Speaker
Description
In this talk, I will review recent advancements in the calculation of QCD higher-order corrections for semileptonic $B$ decays. Specifically, I will present the next-to-next-to-leading-order corrections to the $q^2$ spectrum of the inclusive decay $B \to X_c l\bar{\nu}_l$, which can be utilized to incorporate the recent measurements of $q^2$ moments by Belle and Belle II into global fits of inclusive semileptonic $B$ decays. Additionally, I will discuss recent results for the third-order corrections to the total width of $b \to u l \bar{\nu}_l$ decays. These corrections are crucial for evaluating the phase-space ratio $C = |V_{ub}/V_{cb}|^2 \Gamma(B \to X_c l \bar{\nu}_l)/\Gamma(B \to X_u l \bar{\nu}_l)$, which appears as normalization factor in the branching ratios of $B$ decays mediated by $b \to s$ transitions, such as $B \to X_s \gamma$ and $B \to X_s l^+l^-$.
