Inclusive $B$ decays, lifetimes, and $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$: a unified heavy-quark expansion analysis

We present a global HQE analysis of inclusive semileptonic $\bar{B}\to X_{c}l{\bar{\nu }}_{\mathrm{\ell }}$ moments, partial branching fractions, and $B^{+}$, $B^0$ 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 $O(1\mathrm{/}{m}_b^5)$. In the default scenario, we find $\mathrm{\mid }{V}_{cb}\mathrm{\mid }=(42.32\pm 0.28{\mathrm{\mid }}_{\mathrm{f}\mathrm{i}\mathrm{t}}\pm 0.10{\mathrm{\mid }}_{\mathrm{h}\mathrm{.}\mathrm{o}\mathrm{.}})\times {10}^{-3}=(42.32\pm 0.30)\times {10}^{-3}$ and $\mathcal{B}(\bar{B}\to X_c\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }})=(10.91\pm 0.11{\mathrm{\mid }}_{\mathrm{f}\mathrm{i}\mathrm{t}}\pm 0.21{\mathrm{\mid }}_{\mathrm{h}\mathrm{.}\mathrm{o}\mathrm{.}})\mathrm{\%}$. For the lifetimes we obtain ${\tau }_{B^{+}}=1.89_{-0.22}^{+0.04}$ ps and ${\tau }_{B^0}=1.74_{-0.23}^{+0.03}$ 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 $1.1$-$1.2,\sigma$ below the measurements. For the lifetime ratio, we find ${\tau }_{B^{+}}\mathrm{/}{\tau }_{B^0}=1.082_{-0.013}^{+0.031}$ which agrees with experiment. For the full dataset of $q^2,E_{\mathrm{\ell }}$ and $M_X$ moments, we obtain a poor fit quality, which we investigate using a leave-one-out study. In light of the persisting $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ puzzle, new correlated moment measurements as well as updated branching ratio measurements are highly encouraged.