A calibration of the Belle II hadronic tag-side reconstruction algorithm with $B \rightarrow X\ell \nu$ decays.

Tag-side reconstruction is an important method for reconstructing $B$ meson decays with missing energy. The Belle II tag-side reconstruction algorithm, Full Event Interpretation, relies on a hierarchical reconstruction of $B$ meson decays with multivariate classification employed at each stage of reconstruction. Given the large numbers of classifiers employed and decay chains reconstructed, the performance of the algorithm on data and simulation differs significantly. Here, calibration factors are derived for hadronic tag-side $B$ decays by measuring a signal side decay, $B \rightarrow X\ell \nu$, in $34.6$ fb$^{-1}$ of Belle II data. For a very loose selection on the tag-side $B$ multivariate classifier, the calibration factors are $0.65 \pm 0.02$ and $0.83 \pm 0.03$ for tag-side $B^{+}$ and $B^{0}$ mesons, respectively.