Abstract
We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_5$ modular symmetry. We construct the weight 2, weight 4 and weight 6 modular forms of level 5 in terms of Dedekind eta-functions and Klein forms, and their decomposition into irreducible representation of $A_5$. We construct all the simplest models based on $A_5$ modular symmetry, including scenarios of models with and without flavons in the charged lepton sectors. For each case, the neutrino masses can be generated through either the Weinberg operator or the type I seesaw mechanism. We perform an exhaustive numerical analysis, organising our results in an extensive set of figures and tables.
Highlights
The flavor puzzle, in particular the origin of neutrino mass and lepton mixing, is a major unresolved problem of the Standard Model (SM)
In [34] the neutrino masses are assumed to originate exclusively from the Weinberg operator. (v) We have constructed all the simplest models based on A5 modular symmetry, and we propose 16 possible A5 modular models, as summarized in Table IV, while only two models are built in [34]. (vi) We have performed an exhaustive numerical analysis for each model, the best fitting values and the predicted regions of the mixing parameters are listed, and we present the results in the form of extensive sets of figures and tables
In this paper we have provided a comprehensive analysis of neutrino mass and lepton mixing in theories with Γ5 ≅ A5 modular symmetry
Summary
The flavor puzzle, in particular the origin of neutrino mass and lepton mixing, is a major unresolved problem of the Standard Model (SM). We have constructed the Γð5Þ modular forms by using the Dedekind eta-function and Klein forms, which is an independent method to the Jacobi theta function approach, and we obtain the same q-expansions of the modular forms as those given in [34], up to irrelevant factors. 1⁄2Y3ðY30 Y30 Þ53; 1⁄2Y30 ðY30 Y30 Þ53; 1⁄2Y5ðY3Y30 Þ43; ðY3Yð34;IÞÞ3 1⁄4 1⁄2Y3ðY3Y5Þ33; 1⁄2Y3ðY3Y3Þ53; 1⁄2Y30 ðY3Y30 Þ43; 1⁄2Y30 ðY3Y3Þ53; 1⁄2Y 5 ðY 3 Y 5 Þ3 3 ; 1⁄2Y5ðY30 Y5Þ30 3; ðY5Yð54;IÞÞ3 1⁄4 1⁄2Y5ðY3Y3Þ53; 1⁄2Y5ðY30 Y30 Þ53: we find only two of them are linearly independent and they could be chosen to be ð6Þ 3;I. pffiffi 2 3e033ÞT : In a similar manner, we can construct the following twelve A5 triplet 30 modular forms of weight 6, Þ30. − 2e2e3e02; −2e21e03 − 2e23e01 þ 2 2e1e2e02 þ 2e2e3e03; 2e22e02 − 4e1e3e01ÞT : ð51Þ These weight modular forms are quite useful for constructing modular symmetry models in the charged lepton sector, as shown
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