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rivet Analysis
Measurement of Differential Branching Fractions of Inclusive ${B \to X_u \, \ell^+\, \nu_{\ell}}$ Decays

The Belle collaboration Cao, L. ; Sutcliffe, W. ; Van Tonder, R. ; et al.

Phys.Rev.Lett. 127 (2021) 261801, 2021.

https://inspirehep.net/literature/1895149 Inspire Record 1895149 DOI 10.17182/hepdata.131599 https://doi.org/10.17182/hepdata.131599

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 $\ell = e, \mu$. Differential branching fractions are reported as a function of the lepton momentum, 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 measured distributions are compared to predictions from inclusive and hybrid ${B \to X_u \, \ell^+\, \nu_{\ell}}$ calculations.

50 data tables

Fig. 3 (top left)

The measured differential branching fractions as a function of the lepton energy in the $B$ rest frame ($E_\ell^B$).

Fig. 3 (top right)

The measured differential branching fractions as a function of the four-momentum-transfer squared of the $B$ to the $X_u$ system $q^{2}$.

Fig. 3 (middle left)

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

Fig. 3 (middle right)

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

Fig. 3 (bottom left)

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

Fig. 3 (bottom right)

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

Background-subtracted yields ($E_\ell^B$)

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

Background-subtracted yields ($q^2$)

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

Background-subtracted yields ($M_X$)

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

Background-subtracted yields ($M_X^2$)

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

Background-subtracted yields ($P_+$)

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

Background-subtracted yields ($P_-$)

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

Correlation matrix of bkg-subt. yields ($E_\ell^B$)

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

Correlation matrix of bkg-subt. yields ($q^2$)

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

Correlation matrix of bkg-subt. yields ($M_X$)

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

Correlation matrix of bkg-subt. yields ($M_X^{2}$)

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

Correlation matrix of bkg-subt. yields ($P_{+}$)

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

Ccorrelation matrix of bkg-subt. yields ($P_{-}$)

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

Fig. 5 (middle left)

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

Fig. 5 (middle right)

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

Fig. 5 (top left)

Migration matrix of $M_X$ [in %].

Fig. 5 (top right)

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

Fig. 5 (bottom left)

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

Fig. 5 (bottom right)

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

Fig. 6 (top left)

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

Fig. 6 (top right)

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

Fig. 6 (middle left)

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

Fig. 6 (middle right)

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 ($q^2$).

Fig. 6 (bottom left)

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

Fig. 6 (bottom right)

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

Fig. 7

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 $P_{-}$.

Fig. 8

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 $P_{-}$.

Fig. 9 (left)

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 $P_{-}$

Fig. 9 (right)

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 $P_{-}$.

Fig. 10 (left)

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

Fig. 10 (middle)

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

Fig. 10 (right)

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

Fig. 11 (top left)

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

Fig. 11 (top middle)

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

Fig. 11 (top right)

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

Fig. 11 (middle left)

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

Fig. 11 (center)

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

Fig. 11 (middle right)

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

Fig. 11 (bottom left)

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

Fig. 11 (bottom middle)

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

Fig. 11 (bottom right)

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

Fig. 12 (left)

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

Fig. 12 (middle)

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

Fig. 12 (right)

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

The full experimental correlations of the measured moments.

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.

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