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Register a new userConnecting the Cabbibo-Kobayashi-Maskawa matrix to quark masses
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We show that the Cabbibo-Kobayashi-Maskawa interaction matrix may be constructed with the quark masses.
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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.
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 possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu-Jona-Lasinio model including the Kobayashi-Maskawa-t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi-Maskawa-t Hooft interaction is included, due to the flavor mixing effect. It is also shown that the two kinds of tensor condensates may coexist in a certain quark chemical potential due to the flavor mixing.
In this work the homogeneous 5D space-time metric is introduced. Projection operators that map the 5D space-time manifold into a 4D Lorentzian space-time are explicitly given in matrix form. It is emphasized that the concept of proper time is the criterion for the projection. A homogeneous 5D energy-momentum manifold produces naturally the uncertainty principle, and from which we obtained the 5D metric operator, together with the 5D vector and mass-less spinor fields. A naturally coupled product of these two fields is also a solution of the 5D metric operator. Thus the coupling constant is identified as the unit charge. The charged mass-less spinor is coined as the e-trino. Hence the vector field generated by such e-trinos is derived, such that in the 4x1 Hilbert space this vector potential can be identified as the Maxwell monopole potential. Through gauge invariance the concept of charge per unit mass is introduced, which then leads to the mapping of the 5D energy-momentum into that of SU(2)xL and SU(3)xL via the time-shift projection P0 and the conformal space projection P1, respectively. The P1 projection gives us the fractional charged quarks. These quark currents generate both the meson and baryon gluon fields, which in turn generate the meson and baryon masses given in the Eight-Fold-Way representations, removing the necessity of introducing a Higgs vacuum.
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