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A complete review of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and of the experimental methods for their determination is presented. A critical analysis of the relevant experimental results, and in particular of the most recent ones, allows to improve the accuracies of all the matrix elements. A chi-square minimization with the three-family unitarity constraint on the CKM matrix is performed to test the current interpretation of the CP violating phenomena inside the Standard Model. A complete and unambiguous solution satisfying all the imposed constraints is found. As a by-product of the fit, the precision on the values of the matrix elements is further increased and it is possible to obtain estimates for the important CP violation observables $sin 2beta$, $sin 2alpha$ and $gamma$. Finally, an independent estimation of the CKM elements based on a Bayesian approach is performed. This complementary method constitutes a check of the results obtained, providing also the probability functions of the CKM elements and of the related quantities.
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We show that the Cabbibo-Kobayashi-Maskawa interaction matrix may be constructed with the quark masses.
We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ using the decay $Bto Dell u_ell$ ($ell=e,mu$) based on 711 fb$^{-1}$ of $e^+e^-to Upsilon(4S)$ data recorded by the Belle detector and containing $772 times 10^6$ $Bbar{B}$ pairs. One $B$ meson in the event is fully reconstructed in a hadronic decay mode while the other, on the signal side, is partially reconstructed from a charged lepton and either a $D^+$ or $D^0$ meson in a total of 23 hadronic decay modes. The isospin-averaged branching fraction of the decay $Bto Dell u_ell$ is found to be $mathcal{B}(B^0 to D^- ell^+ u_{ell})=(2.31pm 0.03(mathrm{stat})pm 0.11(mathrm{syst}))%$. Analyzing the differential decay rate as a function of the hadronic recoil with the parameterization of Caprini, Lelouch and Neubert and using the form-factor prediction $mathcal{G}(1)=1.0541pm 0.0083$ calculated by FNAL/MILC, we obtain $eta_mathrm{EW}|V_{cb}|=(40.12pm 1.34)times 10^{-3}$, where $eta_mathrm{EW}$ is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parameterization of Boyd, Grinstein and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find $eta_mathrm{EW}|V_{cb}|=(41.10 pm 1.14)times 10^{-3}$.
We show that the Kobayashi-Maskawa (KM) parametrization of the 3 X 3 lepton flavor mixing matrix is a useful language to describe the phenomenology of neutrino oscillations. In particular, it provides us with a convenient way to link the genuine flavor mixing parameters (theta_1, theta_2, theta_3 and delta_KM) to their effective counterparts in matter (tilde{theta}_1, tilde{theta}_2, tilde{theta}_3 and tilde{delta}_KM). We rediscover the Toshev-like relation sin tilde{delta}_KM sin 2tilde{theta}_2 = sin delta_KM sin 2theta_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matter-corrected flavor mixing parameters in two different experimental scenarios: (a) the neutrino beam energy E is above O(1) GeV and (b) E is below O(1) GeV. As an example, the probability of u_mu -> u_e oscillations and CP-violating effects are calculated for the upcoming NOvA and Hyper-K experiments.
A possibility of a quark spin polarization originated from a pseudovector condensate is investigated in the three-flavor Nambu-Jona-Lasinio model with the Kobayashi-Maskawa-t Hooft interaction which leads to flavor mixing. It is shown that a pseudovector condensate related to the strange quark easily occurs compared with pseudovector condensate related to light quarks. Further, it is shown that the pseudovector condensate related to the strange quark appears at a slightly small chemical potential by the effect of the flavor mixing due to the Kobayashi-Maskawa-t Hooft interaction.
The Cabibbo-Kobayashi-Maskawa parameter $|V_{cb}|$ plays an important role among the experimental constraints of the Yukawa sector of the Standard Model. The present status of our knowledge will be summarized with particular emphasis to the interplay between theoretical and experimental advances needed to improve upon present uncertainties.
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