A. Mondragón

Lepton masses, mixings and FCNC in a minimal S(3)-invariant extension of the Standard Model

The mass matrices of the charged leptons and neutrinos, previously derived in a minimal S{sub 3}-invariant extension of the standard model, were reparametrized in terms of their eigenvalues. We obtained explicit, analytical expressions for all entries in the neutrino mixing matrix, V{sub PMNS}, the neutrino mixing angles, and the Majorana phases as functions of the masses of charged leptons and neutrinos in excellent agreement with the latest experimental values. The resulting V{sub PMNS} matrix is very close to the tribimaximal form of the neutrino mixing matrix. We also derived explicit, analytical expressions for the matrices of the Yukawa couplings and computed the branching ratios of some selected flavor-changing neutral current processes as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S{sub 3}xZ{sub 2} flavor symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector well below the present experimental upper bounds by many orders of magnitude.

Non-Hermitian degeneracy of two unbound states

We numerically solved the implicit, transcendental equation that defines the eigenenergy surface of a degenerating isolated doublet of unbound states in the simple but illustrative case of the scattering of a beam of particles by a double barrier potential. Unfolding the degeneracy point with the help of a contact equivalent approximant, crossings and anticrossings of energies and widths, as well as the changes of identity of the poles of the S-matrix, are explained in terms of sections of the eigenenergy surfaces.

Neutrino masses and mixings in a minimal S3-invariant extension of the standard model

Resumen en: The mass matrices of the charged leptons and neutrinos, that had been derived in the framework of a Minimal S3-invariant Extension of the Standard Model,...

S3-flavour symmetry as realized in lepton flavour violating processes

A variety of lepton flavour violating effects related to the recent discovery of neutrino oscillations and mixings is here systematically discussed in terms of an S3-flavour permutational symmetry. After a brief review of some relevant results on lepton masses and mixings, that had been derived in the framework of a minimal S3-invariant extension of the Standard Model, we derive explicit analytical expressions for the matrices of the Yukawa couplings and compute the branching ratios of some selected flavour-changing neutral current (FCNC) processes as well as the contribution of the exchange of neutral flavour-changing scalars to the anomaly of the muons magnetic moment as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S3 × Z2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector well below the present experimental upper bounds by many orders of magnitude. The contribution of FCNC to the anomaly of the muons magnetic moment is small but non-negligible.

A minimal S3-invariant extension of the Standard Model

We present a minimal S3-invariant extension of the Standard Model. We find that in leptonic sector, the exact S3 × Z2 symmetry, which allows 6 real independent parameters, is consistent with experimental data. With exact S3 symmetry, there are 10 real independent parameters and one independent phase, on which the mixing matrix VCKM depends. A set of values of these parameters that are consistent with experimental observations is given.

Bound states at exceptional points in the continuum

In this work, an example of exceptional points in the continuous spectrum of a Hamiltonian of von Neumann-Wigner type is presented and discussed. Remarkably, these exceptional points are not associated with a double pole in the scattering matrix but with a double pole in the normalization factor of the Jost eigenfunctions normalized to unit flux. At the exceptional points the two unnormalized Jost eigenfunctions are no longer linearly independent but coalesce to give rise to two Jordan cycles of generalized bound state energy eigenfunctions in the continuum and a Jordan block representation of the Hamiltonian. The regular scattering eigenfunction vanishes at the exceptional points and the irregular scattering eigenfunction has a double pole at the exceptional points. The scattering matrix is a regular analytical function of the wave number k for all k real including the exceptional points.

Exceptional points of a Hamiltonian of von Neumann–Wigner type

In this paper, we present and discuss an example of exceptional points in the continuous spectrum of a Hamiltonian of von Neumann–Wigner type associated with a double pole in the normalized Jost eigenfunctions, as functions of the wave number. The two unnormalized Jost energy eigenfunctions are analytic functions of the wave number k for all k complex, but at the exceptional points k = ±q, they coalesce to give rise to Jordan cycles of two generalized bound state quadratically integrable eigenfunctions. The Green function has simple poles at the exceptional points, but the regular scattering eigenfunction vanishes at those points. The scattering matrix is a regular function of the wave number at the exceptional points, that is, S(k) does not have a pole at the exceptional points.

Neutrino masses, mixings, and FCNC’s in an S 3 flavor symmetric extension of the standard model

By introducing threeHiggs fields that are SU(2) doublets and a flavor permutational symmetry, S3, in the theory, we extend the concepts of flavor and generations to the Higgs sector and formulate a Minimal S3-Invariant Extension of the Standard Model. The mass matrices of the neutrinos and charged leptons are re-parameterized in terms of their eigenvalues, then the neutrino mixing matrix, VPMNS, is computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of neutrinos and charged leptons are obtained in excellent agreement with the latest experimental data. We also compute the branching ratios of some selected flavor-changing neutral current (FCNC) processes, as well as the contribution of the exchange of neutral flavor-changing scalars to the anomaly of the magnetic moment of the muon, as functions of the masses of charged leptons and the neutral Higgs bosons. We find that the S3 × Z2 flavor symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector, well below the present experimental bounds by many orders of magnitude. The contribution of FCNC’s to the anomaly of the muon’s magnetic moment is small, but not negligible.

Exceptional point and degeneracy of the neutral heavy Higgs boson system H2−H3

We analyze the masses and mixings of the isolated doublet of neutral, heavy Higgs bosons, H2 and H3 of two Higgs doublet models with CP‐violation. There is a set of Lagrangian parameter values for which the isolated doublet of mass eigenstates is degenerate. Associated with this singularity, the propagator of the mixing H2−H3 neutral Higgs system has one double pole in the complex energy squared s‐plane. This analysis suggests that a detailed study of the lineshape of this Higgs system may provide valuable information on the CP nature of the underlying theory.

Lepton flavour violating processes in an S3-invariant extension of the SM

A variety of lepton flavour violating effects related to neutrino oscillations and mixings will be systematically discussed in the framework of a minimal S3-invariant extension of the Standard Model. After a brief review of some results on neutrino masses and mixings, we will give explicit analytical expressions for the matrices of the Yukawa couplings and the results of a computation of the branching ratios of some selected flavour-changing neutral current (FCNC) processes, as well as, the contribution of the exchange of neutral flavour-changing scalars to the anomaly of the magnetic moment of the muon, in terms of the masses of the charged leptons and the neutral Higgs bosons. It will also be shown that the S3 × Z2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector and give a nearly tri-bimaximal neutrino mixing matrix. The contribution of the FCNCs to the anomaly of the magnetic moment of the muon is small but non-negligible.