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Measurement of the branching fractions of the $B^+ \to η\ell^+ ν_{\ell} $ and $B^+ \to η^{\prime} \ell^+ ν_{\ell} $ decays with signal-side only reconstruction in the full $q^2$ range

The branching fractions of the decays $B^{+} \to η\ell^{+} ν_{\ell}$ and $B^{+} \to η^{\prime} \ell^{+} ν_{\ell}$ are measured, where $\ell$ is either an electron or a muon, using a data sample of $711\,{\rm fb}^{-1}$ containing $772 \times 10^6 B\bar{B}$ pairs collected at the $Υ(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. To reduce the dependence of the result on the form factor model, the measurement is performed over the entire $q^2$ range. The resulting branching fractions are ${\cal B}(B^{+} \rightarrow η\ell^{+} ν_{\ell}) = (2.83 \pm 0.55_{\rm (stat.)} \pm 0.34_{\rm (syst.)}) \times 10^{-5}$ and ${\cal B}(B^{+} \rightarrow η' \ell^{+} ν_{\ell}) = (2.79 \pm 1.29_{\rm (stat.)} \pm 0.30_{\rm (syst.)}) \times 10^{-5}$.