The minimal seesaw model with a modular S 4 symmetry
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Springer
Received: October 25, Revised: March 20, Accepted: April 18, Published: May 5,
2019 2020 2020 2020
Xin Wang and Shun Zhou Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
E-mail: [email protected], [email protected] Abstract: In this paper, we incorporate the modular S4 flavor symmetry into the supersymmetric version of the minimal type-I seesaw model, in which only two right-handed neutrino singlets are introduced to account for tiny Majorana neutrino masses, and explore its implications for the lepton mass spectra, flavor mixing and CP violation. The basic idea is to assign two right-handed neutrino singlets into the unique two-dimensional irreducible representation of the modular S4 symmetry group. Moreover, we show that the matter-antimatter asymmetry in our Universe can be successfully explained via the resonant leptogenesis mechanism working at a relatively-low seesaw scale ΛSS ≈ 107 GeV, with which the potential problem of the gravitino overproduction can be avoided. In this connection, we emphasize that the observed matter-antimatter asymmetry may lead to a stringent constraint on the parameter space and testable predictions for low-energy observables. Keywords: CP violation, Discrete Symmetries, Neutrino Physics ArXiv ePrint: 1910.09473
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)017
JHEP05(2020)017
The minimal seesaw model with a modular S4 symmetry
Contents 1 Introduction
1
2 Modular S4 symmetry
3 5 6 14 19
4 Matter-antimatter asymmetry
21
5 Summary
27
A The Γ4 ' S4 symmetry group
29
1
Introduction
Neutrino oscillation experiments in the past two decades have firmly established that neutrinos are massive and lepton flavor mixing is significant [1, 2]. To account for tiny neutrino masses, one can naturally extend the standard model (SM) by introducing three righthanded neutrinos NiR (for i = 1, 2, 3), which are singlets under the SU(2)L × U(1)Y gauge group of the SM. Therefore, the gauge-invariant Lagrangian relevant for lepton masses and flavor mixing can be written as e R + 1 N C MR NR + h.c. , −Llepton = `L Yl HER + `L Yν HN 2 R
(1.1)
where `L and H denote the left-handed lepton doublet and the Higgs doublet, ER and NR are the right-handed charged-lepton and neutrino singlets, MR is the Majorana mass e ≡ iσ2 H ∗ and N C ≡ CNR T with C = matrix of right-handed neutrinos. In eq. (1.1), H R iγ 2 γ 0 being the charge-conjugation matrix have been defined. After the Higgs doublet √ acquires its vacuum expectation value (vev), i.e., hHi = (0, v/ 2)T with v ≈ 246 GeV, the gauge symmetry is spontaneously broken down, and the charged-lepton and Dirac √ √ neutrino mass matrices are given by Ml ≡ Yl v/ 2 and MD = Yν v/ 2, respectively. At the low-energy scale, the effective Majorana neutrino mass matrix is then obtained via the famous seesaw formula Mν ≈ −MD MR−1 MDT .1 In this canonical seesaw model [3–6], 1
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