Julia Gehrlein

An SU(5)×A5 golden ratio flavour model

Abstract In this paper we study an SU ( 5 ) × A 5 flavour model which exhibits a neutrino mass sum rule and golden ratio mixing in the neutrino sector which is corrected from the charged lepton Yukawa couplings. We give the full renormalisable superpotential for the model which breaks SU(5) and A 5 after integrating out heavy messenger fields and minimising the scalar potential. The mass sum rule allows for both mass orderings but we will show that inverted ordering is not valid in this setup. For normal ordering we find the lightest neutrino to have a mass of about 10–50 meV, and all leptonic mixing angles in agreement with experiment.

An SU(5) x A5 Golden Ratio Flavour Model

Abstract In this paper we study an SU ( 5 ) × A 5 flavour model which exhibits a neutrino mass sum rule and golden ratio mixing in the neutrino sector which is corrected from the charged lepton Yukawa couplings. We give the full renormalisable superpotential for the model which breaks SU(5) and A 5 after integrating out heavy messenger fields and minimising the scalar potential. The mass sum rule allows for both mass orderings but we will show that inverted ordering is not valid in this setup. For normal ordering we find the lightest neutrino to have a mass of about 10–50 meV, and all leptonic mixing angles in agreement with experiment.

Predictivity of Neutrino Mass Sum Rules

Correlations between light neutrino observables are arguably the strongest predictions of lepton flavour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a non-zero value of the lightest neutrino mass and to distinct predictions for the effective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modification of the predictions derived from neutrino mass sum rules. We show that, in most cases, the predictions are fairly stable: while small quantitative changes can appear, they are generally rather mild. We therefore establish the predictivity of neutrino mass sum rules on a level far more general than previously known.

Leptogenesis in an SU(5)×A5 golden ratio flavour model

In this paper we discuss a minor modification of a previous SU(5) × 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 1σ level the current data on neutrino masses, on neutrino mixing and the observed value of the baryon asymmetry.

Renormalisation group corrections to neutrino mass sum rules

A bstractNeutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.

Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model: Addendum

We derive and discuss the solution of the Boltzmann equations for leptogenesis in a phenomenologically viable SU(5)×A5 golden ratio flavour model proposed in [1, 2]. 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 [2] 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 [2]. Among the many predictions of the model we find, for instance, that the neutrinoless double beta decay effective Majorana mass mee lies between 3.3 meV and 14.3 meV. E-mail: julia.gehrlein@student.kit.edu Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria. E-mail: martin.spinrath@kit.edu E-mail: xinyizhang18@gmail.com ar X iv :1 50 8. 07 93 0v 1 [ he pph ] 3 1 A ug 2 01 5

Addendum to “Leptogenesis in an SU(5)×A5 golden ratio flavour model” [Nucl. Phys. B 896 (2015) 311–329]

We derive and discuss the solution of the Boltzmann equations for leptogenesis in a phenomenologically viable SU(5)×A5 golden ratio flavour model proposed in [1, 2]. 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 [2] 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 [2]. Among the many predictions of the model we find, for instance, that the neutrinoless double beta decay effective Majorana mass mee lies between 3.3 meV and 14.3 meV. E-mail: julia.gehrlein@student.kit.edu Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria. E-mail: martin.spinrath@kit.edu E-mail: xinyizhang18@gmail.com ar X iv :1 50 8. 07 93 0v 1 [ he pph ] 3 1 A ug 2 01 5

Neutrino mass sum rules and symmetries of the mass matrix

Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which has not yet been discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but they are simply the result of a reduction of free parameters due to skillful model building.

Addendum to "Leptogenesis in an SU(5) x A(5) golden ratio flavour model"

We derive and discuss the solution of the Boltzmann equations for leptogenesis in a phenomenologically viable SU(5)×A5 golden ratio flavour model proposed in [1, 2]. 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 [2] 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 [2]. Among the many predictions of the model we find, for instance, that the neutrinoless double beta decay effective Majorana mass mee lies between 3.3 meV and 14.3 meV. E-mail: julia.gehrlein@student.kit.edu Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria. E-mail: martin.spinrath@kit.edu E-mail: xinyizhang18@gmail.com ar X iv :1 50 8. 07 93 0v 1 [ he pph ] 3 1 A ug 2 01 5

AnSU(5)×A5golden ratio flavour model

Abstract In this paper we study an SU ( 5 ) × A 5 flavour model which exhibits a neutrino mass sum rule and golden ratio mixing in the neutrino sector which is corrected from the charged lepton Yukawa couplings. We give the full renormalisable superpotential for the model which breaks SU(5) and A 5 after integrating out heavy messenger fields and minimising the scalar potential. The mass sum rule allows for both mass orderings but we will show that inverted ordering is not valid in this setup. For normal ordering we find the lightest neutrino to have a mass of about 10–50 meV, and all leptonic mixing angles in agreement with experiment.