arXiv subjects
Publications and source records attributed to J. Matias.
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.
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.
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.