Inclusive $B$ decays, lifetimes, and $|V_{cb}|$: a unified heavy-quark expansion analysis

Abstract: We present a global HQE analysis of inclusive semileptonic $\bar{B} \to X_c l \bar ν<em>\ell$ moments, partial branching fractions, and $B<sup>+$, $B<sup>0$ lifetime observables. Our fit setup follows a new approach where perturbative scales are treated as correlated nuisance parameters, while missing higher-order power corrections are assessed through order-by-order fits up to $O(1/m_b<sup>5)$. In the default scenario, we find $$|V</em>{cb}| = (42.32 \pm 0.28|<em>{\rm fit} \pm 0.10|</em>{\rm h.o.})\times 10^{-3} = (42.32 \pm 0.30) \times 10<sup>{-3}$$ and $$\mathcal{B}(\bar B \to X_c \ell \bar ν<em>\ell) = (10.91 \pm 0.11|</em>{\rm fit} \pm 0.21|<em>{\rm h.o.})\%$$. For the lifetimes we obtain $τ</em>{B^+} = 1.89<sup>{+0.04}_{-0.22}$ ps and $$τ<em>{B^0} = 1.74^{+0.03}</em>{-0.23}$$ ps, where the strongly asymmetric uncertainty is dominated by the perturbative scale variation of the non-leptonic width. Our predictions are in agreement with previous predictions and the corresponding widths lie $1.1$-$1.2,σ$ below the measurements. For the lifetime ratio, we find $$τ<em>{B^+}/τ</em>{B^0} = 1.082<sup>{+0.031}_{-0.013}$$ which agrees with experiment. For the full dataset of $q^2, E_\ell$ and $M_X$ moments, we obtain a poor fit quality, which we investigate using a leave-one-out study. In light of the persisting $|V_{cb}|$ puzzle, new correlated moment measurements as well as updated branching ratio measurements are highly encouraged.