Measurement of the decay $B^0\to\pi^-\ell^+\nu$ and determination of $|V_{ub}|$

We present a measurement of the charmless semileptonic decay $B^0\to\pi^-\ell^+\nu$ using a data sample containing 657$\times 10^6$ $B\bar{B}$ events collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider operating near the $\Upsilon(4S)$ resonance. We determine the total branching fraction of the decay, $\mathcal{B}(B^0\to\pi^-\ell^+\nu)=(1.49\pm 0.04{(\mathrm{stat})}\pm 0.07{(\mathrm{syst})})\times 10^{-4}$. We also report a new precise measurement of the differential decay rate, and extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ using model-independent and -dependent approaches. From a simultaneous fit to the measured differential decay rate and lattice QCD results, we obtain $|V_{ub}|=(3.43\pm 0.33)\times 10^{-3}$, where the error includes both statistical and systematic uncertainties.