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

Abstract

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 ${\eta }_b(1S)$ and ${\rm Y}(1S)$ 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 $\mathcal{O}({\Lambda }_{\overline{\mathrm{MS}}}^2)$ 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.

14pages, 2 figures, version to appear in PLB

References in corpus (8)

• Quark mass relations to four-loop order
• Precision determination of the CKM element Vcb
• Mass effects in muon and semileptonic b -> c decays
• Three loop calculations and inclusive $V_{cb}$
• Three-Loop Chromomagnetic Interaction in HQET
• Heavy-to-heavy quark decays at NNLO
• Inclusive semileptonic B decays from QCD with NLO accuracy for power suppressed terms
• Semileptonic decays in the limit of a heavy daughter quark