New results on $|V_{ub}|$ using inclusive and exclusive $B$ decays from the Belle experiment
We present two recent measurements of semileptonic B decays at Belle, offering valuable insights into the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$. These analyses use the full Belle dataset, comprising $772 \times 10^6$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance. With an innovative strategy, the inclusive $B \to X_u \ell \nu$ and exclusive $B \to \pi \ell \nu$ decays are simultaneously analyzed for the first time, and the $|V_{ub}|$ ratio is extracted as $|V_{ub}^{\mathrm{excl.}}|/|V_{ub}^{\mathrm {incl.}}|=0.97 \pm 0.12$. Furthermore, we provide preliminary results for the inclusive branching fractions ratio of $B \to X_u \ell \nu$ and $B \to X_c \ell \nu$ decays, accompanied by additional interpretations aimed at deriving the inclusive $|V_{ub}|/|V_{cb}|$ ratio.