Quark Mass Ratios in Semi-Leptonic Quark Decays*

An ambiguity in the calculation of CKM matrix elements from semi-leptonic decay rates is resolved: to every choice of scales for the quark masses in the phasespace factor and in the QCD-correction factor, there corresponds a specific QCDcorrection factor. This factor is modified in such a way as to make the final result independent of the scales. Specific expressions are given for the case of on-shell quark masses and for the case where both masses are taken at a single common scale. A calculation of lVcbl and IVub/Vcb 1 is carried out in view of these clarifications. Invited talk presented at the 2nd International Symposium on the 4th Family of Quarks and Leptons Santa Monica, California, February 23 25, 1989 * Work supported by the Department of Energy, contract DE-AC03-76SF00515. The above-diagonal elements of the Cabibbo Kobayashi Maskawa (CKM) matrix are best determined from semi-leptonic meson decays. The two elements IV&l and [Vu* I are determined from B decays. The B-meson, or correspondingly the b-quark, is heavy enough to allow the use of the spectator quark model for the calculation: r(B -+ Xqev,) = I?(b -+ qev,), (1) with Q = c or u. When the electron mass is neglected and all quarks are taken to be much lighter than the IV-boson, the spectator quark model gives: BR(b t gev,) G$mz Tb = ~Fp~(P)FQCD(p)Iv,b I21 (2) with FPS and FQCD a phase-space factor and a QCD-correction factor respectively. B_oth factors depend on the ratio