Measurement of Lepton Mass Squared Moments in $B \to X_c \ell \bar \nu_{\ell}$ Decays with the Belle II Experiment

We present measurements of the first to fourth moments of the lepton mass squared $q^2$ of \mbox{$B \to X_c \, \ell\, \bar \nu_{\ell}$} decays for $\ell = e, \mu$ and with $X_c$ a hadronic system containing a charm quark. These results use a sample of electron-positron collisions at the $\Upsilon(4S)$ resonance corresponding to $62.8 \, \mathrm{fb}^{-1}$ of integrated luminosity and collected by the Belle II experiment in 2019 and 2020. To identify the $X_c$ system and reconstruct $q^2$, one of the $B$ mesons from an $\Upsilon(4S) \to B \kern 0.18em\overline{\kern -0.18em B}$ decay is fully reconstructed in a hadronic decay mode using a multivariate $B$ tagging algorithm. We report raw and central moments for $ q^2 > 1.5 \; \mathrm{GeV^2/c^4}$ up to $q^2 > 8.5 \; \mathrm{GeV^2/c^4}$, probing up to 77\% of the accessible \mbox{$B \to X_c \, \ell\, \bar \nu_{\ell}$} phase space. This is the first measurement of moments in the experimentally challenging range of $[ 1.5, 2.5 ] \, \mathrm{GeV^2/c^4}$.