A new parametrization of the neutrino mixing matrix

Abstract

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.Key words: neutrinos, neutrino mixing matrix, parametrization PACS: 14.60. Pq, 12.15.Ff, 13.15.+g, 14.60.Lm In recent years, there have been abundant experimental data strongly suggesting the mixing of different generations of neutrinos, just analogous to that of quarks. The K2K [1] and Super-Kamiokande [2] experiments indicated that the atmospheric neutrino anomaly is due to the ν µ to ν τ oscillation with almost the largest mixing angle of θ atm ≈ 45• . The KamLAND [3] and SNO [4] experiments told us that the solar neutrino deficit was caused by the oscillation from ν e to a mixture of ν µ and ν τ with a mixing angle approximately of θ sol ≈ 34• . On the other hand, the non-observation of the ν e to ν e oscillation in the CHOOZ [5] experiment showed that the mixing angle θ chz is smaller than 3• at the best fit point [6,7].These experiments not only confirmed the oscillations of neutrinos, but also measured the mass-squared differences of the neutrino mass eigenstates (the * Corresponding author. Like the Cabibbo-Kobayashi-Maskawa (CKM) [8,9] matrix for quark mixing, the neutrino mixing matrix is described by the unitary Maki-Nakawaga-Sakata (MNS) [10] matrix V , which links the neutrino flavor eigenstates ν e , ν µ , ν τ to the mass eigenstates ν 1 , ν 2 , ν 3 ,

Unified parametrization of quark and lepton mixing matrices

“…The parametrizations of the PMNS matrix on the basis of the bimaximal mixing pattern have been discussed by Rodejohann [14] and us [15]. However, these parametrizations only concern about the experimental data of leptons, without taking into account their relations with quarks.…”

“…(9)). However, in the previous work [14,15], λ in the PMNS matrix is introduced independently, without considering its relation with the Wolfenstein parameter λ in the CKM matrix. Now, we can see that in this unified parametrization these two different deviations of quarks and leptons are correlated essentially, and can be measured by only one single parameter λ, as Raidal pointed out [3].…”

Quark lepton complementarity and renormalization group effects

“…In particular, the CC/NC ratio that gives the most important restriction on mixing is determined by P ∼ cos 4 θ 13 sin 2 θ 12 . The best fit values (14) are along with the trajectory P = constant.…”

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…”