Neutrino mass and mixing in the 3-3-1 model and S 3 flavor symmetry with minimal Higgs content
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UCLEI, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Neutrino Mass and Mixing in the 3–3–1 Model and S3 Flavor Symmetry with Minimal Higgs Content1 V. V. Viena and H. N. Longb a
Department of Physics, Tay Nguyen University Buon Ma Thuot, DakLak, Vietnam b Institute of Physics, VAST Ba Dinh, Hanoi, Vietnam email: [email protected]; [email protected] Received December 20, 2013
Abstract—A new S3 flavor model based on the SU(3)C ⊗ SU(3)L ⊗ U(1)X gauge symmetry responsible for fermion masses and mixings different from our previous work [14, 17] is constructed. The new feature is a twodimensional representation of a Higgs antisextet under S3, which is responsible for neutrino masses and mixings. The neutrinos acquire small masses from only an antisextet of SU(3), which is in a doublet under S3. If the difference of components of the antisextet is regarded as a small perturbation, S3 is equivalently broken into identity, the corresponding neutrino mass mixing matrix acquires the most general form, and the model can fit the latest data on neutrino oscillations. This way of symmetry breaking helps us reduce a content in the Higgs sector, to only one antisextet instead of two as in our previous work [14]. Our results show that the neutrino masses are naturally small and a small deviation from the tribimaximal neutrino mixing form can be realized. The Higgs potential of the model as well as the minimization conditions and gauge boson masses and mixings are also considered. DOI: 10.1134/S1063776114050173 1
1. INTRODUCTION The experiments on neutrino oscillations have indicated that the neutrinos have small masses and mixings [1–4], and therefore the standard model of fundamental particles and interactions must be extended. Among this direction, there have been vari ous models proposed, such as [5, 6] and others. An alternative is to extend the electroweak symmetry SU(2)L ⊗ U(1)Y to SU(3)L ⊗ U(1)X, in which to com plete the fundamental representations of SU(3)L with the standardmodel doublets so as to obtain the neu tral fermions. This proposal, which has nice features and has been extensively studied over the last two decades, is called 3–3–1 models [7–9], with the num ber of fermion families having been proved to be three [7, 10]. The parameters of neutrino oscillations such as the squared mass differences and mixing angles are now very constrained. The data in [4] imply that 2
sin ( 2θ 12 ) = 0.857 ± 0.024 ( t 12 ≈ 0.6717 ), sin ( 2θ 13 ) = 0.098 ± 0.013 ( s 13 ≈ 0.1585 ), 2
(1) –5
2
2
Δm 21 = ( 7.50 ± 0.20 ) × 10 eV , 2
+0.12
–3
2
Δm 32 = ( 2.32 –0.08 ) × 10 eV . 1 The article is published in the original.
representation of S3. Besides the 2 , the S3 group can provide two inequivalent singlet representations 1 and 1' , which play a crucial role in reproducing con
2
sin ( 2θ 23 ) > 0.95,
These large neutrino mixing angles are completely dif ferent from the quark mixing ones defined by the Cabibbo–Kobayashi–Maskawa (CKM) matrix. Therefore, it is very important to find a natural model that
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