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We present measurements of the first to fourth moments of the lepton masssquared $q^2$ 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. Theseresults use a sample of electron-positron collisions at the $\Upsilon(4S)$resonance corresponding to $62.8 \, \mathrm{fb}^{-1}$ of integrated luminosityand 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 ahadronic decay mode using a multivariate $B$ tagging algorithm. We report rawand 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 momentsin the experimentally challenging range of $[ 1.5, 2.5 ] \,\mathrm{GeV^2/c^4}$.

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