Parametrizing the lepton mixing matrix in terms of charged lepton corrections

We consider a parametrization of the lepton mixing matrix in which the deviations from maximal atmospheric mixing and vanishing reactor mixing are obtained in terms of small corrections from the charged lepton sector. Relatively large deviations for the reactor mixing angle from zero as indicated by T2K experiment can be obtained in this parametrization. We are able to further reduce the number of complex phases, thus, simplifying the analysis. In addition, we have obtained the sides of unitarity triangles and the vacuum oscillation probabilities in this parametrization. The Jarlskog rephasing invariant measure of CP violation at the leading order has a single phase difference which can be identified as Dirac-type CP violating phase in this parametrization.     

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.     

An Underlying Symmetry Determines all Elements of CKM and PMNS up to a Universal Constant?

Observing the CKM matrix elements written in different parametrization schemes, one can notice obvious relations among the sine-values of the CP phases in those schemes. Using the relations, we establish a few parametrization-independent equations, by which the matrix elements of the CKM matrix can be completely fixed up to a universal parameter. If it is true, we expect that there should exist a hidden symmetry in the nature, which determines the relations. Moreover, it requires a universal parameter, naturally it would be the famous Jarlskog invariant, which is also parametrization independent. Thus the four parameters (three mixing angles and one CP phase) of the CKM matrix are not free, but determined by the symmetry and the universal parameter. As we generalize the rules to the PMNS matrix for neutrino mixing, the CP phase of the lepton sector is predicted to be within a range of 0~59° centered at 39° (in the P_a parametrization) which will be tested in the future experiments.     

Unitarity boomerang

For the three family quark flavor mixing, the best parametrization is the original Kobayashi–Maskawa matrix, VKM$V_{\mathrm{KM}}$, with four real parameters: three rotation angles θ_1,2,3${\theta }_{1,2,3}$ and one phase δ. A popular way of presentation is by the unitarity triangle which, however, explicitly displays only three, not four, independent parameters. Here we propose an alternative presentation which displays simultaneously all four parameters: the unitarity boomerang.     

Possibility of a Symmetric Weak Mixing and its Implications

A general parametrization of the symmetric KM matrix is given.The unitarity triangle is discussed,which embodies the unitarity of the symmetric KM matrix and CP violation.It is shown that the symmetric KM matrix is consistent with the directly measured values of the KM matrix elements,CP violation parameter │ε│ of K-K system,and B0d-B0d mixing parameter χ_d,provided the t-quark mass is large,m_t≥160GeV.If │V₁₂│=│V₂₁│is confirmed by further experiments,KM matrix will turn out to be symmetric,so that a parameter is reduced in the standard model.     

A flexible parameterization of the CKM matrix via the singular-value-decomposition method

We investigate a flexible method by which we can test the unitarity of the quark flavor-mixing matrix step by step. Singular-value-decomposition (SVD) techniques are used in analyzing the mixing matrix over a broader parameter region than the unitarity region. Unitary constraints let us extract CP-violating properties without any specific parameterization when the magnitudes of at least three mixing-matrix elements in three-generation quark mixing are given. This method can al so be applied to the analysis of lepton flavor mixing, in which only a few moduli are presently measured. Received: 27 November 2002 / Published online: 7 March 2003 RID="a" ID="a" e-mail: cskim@yonsei.ac.kr RID="b" ID="b" e-mail: jdkim@cskim.yonsei.ac.kr     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson rare decays in the light-cone quark model

We investigate the rare decays \(B_{c} \rightarrow D_{s}(1968)\ell \overline{\ell}\) and \(B_{c}\rightarrow D_{s}^{*}(2317) \ell \overline{\ell}\) in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful for investigating the structure of B _c meson and for testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.     

Fermion masses and mixing angles in anSU(2) L ×U(1) model with horizontal interactions

AnSU(2) _L ×U(1) horizontal model is presented, in which fermions mass splitting, quark and lepton family mixing is attributed to the presence of the horizontal interactions. In the quark sector, the Cabibbo angle and the Cabibbo-like angles are evaluated. In the lepton sector, the neutrinos mixing angles, which orginate from the charged leptons mixing, are calculated, the scale of the horizontal interactions is related to the neutrino oscillation length.     

Yukawaon model in the quark sector and nearly tribimaximal neutrino mixing

For the purpose of deriving the observed nearly tribimaximal neutrino mixing, a possible yukawaon model in the quark sector is investigated. Five observable quantities (2 up-quark mass ratios and 3 neutrino mixing parameters sin²2θ_atm, tan²θ_solar and |U₁₃|) are excellently fitted by two parameters (one in the up-quark sector and another one in the right-handed Majorana neutrino sector).     

Charged lepton contributions to bipair neutrino mixing

The bipair neutrino mixing describes the observed solar and atmospheric mixings; however, it predicts vanishing reactor mixing angle, which is inconsistent with the observed data. We explore the ways of minimally modifying the bipair neutrino mixing by including charged lepton contributions. There are two categories of the bipair neutrino mixing which are referred to as case 1 and case 2. It turns out that, without arbitrary phases, a minimal modification is realized by just considering one e–τ$e\text{–}\tau$ contribution from the charged lepton sector in the case 1. On the other hand, not only e–τ$e\text{–}\tau$ contribution but also μ–τ$\mu \text{–}\tau$ contribution is required to realize a minimal modification in the case 2.     

SU(N) elastic rescattering in B and D decays

The treatment of elastic final-state interactions (FSIs) under a symmetry group is presented. The proposed model is based on Watson's theorem, i.e. on symmetry properties of the -matrix and on its unitarity. This theorem provides an easy way to introduce rescattering effects by defining final-state interactions mixing matrices. A symmetry group fixes the structure of such mixing matrices, and the passage from one group to another is studied (for example, SU(2) to SU(3)). Mixings among two charmless pseudoscalar decay product states will be systematically analyzed. Finally, these mixing matrices will be used on quark diagram parametrizations of B and D decay amplitudes. This will have some important consequences on the definition of quark diagrams. It will be argued that these diagrams should not contain any FSI effects, i.e. they should be real (except for CKM factors). FSIs are then introduced at the hadronic level, by mixing basic quark diagram topologies. Received: 17 December 1998 / Revised version: 17 February 1999 / Published online: 28 September 1999     

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.     

The Flavor Physics in Unified Gauge Theory from an S3 × P Discrete Symmetry

We investigate the phenomenological implication of the discrete symmetry S₃ × P on flavor physics in SO(10) unified theory. We construct a minimal renormalizable model which reproduce all the masses and mixing angle of both quarks and leptons. As usually the SO(10) symmetry gives up to relations between the down sector and the charged lepton masses. The underlining discrete symmetry gives a contribution (from the charged lepton sector) to the PMNS mixing matrix which is bimaximal. This gives a strong correlation between the down quark and charged lepton masses, and the lepton mixing angles. We obtain that the small entries V _ub, V _cb, V _td, and V _ts in the CKM matrix are related to the small value of the ratio δ m² _solΔ m² _atm: they come from both the S₃×P structure of our model and the small ratio of the other quark masses with respect to m _t. Wonderfully, with our model, we fit 17 experimental data %with only 13 free relevant combinations of vevs.     

具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)_L×SU(2)_R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下, 关键词： 中微子质量 轻子味混合矩阵 左右对称模型 代对称性     

Neutrino masses from gauge symmetries

A very simple extension of the Standard Model to include an Abelian family symmetry is able to describe the hierarchy of quark and lepton masses and their mixing angles together with the unification of gauge couplings. We consider the implications of this model for neutrino masses and mixing angles and show that they are determined up to a discrete ambiguity corresponding to the representation content of the Higgs sector responsible for the Majorana mass matrix.     

Four-dimensional heterotic string models with third-integral twists

The massless string states are constructed for a four-dimensional heterotic string model with the U(5) gauge group in the untwisted sector. The complete observable gauge group, quark and lepton generations, Higgs scalar structure, quark and lepton mass matrix, couplings to colour triplet scalars, and gauge symmetry breaking are studied for this model.     

Quark mixing and exponential form of the Cabibbo-Kobayashi-Maskawa matrix

Various forms of representation of the mixing matrix are discussed. An exponential parametrization e ^ of the Cabibbo-Kobayashi-Maskawa matrix is considered in the context of the unitarity requirement, this parametrization being the most general form of the mixing matrix. An explicit representation for the exponential mixing matrix in terms of the first and second degrees of the matrix  exclusively is obtained. This representation makes it possible to calculate this exponential mixing matrix readily in any order of the expansion in the small parameter λ. The generation of new unitary parametric representations of the mixing matrix with the aid of the exponential matrix is demonstrated.