},0.290^{+0.002+0.003}_{-0.000-0.003},0.312^{+0.004+0.005}_{-0.000-0.006})$.