The measured differential branching fractions as a function of the invariant hadronic mass squared of the $X_u$ system ($M_X^2$).

The measured differential branching fractions as a function of the light-cone momenta of the hadronic $X_u$ system [$P_+ = (E_X^B - |old{p}_X^B|)$].

The measured differential branching fractions as a function of the light-cone momenta of the hadronic $X_u$ system [$P_- = (E_X^B + |old{p}_X^B|)$].

The background-subtracted yields as a function of $E_\ell^B$.

The background-subtracted yields as a function of $q^2$.

The background-subtracted yields as a function of $M_X$.

The background-subtracted yields as a function of $M_X^2$.

The background-subtracted yields as a function of $P_+$. [$P_+ = (E_X^B - |P_X^B|)$]

The background-subtracted yields as a function of $P_-$. [$P_- = (E_X^B + |P_X^B|)$].

The full experimental correlation matrix for the background-subtracted spectrum of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The full experimental correlation matrix for the background-subtracted spectrum of $q^2$).

The full experimental correlation matrix for the background-subtracted spectrum of $M_X$.

The full experimental correlation matrix for the background-subtracted spectrum of $M_X^2$.

The full experimental correlation matrix for the background-subtracted spectrum of $P_+$.

The full experimental correlation matrix for the background-subtracted spectrum of $P_-$.

Migration matrix of $E_\ell^B$ [in %].

Migration matrix of $q^2$ [in %].

Migration matrix of $M_X$ [in %].

Migration matrix of $M_X^2$ [in %].

Migration matrix of $P_+$ [in %].

Migration matrix of $P_-$ [in %].

The total correction factors and phase space acceptance as a function of the invariant hadronic mass of the $X_u$ system ($M_X$).

The total correction factors and phase space acceptance as a function of the invariant hadronic mass squared of the $X_u$ system ($M_X^2$).

The total correction factors and phase space acceptance as a function of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The total correction factors and phase space acceptance as a function of the four-momentum-transfer squared of the $B$ to the $X_u$ system ($q^2$).

The total correction factors and phase space acceptance as a function of $P_+$.

The total correction factors and phase space acceptance as a function of $P_-$.

The statistical correlations of the differential branching fractions are shown. The matrix elements are ordered for $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The full experimental (statistical and systematical) correlations of the differential branching fractions are shown. The matrix elements are ordered for $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The total partial branching fraction with $E_{\ell}^{B} > 1$ GeV. The order of entries is: the 2D fit result of Phys. Rev. D 104, 012008 (2021), the results calcuated with the differential branching fractions of $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$

The full experimental correlations between the total partial branching fractions from summing the individual bins are shown. The matrix elements are saved in the order of $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The first moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The second moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The third moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The first moment of the measured differential branching fraction of $q^2$.

The second moment of the measured differential branching fraction of $q^2$.

The third moment of the measured differential branching fraction of $q^2$.

The first moment of the measured differential branching fraction of $M_{X}$.

The second moment of the measured differential branching fraction of $M_{X}$.

The third moment of the measured differential branching fraction of $M_{X}$.

The first moment of the measured differential branching fraction of $P_{+}$.

The second moment of the measured differential branching fraction of $P_{+}$.

The third moment of the measured differential branching fraction of $P_{+}$.

The first moment of the measured differential branching fraction of $P_{-}$.

The second moment of the measured differential branching fraction of $P_{-}$.

The third moment of the measured differential branching fraction of $P_{-}$.

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.