Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIcosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
101
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.
rate research
Read More
In this paper we discuss a minor modification of a previous SU(5) x A5 flavour model which exhibits at leading order golden ratio mixing and sum rules for the heavy and the light neutrino masses. Although this model could predict all mixing angles well it fails in generating a sufficient large baryon asymmetry via the leptogenesis mechanism. We repair this deficit here, discuss model building aspects and give analytical estimates for the generated baryon asymmetry before we perform a numerical parameter scan. Our setup has only a few parameters in the lepton sector. This leads to specific constraints and correlations between the neutrino observables. For instance, we find that in the model considered only the neutrino mass spectrum with normal mass ordering and values of the lightest neutrino mass in the interval 10-18 meV are compatible with the current data on the neutrino oscillation parameters. With the introduction of only one NLO operator, the model can accommodate successfully simultaneously even at 1$sigma$ level the current data on neutrino masses, on neutrino mixing and the observed value of the baryon asymmetry.
We derive and discuss the solution of the Boltzmann equations for leptogenesis in a phenomenologically viable SU(5) x A5 golden ratio flavour model proposed in arXiv:1410.2057 [hep-ph], arXiv:1502.00110 [hep-ph] . The model employs, in particular, the seesaw mechanism of neutrino mass generation. We find that the results on the baryon asymmetry of the Universe, obtained earlier in arXiv:1502.00110 [hep-ph] using approximate analytic expressions for the relevant CP violating asymmetry and efficiency factors, are correct, as was expected, up to 20-30 %. The phenomenological predictions for the low energy neutrino observables, derived using values of the parameters of the model for which we reproduce the observed value of the baryon asymmetry, change little with respect to those presented in arXiv:1502.00110 [hep-ph]. Among the many predictions of the model we find, for instance, that the neutrinoless double beta decay effective Majorana mass m_ee lies between 3.3 meV and 14.3 meV.
We furnish a supersymmetric extension of the Standard Model with a flavour discrete symmetry $A_5$ under which the lepton fields transform as an irreducible triplet. Additional (`flavon) superfields are used to break $A_5$ into a $mathbb{Z}_2 times mathbb{Z}_2$ subgroup in the charged-lepton sector and another $mathbb{Z}_2$ subgroup in the neutrino sector. The first column of the resulting lepton mixing matrix is predicted and has entries which are related to the golden ratio. Using the observed $theta_{13}$ as input, our model predicts a solar mixing angle $theta_{12}$ in very good agreement with experiment; it also predicts a correlation between the atmospheric mixing angle $theta_{23}$ and the $CP$-violating Dirac phase $delta$.
The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. We argue that this structure suggests a family symmetric origin in which the magnitude of the mixing angles are related to the existence of a discrete non-Abelian family symmetry. We construct a model in which the family symmetry is the non-Abelian discrete group $Delta(27)$, a subgroup of SU(3) in which the tri-bi-maximal mixing directly follows from the vacuum structure enforced by the discrete symmetry. In addition to the lepton mixing angles, the model accounts for the observed quark and lepton masses and the CKM matrix. The structure is also consistent with an underlying stage of Grand Unification.
We present the $D_4times Z_2$ flavor symmetry, which is different from the previous work by Grimus and Lavoura. Our model reduces to the standard model in the low energy and there is no FCNC at the tree level. Putting the experimental data, parameters are fixed, and then the implication of our model is discussed. The condition to realize the tri-bimaximal mixing is presented. The possibility for stringy realization of our model is also discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
