Starting from a new zeroth order basis for quark mixing (CKM) matrix based on the quark-lepton complementarity and the tri-bimaximal pattern of lepton mixing, we derive a triminimal parametrization of CKM matrix with three small angles and a CP-violating phase as its parameters. This new triminimal parametrization has the merits of fast convergence and simplicity in application. With the quark-lepton complementary relations, we derive relations between the two unified triminimal parametrizations for quark mixing obtained in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler. Parametrization deviating from quark-lepton complementarity is also discussed.
We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity (QLC). We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding QLC lepton mixi…
Current experimental data on neutrino mixing are very well described by TriBiMaximal mixing. Accordingly, any phenomenological parametrization of the MNSP matrix must build upon TriBiMaximal mixing. We propose one particularly natural parametrization, which we call "TriMinimal". The three small deviations of the PDG angles from their TriBiMaximal values, and the PDG phase, parametrize the TriMinimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical n…
We examine how a parametrization of neutrino mixing matrix reflecting quark-lepton complementarity can be probed by considering phase-averaged oscillation probabilities, flavor composition of neutrino fluxes coming from atmospheric and astrophysical neutrinos and lepton flavor violating radiative decays. We discuss about some distinct features of the parametrization by comparing with the triminimal parametrization of perturbations to tri-bimaximal neutrino mixing matrix.
Recent works show that the original Kobayashi-Maskawa (KM) form of fermion mixing matrix exhibits some advantages, especially when discussing problems such as unitarity boomerangs and maximal CP violation hypothesis. Therefore, the KM form of fermion mixing matrix is systematically studied in this paper. Starting with a general triminimal expansion of the KM matrix, we discuss the triminimal and Wolfenstein-like parametrizations with different basis matrices in detail. The quark-lepton complementarity relations play an important role in our discussions on describing quark mixing and lepton mix…
Recently, Qin and Ma (QM) have advocated a new Wolfenstein-like parametrization of the quark mixing matrix based on the triminimal expansion of the Cabibbo-Kobayashi-Maskawa (CKM) parametrization. The CP-odd phase in the QM parametrization is around $90^\circ$ just as that in the CKM parametrization. We point out that the QM parametrization can be readily obtained from the Wolfenstein parametrization after appropriate phase redefinition for quark fields and that the phase $δ$ in both QM and CKM parametrizations is related to the unitarity angles $α$, $β$ and $γ$, namely, $δ= β+γ$ or $π-α$. We …
We propose simple forms of neutrino mixing matrix in analogy with the Wolfenstein parametrization of quark mixing matrix, by adopting the smallest mixing angle $θ_{13}$ as a measure of expansion parameters with the tribimaximal pattern as the base matrix. The triminimal parametrization technique is utilized to expand the mixing matrix under two schemes, i.e., the standard Chau-Keung (CK) scheme and the original Kobayashi-Maskawa (KM) scheme. The new parametrizations have their corresponding Wolfenstein-like parametrizations of quark mixing matrix, and therefore they share the same intriguing f…
We propose a new parametrization for the quark and lepton mixing matrices: the two 12-mixing angles (the Cabibbo angle and the angle responsible for solar neutrino oscillations) are at zeroth order pi/12 and pi/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, V_{us} and U_{e2}, are in this order irrational but simple algebraic numbers. We note that the cosine of pi/5 is the golden ratio divided by two. The difference between pi/5 and the observed best-fit value of solar neutrino mixing is of the same order as the difference between the observed value and the one for tri…
Although different parametrizations of quark mixing matrix are mathematically equivalent, the consequences of experimental analysis may be distinct. Based on the triminimal expansion of Kobayashi-Maskawa matrix around the unit matrix, we propose a new simple parametrization. Compared with the Wolfenstein parametrization, we find that the new form is not only consistent with the original one in the hierarchical structure, but also more convenient for numerical analysis and measurement of the CP-violating phase. By discussing the relation between our new form and the unitarity boomerang, we poin…
We consider various neutrino mixing matrix parametrizations and the dependence of the mixing angles and CP-violating phase on the different parametrizations. The transformations of neutrino mixing parameters between various parametrizations are presented. Although the $θ_{13}$ mixing angle is determined to be small in the conventional parametrization, we note that in several other parametrizations the values of $θ_{13}$ are quite large. Should the value of $θ_{13}$ turn out to be tiny in the conventional parametrization, this study suggests that other alternative mixing matrix representations …
Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parameterize the quark and lepton matrices with the help of quark-lepton complementarity (QLC) in a tri-bimaximal pattern of lepton mixing matrix. In this way, we combine the parametrization of the two matrices with each other. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of CP violation.
Advantages of the original symmetrical form of the parametrization of the lepton mixing matrix are discussed. It provides a conceptually more transparent description of neutrino oscillations and lepton number violating processes like neutrinoless double beta decay, clarifying the significance of Dirac and Majorana phases. It is also ideal for parametrizing scenarios with light sterile neutrinos.
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 paper, we study the relations betwee…
The neutrino mixing matrix is expanded in powers of a small parameter $λ$ in tri-bimaximal mixing pattern. We also present some applications of this parametrization, such as to the expression of the Jarlskog parameter $J$. Comparing with other parametrizations (such as the parametrization in bimaximal mixing pattern), this parametrization converges more quickly, but is of less symmetry.
With the latest results of a large mixing angle $θ_{13}$ for neutrinos by the T2K, MINOS and Double Chooz experiments, we find that the self-complementarity (SC) relations agree with the data in some angle-phase parametrizations of the lepton mixing matrix. There are three kinds of self-complementarity relations: (1) $\vartheta_i+\vartheta_j=\vartheta_k=45^\circ$; (2) $\vartheta_i+\vartheta_j=\vartheta_k$; (3) $\vartheta_i+\vartheta_j=45^\circ$ (where $i$, $j$, $k$ denote the mixing angles in the angle-phase parametrizations). We present a detailed study on the self-complementarity relations i…
We present a classification of possible parametrizations of the 3x3 lepton flavor mixing matrix in terms of the rotation and phase angles. A particular parametrization, which is most convenient to describe the observables of neutrino oscillations and that of the neutrinoless double beta decay, is studied in detail. The possibility to determine the Dirac- and Majorana-type CP-violating phases are also discussed.
We point out the simple reversibility between the fundamental neutrino mixing parameters in vacuum and their effective counterparts in matter. The former can therefore be expressed in terms of the latter, allowing more straightforward extraction of the genuine lepton mixing quantities from a variety of long-baseline neutrino oscillation experiments. In addition to the parametrization-independent results, we present the formulas based on the standard parametrization of the lepton flavor mixing matrix and give a typical numerical illustration.
We propose a flexible and model independent parametrization of the neutrino mixing matrix, which takes advantage of the fact that there are up to three small quantities in neutrino mixing phenomenology: (i) the deviation from maximal mixing of solar neutrinos, (ii) the mixing matrix element U_{e3} and (iii) the deviation from maximal mixing of atmospheric neutrinos. It is possible to quantify those three observations with a parameter λ\sim 0.2, which appears at least linearly in all elements of the mixing matrix. The limit λ-> 0 corresponds to exact bimaximal mixing. Present and future experim…
The three-flavor mixing matrix can be parameterized by the rephasing invariants Gamma_{ijk} = V_{1i} V_{2j} V_{3k}. This formulation brings out the inherent symmetry of the problem and has some appealing features. Examples illustrating the parametrization and applications to quark mixing are presented.
We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of $U(n)$ and $SU(n)$ matrices developed by some of us in Refs.[2] and [3]. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix.
We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine corresponding charged lepton mixing matrix in terms of those three parameters which can deviate bi-maximal or tri-bimaximal mixing. We find that the charged lepton mixing matrices which can deviate bi-maximal mixing matrix and tri-bimaximal mixing matrix exhibit similar structures. Numerical analysis shows that these charged lepton mixing matrices are close to …
We discuss the propagation and the flavour mixing of neutrinos in the context of the Quantum Field Theory. We propose an exact parametrization of the neutrino mixing matrix and its transformation in a simpler form which accounts for a small $ν_e - ν_μ$ and a large $ν_μ- ν_τ$ mixing. Finally, we comment the differences between the charged quark and neutral lepton sector and consider the physical situations that require this approach.
In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe subleading contributions and its applications to tri-bimaximal mixing are discussed. We show that mixing matrices similar to tri-bimaximal-Cabibbo mixing can be obtained by straightforward choices of parameters. To achieve better agreement with the experimental data without increasing the number of free parameters, we impose a simple phenomenological relatio…
We point out that the $τ$-lepton dominance in the one-loop renormalization-group (RG) equations of neutrino mixing quantities allows us to set a criterion to choose the most suitable parametrization of the lepton flavor mixing matrix $U$: its elements $U^{}_{3i}$ (for $i=1,2,3$) should be as simple as possible. Such a novel parametrization is quite different from the "standard" one used in the literature and can lead to greatly simplified RG equations for three mixing angles and the physical CP-violating phase(s) in the standard model or its minimal supersymmetric extension, no matter whether …
We present a unified parametrization of quark and lepton mixing matrices. By using some simple relations between the mixing angles of quarks and leptons, i.e., the quark-lepton complementarity, we parametrize the lepton mixing matrix with the Wolfenstein parameters $λ$ and $A$ of the quark mixing matrix. It is shown that the Wolfenstein parameter $λ$ can measure both the deviation of the quark mixing matrix from the unit matrix, and the deviation of the lepton mixing matrix from the exactly bimaximal mixing pattern.
It is shown that there exist nine different ways to describe the flavor mixing, in terms of three rotation angles and one CP-violating phase, within the standard electroweak theory of six quarks. For the assignment of the complex phase there essentially exists a continuum of possibilities, if one allows the phase to appear in more than four elements of the mixing matrix. If the phase is restricted to four elements, the phase assignment is uniquely defined. If one imposes the constraint that the phase disappears in a natural way in the chiral limit in which the masses of the u and d quarks are …
Under the assumption that the neutrinos are Majorana particles we study how the lepton mass matrices can be transformed into the simple form which has the same physical quantities by removing redundant parameters. We propose the exact parametrization of the lepton mass matrices which reflects the small nu_e-nu_mu mixing and the large nu_mu-nu_tau mixing. The relations between the twelve parameters and the physical quantities are shown. Furthermore we calculate the MNS matrix by applying the assumptions used in the quark sector. Finally we also check the validity of these assumptions from the e…
The neutrino mixing matrix is expanded in powers of a small parameter $λ$, which approximately equals to 0.1. The meaning of every order of the expansion is discussed respectively, and the range of $λ$ is carefully calculated. We also present some applications of this new parametrization, such as to the expression of the Jarlskog parameter $J$, in which the simplicities and advantages of this parametrization are shown.
We obtain a general parametrization for the neutrino Majorana mass matrix in which all possible deviations from tribimaximal mixing are given by three complex parameters, and the deviation from each tribimaximal mixing eigenvector is identified with precisely two of them. This parametrization provides a useful tool for classifying the corrections to exact tribimaximal mixing in flavor models.
We use hyperbolic functions to parametrize lepton mixing matrix using only one input parameter $ϕ$. This matrix has three mixing angles as outputs therefore giving two predictions. In particular it predicts $U_{e3}=0$ besides predicting correct solar and atmospheric mixing. We confine us to real $ϕ$. For complex $ϕ$ mixing matrix is no longer unitary. Next we accentuate this unitary mixing matrix with an additional small parameter $δ$ while keeping unitarity of the matrix exact. When this second parameter is included, with this framework, one can handle small but non-zero $U_{e3}$. In the seco…
Hints for sizable $\sin^2 θ_{13}$ have been reported in earlier global neutrino oscillation data analyses as well as will be reported in this work, and quite recently by the Double Chooz experiment. However, as we enter the era of precision neutrino oscillation experiments, terms linear in $\sinθ_{13}$ will no longer be negligible, and its sign would affect the extraction of other oscillation parameters. The sign of $\sinθ_{13}$ also plays a crucial role in the determination of the CP-violating phase. In this work we show that by adopting an alternative parametrization for the Pontecorvo-Maki-…
We investigate a flexible method in 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 make us extract CP violating properties without any specific parametrization when the magnitudes of at least three mixing matrix elements in three generation quark mixing are given. This method can also be applied to the analysis of lepton flavor mixing, in which only a few moduli are presently measured.
Global fits to neutrino oscillation data are compatible with tri-bimaximal mixing pattern, which predicts $θ_{23} = \fracπ{4}, θ_{12} = \sin^{-1} (\frac{1}{\sqrt{3}})$ and $θ_{13} = 0$. We propose here to parametrize the tri-bimaximal mixing matrix $V_{TBM}$ by its hermitian generator $H_{TBM}$ using the exponential map. Then we use the exponential map to express the deviations from tri-bimaximal pattern by deriving the hermitian matrices $H_{z=0}$ and $H_1$. These deviations might come from the symmetry breaking of the neutrino and charged lepton sectors.
In addition to three active neutrinos, one or more light sterile neutrinos have been conjectured to account for the LSND, MiniBooNE and reactor antineutrino anomalies (at the sub-eV mass scale) or for warm dark matter in the Universe (at the keV mass scale). Heavy Majorana neutrinos at or above the TeV scale have also been assumed in some seesaw models. Such hypothetical particles can weakly mix with active neutrinos, and thus their existence can be detected at low energies. In the (3+3) scenario with three sterile neutrinos we present a full parametrization of the 6 X 6 flavor mixing matrix i…
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 (θ_1, θ_2, θ_3 and δ_KM) to their effective counterparts in matter (\tildeθ_1, \tildeθ_2, \tildeθ_3 and \tildeδ_KM). We rediscover the Toshev-like relation sin \tildeδ_KM sin 2\tildeθ_2 = sin δ_KM sin 2θ_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matt…
In this paper we study three active neutrino oscillations, favored by recent data from SuperK and SNO, using a new parametrization of the lepton mixing matrix $V$ constructed from a linear combination of the unit matrix $I$, and a hermitian unitary matrix $U$, that is, $V = \cosθI + i\sin θU$. There are only three real parameters in $V$ including the parameter $θ$. It is interesting to find that experimental data on atmospheric neutrino dictates the angle $θ$ to be $π/4$ such that the $ν_μ$ and $ν_τ$ mixing is maximal. The solar neutrino problem is solved via the MSW effect with a small mixing…
We show that the $3\times 3$ lepton flavor mixing matrix $V$ can be expanded in powers of a Wolfenstein-like parameter $Λ\equiv |V_{μ3}| \sim 1/\sqrt{2}$, which measures the strength of flavor conversion in atmospheric neutrino oscillations. The term of ${\cal O}(Λ^2)$ is associated with the large mixing angle in solar neutrino oscillations. The Dirac phase of CP violation enters at or below ${\cal O}(Λ^8)$, and the Majorana phases of CP violation are not subject to the $Λ$-expansion. Terrestrial matter effects on this new parametrization in realistic long-baseline neutrino oscillation experim…
We calculate the rephasing invariants of CP and T violation in a favorable parametrization of the 4x4 lepton flavor mixing matrix. Their relations with the CP- and T-violating asymmetries in neutrino oscillations are derived, and the matter effects are briefly discussed.
A parametrization of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix, $V$, is presented in which the parameters are the eigenvalues and the components of its eigenvectors. In this parametrization, the small departure of the experimentally determined $V$ from being moduli symmetric (i.e. $|V_{ij}|=|V_{ji}|$) is controlled by the small difference between two of the eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli symmetric $V$ depending on only three parameters. Our parametrization gives very good fits to the available data including CP-violation. Our value of $\sin 2β\…
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…
The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases.…
We propose a parametrization of the lepton mixing matrix in terms of an expansion in powers of the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimaximal values. We show that unitarity triangles and neutrino oscillation formulae have a very compact form when expressed in this parametrization, resulting in considerable simplifications when dealing with neutrino phenomenology. The parametrization, which is completely general, should help to establish possible relations between the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimax…
The $μ-τ$ reflection symmetry of the lepton mixing matrix accommodates maximal atmospheric mixing ($θ_{23}=π/4$) as well as maximal Dirac CP phase ($δ=\pm π/2$) for the Dirac case. In the standard parametrization of the PMNS matrix the reflection symmetric nature is not directly visible while substituting the maximal values of the mixing parameters. This issue has been addressed in this paper. It is found that the reflection symmetry in the 'standard' PMNS matrix can be restored by allowing maximal values of the Majorana CP phases ($α$, $β$) as well, along with maximal $δ$. To accommodate non-…
We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is $π/4$. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that $|V_{us}/V_{ud}| + |V_{e2}/V_{e1}| + |V…
Current data indicates that lepton mixing is very close to the tri-bimaximal mixing scenario. In general, however, one expects deviations from any mixing scenario. We discuss several examples to perturb tri-bimaximal mixing, namely soft breaking, renormalization group running and charged lepton corrections. We also present a convenient parametrization of the PMNS matrix which takes advantage of the apparently close to tri-bimaximal mixing pattern. Finally, it is discussed how to generate values of U_{e3} which correspond to the recently found hint for non-zero U_{e3}.
The sets of charged-lepton (L) and quark (D,U) masses may be parametrized in a Z_3-symmetric language appropriate for the discussion of Koide's formula. Experiment suggests that at the low-energy scale the relevant phase parameters δ_f take on possibly exact values of δ_L=3δ_D/2=3δ_U=2/9. For k_f (the other parameter relevant for the pattern of masses), a similarly simple expression (k_L=1) is known for charged leptons only. Using the Fritzsch-Xing decomposition of quark-mixing matrices, we show that the suggested pattern of low-energy quark masses is consistent with an earlier conjecture that…
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way to the known phenomenologically useful parametrizations of the mixing matrix.
The quark-lepton complementarity (QLC) is very suggestive in understanding possible relations between quark and lepton mixing matrices. We explore the QLC relations in all the possible angle-phase parametrizations and point out that they can approximately hold in five parametrizations. Furthermore, the vanishing of the smallest mixing angles in the CKM and PMNS matrices can make sure that the QLC relations exactly hold in those five parametrizations. Finally, the sensitivity of the QLC relations to radiative corrections is also discussed.
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…
We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $δ_e$ and the leptonic Wolfenstein parameters $λ_e$, $A_e$, $ρ_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the le…
Inspired by a new relation $θ_{13}^{\rm PMNS}={θ_C}/{\sqrt{2}}$ observed from the relatively large $θ_{13}^{\rm PMNS}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the PMNS matrix are all related to the Wolfenstein parameter $λ$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $λ$, A, and a Dirac CP-violating phase $δ$. Such parametrizations for the PM…
We derive a new set of sum rules between the neutrino mass and mixing parameters in vacuum and their effective counterparts in matter. The moduli of nine genuine lepton mixing matrix elements can then be calculated in terms of the matter-corrected ones, and the latter can directly be determined from a variety of long-baseline neutrino oscillations. We show that it is possible to reconstruct the leptonic unitarity triangles and CP violation in a similar parametrization-independent way.
We study the exactly degenerate case for three lefthanded Majorana neutrinos building a general parametrization for the leptonic mixing matrix characterized by two angles and one CP violating phase and identify a weak-basis invariant relevant, in this case, for CP violation. After lifting the degeneracy, this parametrization accommodates the present data on atmospheric and solar neutrinos, as well as neutrinoless double beta decay. Some of the leptonic mixing ansätze suggested in the literature correspond to special cases of this parametrization.
Introducing n right-handed neutrinos to the Standard Model yields, in general, massive active neutrinos. We give explicit parametrizations for the involved mixing and coupling matrices in terms of physical parameters for both the top-down and the bottom-up approach for arbitrary n. Bounds on the complex mixing angles in the bottom-up approach from perturbativity of the Yukawa couplings to charged lepton flavor violation are discussed. As a novel illustration of possible effects from n != 3, we extend the neutrino anarchy framework to arbitrary n; we show that while the anarchic mixing angles a…
We study the texture two zeros neutrino mass matrices using the standard parametrization for the neutrino mixing matrix. We find that if the origin of CP violation in the leptonic sector is not due to the Dirac-type complex phase of the mixing matrix but because of some non-standard phenomena then some of the possible texture two mass matrices, which are allowed by standard parametrization, are found to be unsuitable to accommodate the observed data in the neutrino sector. Furthermore, incorporating nonzero Dirac phase in our analysis we find that many of them do not exhibit normal hierarchy.
We use the effective Lagrangian formalism to describe quark mixing. The new W, Z and H couplings generalizing the CKM matrix and the GIM mechanism fulfil relations and inequalities which allow to discriminate among different SM extensions. As a by-product we give a useful parametrization of the generalized CKM matrix. We also show that the largest possible departures from the SM predictions result from heavy exotic fermions, which can induce, for example, top FCNC large enough to be observable at future colliders.
The phase equivalence of the theoretical quark mixing matrix ${\bf V}^{th}$ derived from the breaking of the flavour permutational symmetry and the phenomenological parametrizations ${\bf V}^{PDG}$ and ${\bf V}^{KM}$ is explicitly exhibited. From here, we derive exact explicit expressions for the three mixing angles and the CP violating phase of the two phenomenological parametrizations in terms of the quark mass ratios $(m_{u}/m_{t}, m_{c}/m_{t}, m_{d}/m_{b}, m_{s}/m_{b})$ and the parameters $Z^{*1/2}$ and $Φ^*$ characterizing the preferred symmetry breaking pattern. The computed values for t…
We point out that there is a unique parametrization of quark flavor mixing in which every angle is close to the Cabibbo angle θ_C \simeq 13^\circ with the CP-violating phase ϕ_q around 1^\circ, implying that they might all be related to the strong hierarchy among quark masses. Applying the same parametrization to lepton flavor mixing, we find that all three mixing angles are comparably large (around π/4) and the Dirac CP-violating phase ϕ_l is also minimal as compared with its values in the other eight possible parametrizations. In this spirit, we propose a simple neutrino mixing ansatz which …
Current experimental data indicate that two unitarity triangles of the CKM quark flavor mixing matrix V are almost the right triangles with α\approx 90^\circ. We find that α= 90^\circ actually points to {\rm Re}(V_{tb}V_{ud}V^*_{td}V^*_{ub}) = 0. Considering a very suggestive parametrization of V, we show that its CP-violating phase ϕis nearly equal to α(i.e., ϕ- α\approx 1.1^\circ). Both ϕand αare stable against the renormalizaton-group evolution from the electroweak scale M_Z to a superhigh energy scale M_X or vice versa, and thus it is impossible to obtain α= 90^\circ at M_Z from ϕ= 90^\cir…
