[en] This School continued with the tradition of promoting High Energy Physics in Mexico, and it was aimed particularly at students and young researchers. To fulfill this purpose worldwide experts were brought together to give a series of courses and plenary lectures. There were also research seminars given by the participants to discuss their own work

[en] After a brief review of some relevant results on lepton masses and mixings, that had previously 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 processes as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S₃ X 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. (Author)

[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, are re parametrized in terms of the masses of the charged leptons and neutrinos. Then, the neutrino mixing matrix VPMNS is computed and we obtain explicit, analytic and exact expressions for the neutrino mixing angles as function of the masses of the charged leptons and neutrinos. By comparison with the experimental data on neutrino mixings, we obtain numerical values for the neutrino masses in good agreement with the experimental bounds extracted from neutrinoless double beta decay and precision cosmological observations. (Author)

[en] Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the s-spectrum in the dimensionful sector. Here we examine the predictions of two FUTs taking into account the various theoretical and experimental constraints as well as their restricted parameter space. For the first we present the results of a detailed scanning concerning the Higgs mass prediction, while for the second we present a representative prediction of its spectrum. (author)

[en] We present results of a study of two phenomenologically interesting SU(5) supersymmetric Grand Unified models, which are finite to all-loops before spontaneous symmetry breaking. The finiteness conditions provide us with relationships among the Yukawa and gauge couplings at the unification point, which in turn predict a heavy top quark mass ( similar 175-190GeV). ((orig.))

[en] We present results of a study of phenomenologically interesting SU(5) supersymmetric GUT's, which are finite to all-loops before spontaneous symmetry breaking. The finiteness conditions provide the spontaneously broken theory with relationships among the Yukawa and gauge couplings at the unification point. These in turn predict a heavy top quark mass (∼175-190 GeV). (orig.)

[en] The mass matrices of the charged leptons and neutrinos, previously derived in a minimal S₃-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_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_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 S₃xZ₂ 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

[en] Analyzing the observable sector of the Z₃ orbifold with two Wilson lines, the only 9 inequivalent models which are candidates to standard model are obtained. The drastic reduction of the ≅ 50 000 models which in principle can be constructed, is carried out using the fact that models related through a certain number of operations (Weyl reflections and others that are described in the text) are equivalent. This result is encouraging since it can allow a systematic analysis of the phenomenological prospects of the Z₃ orbifold. This is a general formalism to reduce the number of interesting models and therefore it can be applied to any Z_N orbifold. (orig.)

[en] We study the phenomenological implications of Finite Unified Theories (FUTs). In particular we look at the predictions for the lightest Higgs mass and the s-spectra of two all-loop finite models with SU(5) as gauge group. We also consider a two-loop finite model with gauge group SU(3)³, which is finite if and only if there are exactly three generations. In this latter model we concetrate here only on the predictions for the third generation of quark masses.

[en] We present an analysis of the theoretical neutrino mixing matrix, V_PMNS^th, previously derived in the framework of the minimal S₃-invariant extension of the Standard Model. All entries in the neutrino mixing matrix, V_PMNS^th, the mixing angles and the Majorana phases are given as exact, explicit analytical functions of the mass ratios of the charged leptons and neutrinos, and one Dirac phase, in excellent agreement with the the latest experimental data. Here, it will be shown that all entries in V_PMNS^th are numerically very close to the tri-bimaximal form of the neutrino mixing matrix, so that V_PMNS^th may be written as V^tri+ΔV_PMNS^tri. The small correction ΔV_PMNS^tri is expressed as a sum of two terms: first, a small correction term proportional to m_e/m_μ depending only on the charged lepton mass ratios and, second, a Cabbibo-like, small term, δt₁₂, which is a function of both the charged lepton and the neutrino mass ratios