Inverted Neutrino Mass Hierarchy in the Standard Model with Q 6 Flavor Symmetry
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ELEMENTARY PARTICLES AND FIELDS Theory
Inverted Neutrino Mass Hierarchy in the Standard Model with Q 6 Flavor Symmetry∗ V. V. Vien1), 2)** Received June 5, 2018; in final form, August 17, 2018
Abstract—We construct a Standard Model extension with Q6 flavor symmetry in the framework of sewsaw mechanism in which the inverted neutrino mass spectrum is naturally explained without using perturbation theory. DOI: 10.1134/S1063778819010198
1. INTRODUCTION Neutrino mass and mixing can be regarded as one of the most important evidences of beyond Standard Model (SM) physics. Among the possible extensions of the SM, probably the simplest one is the neutrino minimal SM which has been studied in [1–6], however, these extensions do not provide a natural explanation for large mass splitting between neutrinos and the lepton mixing was not explicitly explained. On the experimental side, the best-fit values of the three neutrino oscillation parameters, derived from a global fit of the current neutrino oscillation data in [7], are given as follows: Δm221 = 7.53 × 10−5 eV2 ,
(1)
Δm232 = 2.44 × 10−3 eV2 (normal spectrum), Δm232 = −2.51 × 10−3 eV2 (inverted spectrum), sin2 (θ12 ) = 0.304, sin2 (θ13 ) = 0.0219, sin2 (θ23 ) = 0.51 (normal spectrum), sin2 (θ23 ) = 0.50 (inverted spectrum), where Δm221 = m22 − m21 > 0 and Δm232 = m23 − m22 thus Δm232 > 0 for the normal spectrum, i.e, m1 < m2 < m3 and Δm232 < 0 for the inverted spectrum, i.e, m3 < m1 < m2 . The large neutrino mixing angles as given in Eq. (1) have stimulated to use non-Abelian discrete symmetries that can lead to the flavor mixing patterns ∗
The text was submitted by the author in English. Institute of Research and Development, Duy Tan University, Da Nang City, Vietnam. 2) Department of Physics, Tay Nguyen University, Buon Ma Thuot City, DakLak, Vietnam. ** E-mail: [email protected] 1)
which were proposed in various articles (the reader is referred to [8] and references therein). Q6 group has been studied in [9–15], where the first two families are put in the 2 and the third one in the singlet. A different alignment, in which the first family in the singlet and the second and third one in the doublet, was presented in [16]. In this work, we investigate another choice with Q6 group in which the first family in the singlet and the second and third one in the doublet which is different from those in previous work [16]. The outline of the paper is as follows. In Section 1 we present the fundamental elements of the model and introduce necessary Higgs fields responsible for the fermion mass and mixing. We summarize the results in Section 2. Appendix presents a brief of the Q6 group. 2. RESULTS AND DISCUSSION
2.1. Lepton Mass and Mixing In the model under consideration, the electroweak sector of the SM is supplemented by an auxilliary symmetry U (1)X and a Q6 flavor symmetry. The reason for adding the auxiliary symmetry U (1)X was discussed fully in [17]. In the model under consideration, ψjL , ljR (j = 1, 2, 3) in Eq. (2) and Φ in Eq. (7) have X equal to 1 while all other fields have X
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