Unified parametrization of quark and lepton mixing matrices

Abstract

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.PACS numbers: 14.60. Pq; 12.15.Ff Introduction-To describe the behaviors of quarks and leptons in a grand unified theory (GUT) is one of main goals of particle physics. Among all the characters of quarks and leptons, the mixing between different generations is one of the fundamental problems. Before more underlying theory of the origin of the mixing is found, to parametrize the quark mixing (CKM) matrix [1] and the lepton mixing (PMNS) matrix [2] phenomenologically is the first step to understand this problem. However, these two mixing matrices were parametrized in isolated ways, with the parameters in these two mixing matrices being uncorrelated with each other. The purpose of this work is to show that one can parametrize the quark and lepton mixing matrices in a unified way by adopting some simple relations between the mixing angles of quarks and leptons

Exponential parameterization of the neutrino mixing matrix: comparative analysis with different data sets and CP violation

“…We will omit the Majorana phases for simplicity; it was shown that they interplay with the CP phase in some entries of the exponential matrix and just produce more complex terms (see [35]). Let us consider first of all only the real rotational part and compare the rotational matrix (18) with the TBM form of the mixing matrix [20,28]. With the help of (19), (20), (21), (22), we obtain the following values for the parameters of the exponential parameterization (18), corresponding to the TBM parameterization: • .…”

“…Let us consider first of all only the real rotational part and compare the rotational matrix (18) with the TBM form of the mixing matrix [20,28]. With the help of (19), (20), (21), (22), we obtain the following values for the parameters of the exponential parameterization (18), corresponding to the TBM parameterization: • . (33) Now, from the data set, reported in [14,28], we obtain for neutrinos To avoid the uncertainty, originating from largely undetermined CP-violating phase, we calculated the fit with the experimentally determined values of the entries of the PMNS matrix, which contain only the mixing angles θ i, j and do not depend on the CP violation, described by δ.…”

“…The QLC is an important subject of this study, and there are many other studies in this line, such as [31][32][33]. In the following we will explore this topic in the context of the rotation axes direction in three dimensional space in the exponential parameterization of the mixing matrix.…”

“…Completed parameterization, based on the TBM pattern, was described in [20,27,28]). The TBM parameterization has the mixing angles θ 12 = arctan 1/ √ 2 ∼ = 35.25 • , θ 23 = π/4 = 45 • , which agree very well with the values, obtained from experimental sets, and only θ 13 = 0 contradicts recent data, which indicates it is not zero.…”

Perturbation to TBM mixing and its phenomenological implications

“…[3] are given in Table I Initially neutrino oscillation experiments indicated the atmospheric mixing angle, θ 23 is maximal i.e., θ 23 = π/4 and reactor mixing angle θ 13 is vanishingly small and motivated by such anticipation many models for neutrino mixing were proposed such as Bimaximal mixing (BM) [6][7][8][9][10][11], Tri-bimaximal mixing (TBM) [12][13][14][15][16][17][18][19][20], Golden ratio type-A (GRA), type-B (GRB) [21,22] and Hexagonal mixing (HG), etc. All such models are based on some discrete symmetries such as A 4 , S 4 [23,24] etc and can be represented as…”