Topics in QCD and electroweak theory

Two frontier topics, one in QCD (the light scalar meson puzzle) and the other one in electroweak theory (the problem of neutrino masses and mixings), are treated in this work. We consider a generalized linear sigma model which contains two chiral nonets, one with a two quark structure, the other one with four quark fields. The model tries to explain, among other things, the inverted mass spectrum of the scalar mesons. We study this type of model using two approaches. The first one relies on the generating equations and leads to Ward identity type relations based only on the chiral symmetry. Using this approach we were able to find masses and mixings for the pseudoscalar and scalar states and also to prove that the low energy theorems for the pion-pion scattering hold in the limit of massless quarks. The second approach is based on a specific choice of terms in the Lagrangian. This allowed us to obtain information about all the masses and mixings in the model and also to give an exact numerical treatment for the scattering of two pions. Using both these methods we found consistently that while the lightest pseudoscalar states are mostly quark-antiquark structures, the lightest scalars have a large four quark component. The instanton dynamics generates effective terms in the chiral lagrangian which violate explicitly the U(1) A symmetry. While the first term has the form of a determinant, the second one does not have a clear interpretation in the usual linear sigma model. We show that this this term can be viewed as mixing one between the two quark and four quark fields in our generalized model. This establishes a connections between the instanton approach and the effective Lagrangian one. The leptonic mixing matrix in the electroweak theory is well known from experiments as being very close to the so-called tribimaximal form. This form is natural in the context of S 3 symmetry, where it is just the transformation matrix from the three dimensional defining representation to a sum of a one dimensional and a two dimensional irreducible representation. We consider that the S 3 symmetry holds as a first order approximation for the electroweak theory. We obtain in this way the desired tribimaximal form for the leptonic mixing matrix and we briefly discuss possible S 2 perturbation terms