Supersymmetry and GUTs in Mexico
Here I review briefly some of the work done in Mexico in Supersymmetry and Grand Unified Theories. The emphasis will be mainly in work that has some relation to phenomenology.

title: Conditions for vacuum stability in an S3 extension of the Standard Model
abstract: In this work we study the Higgs sector in the minimal S3 extension of the Standard Model. The S3 extended Standard Model, which has three Higgs doublets fields that belong to the three-dimensional reducible representation of the permutation group S3, has naturally new phenomena: there are several Higgs bosons, charged, neutral and pseuodscalar ones, and more than one potential minimum. We analyzed the stability of the minimal S3 invariant extension of the Higgs potential and show that at tree-level, the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one.

title: Finite GUTs within conventional N=1 gauge theories
abstract: Finite Unified Theories (FUTs) are conventional 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 leads to 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. Among the characteristics of the latter ones are: 1) The lightest Higgs boson mass is predicted to be in the window 120–130 GeV, in case the LSP is neutralino, while in case the LSP is the τ (which can be consistently accommodated in presence of bilinear R-parity violating terms) it can be as light as 111 GeV. 2) The s-spectrum starts above several hundreds of GeV.

title: Top quark mass predictions from gauge Yukawa unification
abstract: Gauge-Yukawa Unification (GYU) is a renormalization group invariant functional relation among gauge and Yukawa couplings which holds beyond the unification point in Grand Unified Theories (GUTs). Here, GYU is obtained by requiring finiteness and reduction of couplings to all orders in perturbation theory. We examine the consequences of GYU in various supersymmetric GUTs and in particular the predictions for the top quark mass. These predictions are such that they distinguish already GYU from ordinary GUTs. Moreover, when more accurate measurements of the top quark mass are available, it is expected that it will be possible to discriminate among the various GYUs.

title: Finite unification at all-loops

title: Finite unified theories and the top quark mass
abstract: 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 (∼ 175 – 190 GeV).

title: Search for new dielectron resonances and Randall-Sundrum gravitons at the collider detector at Fermilab.
abstract: A search for new dielectron-mass resonances using data recorded by the CDF II detector and corresponding to an integrated luminosity of 5.7  fb(-1) is presented. No significant excess over the expected standard model prediction is observed. In this data set, an event with the highest dielectron mass ever observed (960  GeV/c(2)) was recorded. The results are interpreted in the Randall-Sundrum (RS) model. Combined with the 5.4  fb(-1) diphoton analysis, the RS-graviton lower-mass limit for the coupling k/M¯(Pl)=0.1 is 1058  GeV/c(2), making it the strongest limit to date.

title: Top-quark mass measurement using events with missing transverse energy and jets at CDF.
abstract: We present a measurement of the top-quark mass using a sample of t ̄t events in 5.7 fb(-1) of integrated luminosity from p ̄p collisions at the Fermilab Tevatron with √s=1.96 TeV and collected by the CDF II Detector. We select events having large missing transverse energy, and four, five, or six jets with at least one jet tagged as coming from a b quark, and reject events with identified charged leptons. This analysis considers events from the semileptonic t ̄t decay channel, including events that contain tau leptons. The measurement is based on a multidimensional template method. We fit the data to signal templates of varying top-quark masses and background templates, and measure a top-quark mass of M(top)=172.32±2.4(stat)±1.0(syst)  GeV/c(2).

title: Measurement of the top quark mass in the all-hadronic mode at CDF
abstract: A measurement of the top quark mass ( M top ) in the all-hadronic decay channel is presented. It uses 5.8 fb−1 of p p ¯ data collected with the CDF II detector at the Fermilab Tevatron Collider. Events with six to eight jets are selected by a neural network algorithm and by the requirement that at least one of the jets is tagged as a b-quark jet. The measurement is performed with a likelihood fit technique, which simultaneously determines M top and the jet energy scale (JES) calibration. The fit yields a value of M top = 172.5 ± 1.4 ( stat ) ± 1.0 ( JES ) ± 1.1 ( syst ) GeV / c 2 .