Natural neutrino sector in a 331-model with Froggatt-Nielsen mechanism

Published for SISSA by Springer Received: September Revised: January Accepted: February Published: February 12, 14, 12, 26, 2019 2020 2020 2020 Katri Huitu, Niko Koivunen and Timo J. Kärkkäinen Department of Physics, and Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland E-mail: , , Abstract: The extensions of the Standard Model based on the SU(3)c × SU(3)L × U(1)X gauge group (331-models) have been advocated to explain the number of fermion families in nature. It has been recently shown that the Froggatt-Nielsen mechanism, a popular way to explain the mass hierarchy of the charged fermions, can be incorporated into the 331-setting in an economical fashion (FN331). In this work we extend the FN331-model to include three right-handed neutrino singlets. We show that the seesaw mechanism is realized in this model. The scale of the seesaw mechanism is near the SU(3)L × U(1)X -breaking scale. The model we present here simultaneously explains the mass hierarchy of all the fermions, including neutrinos, and the number of families. Keywords: Beyond Standard Model, Global Symmetries, Neutrino Physics, Spontaneous Symmetry Breaking ArXiv ePrint: 1908.09384 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP02(2020)162 JHEP02(2020)162 Natural neutrino sector in a 331-model with Froggatt-Nielsen mechanism Contents 1 2 Particle content 2.1 Fermion representations 2.2 Scalar sector 2.3 Gauge sector 2.3.1 Charged gauge bosons 3 3 4 6 6 3 The Yukawa sector and the Froggatt-Nielsen mechanism in the 331framework 7 4 Charged lepton Yukawa couplings and masses 9 5 Neutrino mass matrix 9 6 Neutrino masses and eigenstates 6.1 Neutrino mass matrices 6.2 Neutrino eigenstates 11 12 14 7 Neutrino coupling to charged gauge bosons and PMNS-matrix 14 8 Constraints and numerical examples 8.1 The FN-charges for the numerical example 8.2 Numerical values for leptons 16 17 18 9 Conclusion 20 A Scalar mass matrices A.1 CP-even scalars A.2 CP-odd scalars A.3 Charged scalars 22 22 22 22 B Neutral gauge boson masses 22 1 Introduction After the discovery of the Higgs boson at the Large Hadron Collider, the last elementary particle predicted by the Standard Model (SM) has been confirmed. Today, particle physics has moved on to a new era, where we attempt to answer the problems plagueing the SM –1– JHEP02(2020)162 1 Introduction where the parameter β defines the particle content of the model. The models with β = √ √ ± 3 [8]–[12] and β = ±1/ 3 [13]–[22]1 are extensively studied in the literature. The √ models with β = ± 3 contain particles with exotic electric charges such as doubly charged scalars and gauge bosons. They also contain a very large scalar sector, composed of three √ SU(3)L -triplets and an SU(3)L -sextet. The models based on the β = ±1/ 3 on the other hand have simpler scalar sector, composed from only three SU(3)L -triplets. The models √ based on β = ±1/ 3 do not contain particles with exotic electric charges. Also the models with β = 0 have been studied [23]. Even though the 331-models can shed light on the number of fermion familes, the fermion mass hierarchy is left unexplained in the traditional models. Recently it was shown that the Froggatt-Nielsen mechanism [24] can be incorporated into the 331-models with √ β = ±1 3 without extending the scalar sector [25, 26]. The Froggatt-Nielsen mechanism (FN) is a well established method to explain the mass hierarchy of the fermions, and a 331model with incorporated FN-mechanism (FN331) can therefore simultaneously explain both the number of fermion families and the mass hierarchy of the charged fermions. The neutrino masses and mixings are not naturally explained in FN331-model, however. The neutrino mass matrix is antisymmetric in the FN331-model and therefore one of the neutrinos is massless and the two other mass degenerate at tree-level. Loop corrections are needed to lift the one eigenvalue from zero and to break the degeneracy of the other two [15]. This neutrino sector is identical to the one presented in [14]–[22]. 1 The model presented in [13] does not exhibit the cancellation of gauge anomalies and does not explain the number of fermion families. –2– JHEP02(2020)162 with economical extensions. The problems include number of generations, nonzero neutrino mass, neutrino mixing and fermion mass hierarchies. In Nature three generations of quarks and leptons have been observed. Number of neutrino flavours is 2.984±0.008 [1]–[7], which is a statistical fit to SM using LEP data. This is a strong indication for exactly three generations of matter, which, however, is not imposed by SM itself. We know from neutrino oscillation experiments that at least two of the three SM neutrinos are massive, with masses less than 0.1 eV and the sum of their masses is less than 0.12 eV from cosmological constraints by the PLANCK experiment. Neutrino masses are not included in the Standard Model, and they are six orders of magnitude lighter than the next lightest massive particle, electron, and twelve orders of magnitudes lighter than the heaviest particle, top quark. This huge range of different masses gives birth to the flavour problem. Extensions of the Standard Model based on the SU(3)c × SU(3)L × U(1)X gauge group (331-models) have been proposed in the literature to explain the number of fermion families in Nature. In the traditional 331-models [8]–[22] the gauge anomalies cancel only if the number of fermion familes is three. The SU(3)c × SU(3)L × U(1)X gauge group contains one additional diagonal generator compared to the SM-gauge group SU(3)c × SU(2)L × U(1)Y . This means that the electric charge can be defined in multiple different ways in the 331-models: Q = T3 + βT8 + X, (1.1) 2 Particle content We propose a model where the gauge group of the Standard Model is extended to SU(3) C × SU(3)L × U(1)X . We define the electric charge as:2 1 Q = T3 − √ T8 + X, 3 (2.1) where the T3 and T8 are the diagonal SU(3)L generators. We also introduce global U(1)F N symmetry, under which fermions and some of the scalars are charged. 2.1 Fermion representations Let us now write down the fermion representations. The left-handed leptons are assigned to SU(3)L -triplets and the right-handed leptons are assigned to SU(3)L -singlets:     νi 1   LL,i =  ei  ∼ 1, 3, − , i = 1, 2, 3, eR,i ∼ (1, 1, −1), NR,i ∼ (1, 1, 0). (2.2) 3 0 νi L 2 The choice β = + √13 would result in essentially a same model. –3– JHEP02(2020)162 Our aim is to extend the neutrino sector to make it natural and explain the neutrino masses and mixings without fine-tuning at tree-level. We propose an extension of the FN331-model where we add three right-handed neutrino singlets to the model. This allows the tree-level masses for all the neutrinos and implementation of seesaw mechanism [29]– [34] for the neutrino sector. Here the seesaw is combined with the FN-mechanism, which allo (...truncated)