arXiv subjects

Marek Zrałek

Publications and source records attributed to Marek Zrałek.

7 recordsLinked to original sources

arXiv2025

Partial $A_4$ flavor symmetry of the leptonic 3HDM

When the Higgs doublets in the 3HDM transform as a flavor triplet of the $A_4$ group, the lepton mass matrices accommodate the experimental neutrino mixing angles at arbitrary precision while maintaining the correct mass ordering of the charged and neutral leptons, the latter being Dirac neutrinos in the normal spectrum. Under $A_4$ symmetry, also agreement of the lepton masses with experimental data is obtained for Higgs vacua differing from those for fitting $U_{\text{PMNS}}$. For groups of order equal or less than 600 no contractions different from the one found for $A_4$ yield better agreement with experimental data, and the solution structure presented is unique within the set of groups studied.

hep-ph↗

arXiv2024

Flavor invariance of leptonic Yukawa terms in the 3HDM

As an extension of the Standard Model (SM), the 3HDM (Three-Higgs-Doublet Model) defines additional relationships among the fermions. In the visible leptonic Yukawa sector of the 3HDM, we investigate the existence of flavor symmetries under discrete non-abelian groups up to order 1032. When the VEVs are not allowed to depart from their alignment imposed by the condition of minimal potential in the Higgs scalar sector, there will be severe mass degeneracies and a lack of lepton flavor mixing for any nontrivial flavor group. Yet we propose to study the Yukawa terms of the lepton sector for in case the VEV alignment would not be protected, hence leaving the VEV ratios as free parameters. Then, as it turns out, mass splitting for the charged leptons and the neutrinos is obtained although it is still impossible to obtain correct fits to the experimentally known lepton mass spectrum and to the PMNS matrix simultaneously.

hep-ph↗

arXiv2023

Lepton masses and mixing in a three-Higgs doublet model

In the three-Higgs doublet model (3HDM) frame, we search for discrete flavour symmetries that give relations among the lepton masses and their mixing angles. We explore discreet non-Abelian groups of order less than 1035, treating neutrinos as Majorana or Dirac particles. Despite the free dynamic parameters available in the model, none of the groups fully predicts the lepton data. However, some of the scanned groups provide either the correct neutrino masses and mixing angles or the correct masses of the charged leptons. $Δ(96)$ is the smallest group compatible with the experimental data of neutrino masses and PMNS mixing. $S_4$ is an approximate symmetry of Dirac neutrino mixing, with parameters staying about $3σ$ apart from the measured $θ_{12}$, $θ_{23}$, $θ_{13}$.

hep-ph↗

arXiv2018

Lepton masses and mixing in a two-Higgs-doublet model

Within the framework of the two-Higgs Doublet Model (2HDM), we attempt to find some discrete, non-abelian flavour symmetry which could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavour symmetry to be broken. With the GAP program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.

hep-ph↗

arXiv2016

The flavour problem and family symmetry beyond the Standard Model

In the frame of two Higgs doublet model we try to explain the lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the 1025 order are considered. Like in the one Higgs Standard Model, we found that discrete family symmetries do not give satisfactory answer for this basic questions in the flavour problem.

hep-ph↗

arXiv2016

The discrete family symmetry as a possible solution to the flavour problem

In order to explain the fermions masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-abelian subgroup of $U(3)$ is added to the gauge group $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.

hep-ph↗

arXiv2016

Texture zeros in neutrino mass matrix

The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle θ13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries. Nowadays, assuming one Higgs doublet, it is unlikely that this is still valid. Texture zeroes, that are combined with abelian symmetries, are intensively studied. The neutrino mass matrix is a natural way to study such symmetries.

hep-ph↗