| Abstract: | We present a measurement of the ratio of partial branching fractions of the
semi-leptonic inclusive decays, $overline{B} o X_{u} ell overline{
u}$ to
$overline{B} o X_{c} ell overline{
u}$, where $ell = (e, mu)$, using
the full Belle sample of $772 imes 10^{6}$ $B kern 0.18emoverline{kern
-0.18em B}$ pairs collected at the $Upsilon(4S)$ resonance. The ratio is
measured via a two-dimensional fit to the squared four-momentum transfer to the
lepton pair, and the charged lepton energy in the $B$ meson rest frame, where
the latter must be larger than $1$ Gekern -0.1em V, covering approximately
$86\%$ and $78\%$ of the $overline{B} o X_{u} ell overline{
u}$ and
$overline{B} o X_{c} ell overline{
u}$ phase space, respectively. We find
$Delta mathcal{B}(overline{B} o X_{u} ell overline{
u})/ Delta
mathcal{B}(overline{B} o X_{c} ell overline{
u}) = 0.0196(1 pm
8.4\%_{
m stat} pm 7.9\%_{
m syst})$ where the uncertainties are statistical
and systematic, respectively. In addition, we report the partial branching
fractions separately for charged and neutral $B$ meson decays, and for electron
and muon decay channels. We place a limit on isospin breaking in $overline{B}
o X_{u} ell overline{
u}$ decays, and find no indication of lepton flavor
universality violation in either the charmed or charmless mode. Furthermore, we
unfold the $overline{B} o X_{u} ell overline{
u}$ and $overline{B} o
X_{c} ell overline{
u}$ yields and report the differential ratio in lepton
energy and four-momentum transfer squared. |
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