Realistic model with a type II Dirac neutrino seesaw mechanism
Here we propose a realistic electroweak gauge model with enlarged Higgs sector. The scheme allows for the natural implementation of a type II seesaw mechanism for Dirac neutrinos, while charged lepton and quark masses are reproduced in a natural way thanks to the presence of new scalars. The new energy scale characterizing neutrino mass generation could be accessible to the current LHC experiments.
pacs:14.60.Pq, 12.60.Cn, 14.60.St
Despite the fierce experimental effort over the last decades the long-standing challenge concerning the question of whether neutrinos are their own anti-particles remains Barabash (2010); Avignone et al. (2008); Blot (2016). Although neutrinos could be Dirac or Majorana fermions, the leading theoretical expectation is that they are Majorana, the general belief being that the smallness of neutrino masses relative to the other Standard Model fermion masses is due to their charge neutrality. This fits naturally to the idea that neutrinos acquire Majorana masses from Weinberg’s dimension five operator. Realizations include various varieties of type I Gell-Mann et al. (1979); Yanagida (KEK lectures, 1979); Mohapatra and Senjanovic (1980); Schechter and Valle (1980, 1982) or type II Schechter and Valle (1980, 1982); Lazarides et al. (1981); Grimus et al. (2009) seesaw mechanisms, irrespective of whether the seesaw is realized at high or at low mass scale Boucenna et al. (2014a). Until the observation of neutrinoless double beta decay Klapdor-Kleingrothaus et al. (2004) becomes a reality Barabash (2010) we must keep an eye open to the possibility that neutrinos can be Dirac particles as well.
There are two issues that Dirac neutrino models must face, namely predicting the Dirac nature of neutrinos, and understanding their small mass. Dirac neutrinos require extra symmetries beyond gauge symmetry, otherwise massive neutrinos are generally expected to be Majorana fermions. Within the standard electroweak gauge structure this can be ensured by imposing a conserved lepton numberlike symmetry, continuous Peltoniemi et al. (1993) or discrete Chuliá et al. (2016). Likewise, one may consider schemes based on flavor symmetries, as suggested in Aranda et al. (2014) or appealing to the existence of extra dimensions Arkani-Hamed et al. (2002); Chen et al. (2016). Alternatively one may extend the gauge group, so as to include the lepton number symmetry Ma et al. (2015), for example, by using the extended gauge structure Singer et al. (1980) although most formulations lead to Majorana neutrinos Tully and Joshi (2001); Kitabayashi and Yasue (2001a, b); Montero et al. (2002); Chang and Long (2006); Dong et al. (2007); Mizukoshi et al. (2011); Boucenna et al. (2014b, 2015a); Okada et al. (2016); Boucenna et al. (2015b); Vien et al. (2016).
Because of the special features of the based models with respect to other electroweak extensions based, for example, on left-right symmetry, in this paper we focus on the possibility of having naturally light Dirac neutrinos with seesaw-induced masses, within the gauge structure. However, in contrast to Ref. Valle and Vaquera-Araujo (2016) in order to predict realistic quark masses in a natural way, two extra antitriplet scalar multiplets are included. As before, we have a lepton numberlike symmetry , preserved in the leptonic and quark sector. This symmetry is softly broken in the scalar sector by the term so that in the limit the Lagrangian symmetry gets enhanced. We show that the smallness of is related to the smallness of neutrino mass. This way we recover the new variant of type II seesaw mechanism for Dirac neutrinos recently considered in Valle and Vaquera-Araujo (2016). However, in contrast to the previous Ref. Valle and Vaquera-Araujo (2016), here the naturally small induced vacuum expectation values (vevs) responsible for neutrino mass generation are decoupled from the quark sector. This eliminates the need of fine-tuning the Yukawa couplings so that all fermion masses are naturally reproduced in a realistic way, since exotic quarks and standard model quarks are now decoupled. The scales associated to neutrino mass generation and the new gauge interactions could be accessible to the current LHC experiments.
The model is a modified version of the one presented in Ref. Valle and Vaquera-Araujo (2016). In the new setup, two extra scalar triplets are included and an auxiliary symmetry is implemented in order to decouple heavy quarks. The matter content and the transformation properties of the fields are contained in Table 1
In terms of the gauge group generators, the electric charge is expressed as
while lepton number is defined as
The symmetry breaking pattern is assumed to be of the form
with and .
The Yukawa interactions invariant under all the defining symmetries of the model are
In this setup, and are completely decoupled from the quark sector and are responsible for the neutrino mass generation, whereas and contribute exclusively to the quark masses. After spontaneous symmetry breaking, the above interactions lead to the following mass matrices for the fermion fields:
up-type quarks, basis :
down-type quarks, basis :
Realistic quark masses can be readily obtained as the standard model and exotic sectors are independent by virtue of the symmetry. This also implies that the Cabibbo-Kobayashi-Maskawa matrix describing quark mixing is unitary.
Moreover, from the diagonalization of , the mass of the light neutrino in the one-family approximation is given by
Notice that the Dirac nature of neutrinos is ensured by the discrete group. In what follows, we specialize to the case and show that the smallness of the neutrino mass can be understood as emerging from a type II seesaw mechanism for Dirac neutrinos. This links the emergence of the small induced scale to the breaking of the global symmetry Valle and Vaquera-Araujo (2016).
The scalar potential of the model is
where the term breaks explicitly the symmetry. Assuming real vevs and parameters in the potential, the tadpole equations can be solved for the parameters , , and as follows
Assuming that the bracketed factor in the rhs of Eq.(18) is nonvanishing, can be interpreted as an induced vev, whose smallness is related to the scale of symmetry breaking, characterized by , in the sense that in the limit , the symmetry of the potential is enhanced by .
We conclude this section with an estimate of the scales involved and the resulting light neutrino mass
Taking , , and quartic couplings of in Eq.(18), the resulting scale can accommodate easily a neutrino mass of without invoking tiny Yukawa couplings or large values for the vacuum expectation values . Finally, note that the light neutrino mass in Eq.(19) is mostly insensitive to the values of and , and therefore new physics in this model can lie within reach of the LHC experiments.
Iii Summary and discussion
Here we have proposed a realistic electroweak gauge model with an enlarged Higgs sector. The scheme leads to Dirac neutrinos, and allows for the natural implementation of a type II seesaw mechanism. The model substantially improves the one previously considered in Ref. Valle and Vaquera-Araujo (2016), in that here the small vacuum expectation values associated to neutrino mass generation are decoupled from the quark sector. The charged lepton and quark masses are reproduced in a realistic way, avoiding the mixing between exotic and standard model quarks. The energy scales characterizing neutrino mass generation and the new gauge interactions arising from the enlarged gauge symmetry could be accessible to the current LHC experiments.
This work is supported by the Spanish grants FPA2014-58183-P, Multidark CSD2009-00064, SEV-2014-0398 (MINECO) and PROMETEOII/2014/084 (Generalitat Valenciana). C.A.V-A. acknowledges support from CONACyT (Mexico), grant 251357.
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