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

Abstract

We present a global HQE analysis of inclusive semileptonic $\bar{B} \to X_c l \bar ν_\ell$ 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 $O(1/m_b^5)$. In the default scenario, we find $|V_{cb}| = (42.32 \pm 0.28|_{\rm fit} \pm 0.10|_{\rm h.o.})\times 10^{-3} = (42.32 \pm 0.30) \times 10^{-3}$ and $\mathcal{B}(\bar B \to X_c \ell \bar ν_\ell) = (10.91 \pm 0.11|_{\rm fit} \pm 0.21|_{\rm h.o.})\%$. For the lifetimes we obtain $τ_{B^+} = 1.89^{+0.04}_{-0.22}$ ps and $τ_{B^0} = 1.74^{+0.03}_{-0.23}$ 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 $τ_{B^+}/τ_{B^0} = 1.082^{+0.031}_{-0.013}$ 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.