Relations between quark and lepton mixing angles and matrices

We discuss the relations between the mixing angles and the mixing matrices of quarks and leptons. With Raidal’s numerical relations, we parameterize the lepton mixing (PMNS) matrix with the parameters of the quark mixing (CKM) matrix, and calculate the products of V_CKMU_PMNS and U_PMNSV_CKM. Also, under the conjectures V_CKMU_PMNS = U_bimax or U_PMNSV_CKM = U_bimax, we get the PMNS matrix naturally, and test Raidal’s relations in these two different versions. The similarities and the differences between the different versions are discussed in detail.Received: 6 April 2005, Published online: 18 May 2005PACS: 14.60.Pq, 12.15.Ff     

Rephasing-invariant parametrization of the quark mixing matrix

We suggest that within the context of the standard model with three generations, the most convenient way of parametrizing the Kobayashi-Maskawa matrix is through four independent moduli of its matrix elements. For three generations the strength of CP violation is completely determined from the knowledge of a set of independent moduli. We extend this parametrization to the case of four generations and analyze in detail the unitarity constraints on the quark mixing matrix. These unitarity constraints are expressed in terms of independent moduli of the quark mixing matrix and can be a useful tool in obtaining precise experimental tests of unitarity.     

Phenomenological relations for quark and neutrino mixing angles

The most recent experimental data on quark and neutrino mixing angles are discussed. It is indicated that the results of the latest kaon-decay experiments are consistent with the unitarity condition for the first row of the Cabibbo-Kobayashi-Maskawa matrix if the currently available world-average value of the neutron lifetime is used to determine the element V _ud of this matrix. The quark mixing angles are calculated within the Fritzsch-Scadron-Delbourgo-Rupp phenomenological approach on the basis of values of the masses of light and heavy constituent quarks. The neutrino mixing angles are calculated to a high precision with the aid of the hypothesis that the quark and neutrino mixing angles are complementary. The results are compatible with experimental data.     

Unitarity boomerangs of quark and lepton mixing matrices

The most popular way to present mixing matrices of quarks (CKM) and leptons (PMNS) is the parametrization with three mixing angles and one CP-violating phase. There are two major options in this kind of parametrizations, one is the original Kobayashi–Maskawa (KM) matrix, and the other is the Chau–Keung (CK) matrix. In a new proposal by Frampton and He, a unitarity boomerang is introduced to combine two unitarity triangles, and this new presentation displays all four independent parameters of the KM parametrization in the quark sector simultaneously. In this Letter, we study the relations between KM and CK parametrizations, and also consider the quark–lepton complementarity (QLC) in the KM parametrization. The unitarity boomerang is discussed in the situation of the CK parametrization for comparison with that in the KM parametrization in the quark sector. Then we extend the idea of unitarity boomerang to the lepton sector, and check the corresponding unitarity boomerangs in the two cases of parametrizations.     

New determination of quark mixing angles and phase

The Kobayashi-Maskawa angles and phase are determined with accuracy using recent B meson lifetime measurements together with the CP violation parameters of the K⁰ system. We get 0.032?sinθ₂?0.125, 0?sinθ₃?0.06, 140°?δ?179° (δ in the second quadrant). some implications, namely possible large B⁰-$\text{B}$⁰ mixing, are discussed.     

Realistic quark masses and mixing angles without scalars?

A model in which the three family quark mass matricesa M^U and M^D is related to the extended technicolor vector boson mass matrix is presented. A phenomenological mass matrix is consistent with the model when the u-quark mass is about 50 MeV.     

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting theta(sol)+theta(C)=pi/4, where theta(C) is the Cabibbo angle, theta(atm)+theta(CKM)(23)=pi/4 and theta(MNS)(13) approximately theta(CKM)(13) approximately O(lambda(3)), in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.     

Experimental constraints on weak mixing angles in the six quark scheme

Experimental results on charm production by neutrinos and onB meson decays are used to derive bounds on the quark mixing anglesθ ₂ andθ ₃ in the six quark model of Kobayashi and Maskawa.     

Experimental determination of weak mixing angles in the six quark scheme

Experimental results on weak decays of hyperons and B mesons, on neutrino production of charm quarks and on the B lifetime are used to obtain, in a combined fit, values for the three mixing angles in the Kobayashi-Maskawa scheme: sinθ₁=0.231±0.003, 0.0152<0.09 and sinθ₃<0.04. In the Maiani parametrization, the angles obtained are: sinθ=0.231±0.003, |sinγ|=0.052_−0.010^+0.015 and sinβ<0.008.     

Experimental analysis of weak mixing angles between three or four quark generations

New data on weak quark decays and on weak heavy quark production are used to obtain the allowed ranges of elements of the quark mixing matrix for three or four generations of sequential quarks. The analysis yields allowed ranges for the three mixing angles in the six-quark case and for the six mixing angles in the eight-quark case.