"The full experimental correlations of the measured moments." of "Measurement of Differential Branching Fractions of Inclusive ${B \to X_u \, \ell^+\, \nu_{\ell}}$ Decays"

The first measurements of differential branching fractions of inclusive semileptonic $B \to X_u \, \ell^+\, \nu_{\ell}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $\Upsilon(4S)$ resonance and for $\ell = e, \mu$. With the availability of these measurements, new avenues for future shape-function model-independent determinations of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ can be pursued to gain new insights in the existing tension with respect to exclusive determinations. The differential branching fractions are reported as a function of the lepton energy, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic $B \to X_c \, \ell^+\, \nu_{\ell}$ decays and other processes, and corrected for resolution and acceptance effects.

The matrix elements are saved in the order of $M_{X}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$. For each variable, the entries is ordered for the first, second and third moments.