Padé approximants to B→πℓνℓ and Bs→Kℓνℓ and determination of |Vub|

We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element

| V_{c b} |

from the decay

B \to D ℓ ν_{ℓ}

using a

365 {fb}^{- 1}

e^{+} e^{-} \to ϒ (4 S) \to B \bar{B}

data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one

B

meson is reconstructed in the modes

B^{0} \to D^{-} (\to K^{+} π^{-} π^{-}) ℓ^{+} ν_{ℓ}

and

B^{+} \to {\bar{D}}^{0} (\to K^{+} π^{-}) ℓ^{+} ν_{ℓ}

, where

ℓ

denotes either an electron or a muon. Charge conjugation is implied. The second

B

meson in the

ϒ (4 S)

event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable

w = v_{B} \cdot v_{D}

, where

v_{B}

and

v_{D}

are the four-velocities of the

B

and

D

mesons. We measure the total decay branching fractions to be

B (B^{0} \to D^{-} ℓ^{+} ν_{ℓ}) = (2.06 \pm 0.05 (stat) \pm 0.10 (sys)) %

and

B (B^{+} \to {\bar{D}}^{0} ℓ^{+} ν_{ℓ}) = (2.31 \pm 0.04 (stat) \pm 0.09 (sys)) %

. We probe lepton flavor universality by measuring

B (B \to D e ν_{e}) / B (B \to D μ ν_{μ}) = 1.020 \pm 0.020 (stat) \pm 0.022 (sys)

. Fitting the partial decay branching fraction as a function of

w

and using the average of lattice QCD calculations of the

B \to D

form factor, we obtain

| V_{c b} | = (39.2 \pm 0.4 (stat) \pm 0.6 (sys) \pm 0.5 (th)) \times 10^{- 3}

.