Abstract:
The formalism of the matching conditions between transverse connected Green functions is extended to include the two next to leading corrections, namely the two-loop $M_{H}^{2}$ and the one-loop $1/M_{H}^{2}$ contributions to the coefficients of the electroweak chiral lagrangian which are relevant to the LEP1 physics: $a_{0}$, ${\hat a}_{1}$ and ${\hat a}_{8}$. We derive general expressions for these three coefficients in terms of just bare gauge boson self-energies. By means of the screening theorem, it is shown that the same expressions can be used to get directly from a MSM calculation, the leading Higgs mass contribution to these coefficients at each loop order. In a more general framework, we solve the problems concerning the loss of gauge invariance and the inclusion of only gauge invariant operators by proposing a new formulation of the matching conditions at two and higher loop order. As an example of the usefulness of using an electroweak chiral lagrangian to parametrize the MSM, we will give a simple proof of an extra screening for the renormalized photon self-energy in the on-shell scheme at all orders. In addition it is shown the automatic cancellation of the unphysical $M_{H}^4$ terms in the other gauge boson self-energies at two-loops in this scheme. Finally we will apply the obtained electroweak chiral lagrangian to compute the different Higgs mass contributions to the bosonic part of $\Delta \rho$, $\Delta r$ and $\Delta \kappa$, analyzing carefully the hierarchy between corrections.

Abstract:
A new type of gauge extension of the SM is proposed. It is based on a SU(2)xSU(2)xU(1) group with the peculiarity that the gauge bosons of the extra SU(2) do not couple to fermions. This feature relaxes some of the constraints on the masses of the new gauge bosons, leaving the possibility of having lighter masses than in traditional extensions. The model exhibits several interesting properties, it is anomaly free and at tree level it does not have FCNC while loop induced effects are strongly suppressed. Also, from the analysis of $\Delta \rho$ at one loop, two configurations for the vevs giving rise to a screening phenomenon are identified. One of these configurations can also be related with the Bess model. A tree level fit to the most recent electroweak data is performed confirming the possibility of having new light gauge boson masses. The constraints coming from different FCNC processes like $b \to s \gamma$, $B_{0}-{\bar B}_{0}$ and $K_{0}-{\bar K}_{0}$ mixing are also taken into account. Finally, a generalization of this model for the case of having several extra copies of SU(2) groups is commented, focusing on the presence of screening configurations and the corresponding mass spectrum.

Abstract:
We present the contributions of new CP phases in CP asymmetries of two-body neutral $B_s$ decays coming from a left--right model with spontaneous CP violation. Large deviations from the Standard Model predictions can be accommodated in a natural way by this type of models. The new physics effects on the mixing, width difference and decays are analysed. In particular, we show how the measurement of the angle $\gamma$ in electroweak penguin-dominated processes can be largely affected.

Abstract:
The computation of the polarized amplitudes and cross section of the processes $\gamma\nu\to\gamma\gamma \nu$, $\gamma\gamma \to \gamma\nu\bar\nu$ and $\nu\bar\nu \to \gamma\gamma\gamma$ is described. We used an effective lagrangian approach for energies below the threshold for $e^+e^-$ pair production and the complete computation at higher energies for application in supernova dynamics. Leading contributions of physics beyond the SM are also commented.

Abstract:
Motivated by some previous work on fermions on random lattices and by suggestions that impurities could trigger parity breaking in 2d crystals, we have analyzed the spectrum of the Dirac equation on a two dimensional square lattice where sites have been removed randomly --- a doped lattice. We have found that the system is well described by a sine-Gordon action. The solitons of this model are the lattice fermions, which pick a quartic interaction due to the doping and become Thirring fermions. They also get an effective mass different from the lagrangian mass. The system seems to exhibit spontaneous symmetry breaking, exactly as it happens for a randomly triangulated lattice. The associated ``Goldstone boson" is the sine-Gordon scalar. We argue, however, that the peculiar behaviour of the chiral condensate is due to finite size effects.

Abstract:
We study the effect of supersymmetric contributions to the effective quark transition $b\to s\gamma\gamma$, including leading order QCD effects. We apply the discussion to the decay $B_s\to\gamma\gamma$. Even though one-particle irreducible contributions could play a role, numerical cancelations make the amplitude for the two-photon emission strongly correlated to the $b\to s\gamma$ amplitude which is sharply constrained by experiment. A quite general statement follows: as long as non-standard physics effects appear only in the matching of the Wilson coefficients of the standard effective operator basis, the deviations from the standard model expectations of the decay rates induced by $b\to s\gamma\gamma$ are bound to follow closely the corresponding deviations on $b\to s\gamma$. Effects of new physics are therefore bound to be small.

Abstract:
We perform an exhaustive analysis of the Equivalence Theorem both in the minimal Standard Model and in an Effective Electroweak Chiral Lagrangian up to ${\cal O}(p^4)$. We have considered the leading corrections to the usual prescription consisting in just replacing longitudinally polarized $W$ or $Z$ by the corresponding Goldstone bosons. The corrections appear through an overall constant multiplying the Goldstone boson amplitude as well as through additional diagrams. By including them we can extend the domain of applicability of the Equivalence Theorem, making it suitable for precision tests of the symmetry breaking sector of the Standard Model. The on-shell scheme has been used throughout. When considering the Equivalence Theorem in an Effective Chiral lagrangian we analyze its domain of applicability, as well as several side issues concerning gauge fixing, Ward identities, on-shell scheme and matching conditions in the effective theory. We have analyzed in detail the processes $W^+ W^- \to W^+W^-$ and $W^+W^+\to W^+W^+$ to illustrate the points made.

Abstract:
Chiral lagrangians describing the interactions of Goldstone bosons in a theory possessing spontaneous symmetry breaking are effective, non-renormalizable field theories in four dimensions. Yet, in a momentum expansion one is able to extract definite, testable predictions from perturbation theory. These techniques have yielded in recent years a wealth of information on many problems where the physics of Goldstone bosons plays a crucial role, but theoretical issues concerning chiral perturbation theory remain, to this date, poorly treated in the literature. We present here a rather comprehensive analysis of the regularization and renormalization ambiguities appearing in chiral perturbation theory at the one loop level. We discuss first on the relevance of dealing with tadpoles properly. We demonstrate that Ward identities severely constrain the choice of regulators to the point of enforcing unique, unambiguous results in chiral perturbation theory at the one-loop level for any observable which is renormalization-group invariant. We comment on the physical implications of these results and on several possible regulating methods that may be of use for some applications.

Abstract:
We analyze the matching conditions to determine the values that the ${\cal O}(p^4)$ coefficients of an Effective Chiral Lagrangian take in the Standard Model in the limit of a large Higgs mass, pointing out a number of subtleties that appear to have gone unnoticed previously. We apply the resulting Effective Chiral Lagrangian, including the leading two loop effects, to analyze the most recent electroweak data assuming $m_{top}=174\pm 10$ GeV.

Abstract:
The minimum number of colors is a challenging knot invariant since, by definition, its calculation requires taking the minimum over infinitely many minima. In this article we estimate and in some cases calculate the minimum number of colors for the Turk's head knots on three strands.