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

TL;DR

This paper accurately determines the CKM matrix element |V_{cb}| by applying third-order perturbative calculations to inclusive B decay widths and bottomonium 1S masses, highlighting the impact of mass scheme choices and non-perturbative effects.

Contribution

It introduces a precise determination of |V_{cb}| using N^3LO corrections and compares different bottomonium 1S mass schemes, emphasizing the dominant uncertainty from mass splitting descriptions.

Findings

|V_{cb}| = 0.0425 with an uncertainty of 0.0011

Significant difference in |V_{cb}| between 1S mass schemes

Non-perturbative effects are relevant but within current perturbative accuracy

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 $\Upsilon(1S)$ 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 $\mathcal{O}(\Lambda_{\overline{\rm MS}}^2)$ 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.