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Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

We determine $|V_{cb}|$ using the third-order perturbative series for the inclusive semileptonic $B$ decay width and for the masses of the bottomonium 1S states. We use the masses of $η_b(1S)$ and $Υ(1S)$ as short-distance masses and point out that there is a sizable difference of $|V_{cb}|$ between the two 1S mass schemes. This is the dominant error of our determination and stems from insufficiency to describe theoretically the observed mass splitting of the bottomonium 1S states. We also study the significance of the $\mathcal{O}(Λ_{\overline{\rm MS}}^2)$ non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result $|V_{cb}|=0.0425 (11)$ is consistent with the PDG value determined from the inclusive decays and has a slightly larger error.