Flavor symmetries in an SU(5) model of grand unification

Malte Lindestam,Tommy Ohlsson,Marcus Pernow

doi:10.1007/jhep01(2022)009

Malte Lindestam, Tommy Ohlsson + Show 1 more

Open Access

https://doi.org/10.1007/jhep01(2022)009

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Abstract

We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric SU(5) grand unified theory, without introducing additional flavor-related fields. Such symmetries reduce the number of free parameters in the model and therefore lead to more predictive models. We consider the Yukawa sector of the Lagrangian, and search for all possible flavor symmetries. As a result, we find 25 distinct realistic flavor symmetry cases, with ℤ2, ℤ3, ℤ4, and U(1) symmetries, and no non-Abelian cases.

Highlights

JHEP01(2022)009 texture zeros on the Yukawa matrices, these so-called flavor symmetries can help provide natural explanations for why the experimentally observed masses and mixing parameters of the fermions obtain the values that they do
We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric SU(5) grand unified theory, without introducing additional flavor-related fields
As an adaptation of the work performed in refs. [11, 12], we have constructed a minimal SU(5) GUT upon which flavor symmetries may be imposed

Summary

Lagrangian of the model

We study a non-supersymmetric renormalizable model with an additional scalar field in the 45 representation to solve the problems of down-type quark masses and gauge coupling unification [3]. A type II seesaw mechanism is introduced using a scalar in the 15 representation. In the Yukawa sector, the relevant scalars are 5S, 45S, and 15S, with the first two generating charged fermion masses and the latter generating neutrino masses through the type II seesaw mechanism. All indices not mentioned have a VEV of zero With these VEVs, the Yukawa sector results in mass terms for all fermions. The assumption is made that the different generations of each kind of fermion have different masses at the GUT scale While this is known to be true at lower energies, it may cease to be the case due to the RG running of the masses. RG running of fermion masses to the GUT scale using the SM results in all different masses [27, 28], which lends credence to this assumption

Flavor symmetry transformations

Flavor symmetry cases

Numerical fits

Summary and conclusions

A Found symmetry cases

B Non-Abelian symmetry cases