Measurement of Hadronic Mass Moments $\langle M_X^n \rangle $ in $B \rightarrow X_c \ell \nu $ Decays at Belle II

We present measurements of the first six hadronic mass moments in semileptonic $B \rightarrow X_c \ell \nu $ decays. The hadronic mass moments, together with other observables of inclusive $B$ decays, can be used to determine the CKM matrix element $|{V_{cb}}|$ and mass of the $b$-quark $m_b$ in the context of Heavy Quark Expansions of QCD. The Belle~II data recorded at the $\Upsilon (4S)$ resonance in 2019 and 2020 (March-July), corresponding to an integrated luminosity of $34.6\;\mathrm{fb}^{-1}$, is used for this measurement. The decay $\Upsilon (4S) \rightarrow B \overline{B}$ is reconstructed by applying the hadronic tagging algorithm provided by the Full Event Interpretation to fully reconstruct one $B$ meson. The second $B$ meson is reconstructed inclusively by selecting a high-momentum lepton. The $X_c$ system is identified by the remaining reconstructed tracks and clusters in the electromagnetic calorimeter. We report preliminary results for the hadronic mass moments $\langle M_X^n \rangle $ with $n=1,\dots,6$, measured as a function of a lower cut on the lepton momentum in the signal $B$ rest frame.