Abstract
We compute corrections of order $\alpha_s^3$ to the decay $b \to c \ell \bar\nu$ taking into account massive charm quarks. In the on-shell scheme large three-loop corrections are found. However, in the kinetic scheme the three-loop corrections are below 1\% and thus perturbation theory is well under control. We furthermore provide results for the order $\alpha_s^3$ corrections to $b \to u \ell \bar\nu$ and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant $G_F$.
Highlights
The Cabibbo-Kobayashi-Maskawa (CKM) matrix determines the mixing strength in the quark sector and provides the source for charge-parity (CP) violation in the Standard Model (SM)
The most recent determination in the so-called kinetic scheme jVcbj 1⁄4 ð42.19 Æ 0.78Þ × 10−3 [11] has a relative error of about 1.8%, which is mostly dominated by theoretical uncertainties
The analysis clearly shows the advantage of the kinetic scheme which is constructed such that large corrections are resummed into the quark mass value
Summary
The Cabibbo-Kobayashi-Maskawa (CKM) matrix determines the mixing strength in the quark sector and provides the source for charge-parity (CP) violation in the Standard Model (SM). In this article we address the elements Vub and Vcb which are accessible via semileptonic B meson decays. The value of jVcbj from inclusive B → Xclνdecays is obtained from global fits [1,2,3]. The experimental inputs are the semileptonic width and the moments of kinematical distributions measured at Belle [4,5] and BABAR [6,7], together with earlier data from CDF [8], CLEO [9], and DELPHI [10]. Global fits in the 1S scheme yield jV1cbSj 1⁄4 ð41.98 Æ 0.45Þ × 10−3 [11,12]
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