Some Aspects of Chirality: fermion masses and chiral p-forms

Abstract: This thesis deals with different types of chiral fields. The properties of fermion masses are investigated from different poits of view, both within the Standard Model and in extensions of the model. It is shown how mass matrix invariants are used to define the measurables of the quark mixing matrix as invariant functions of the mass matrices. One model is presented where the family pattern is suggested to originate from a kind of mass scaling. A Lagrangian density is defined for an entire charge sector, such that the existence of a Dirac field with a certain mass implies the existence of other Dirac fields, where the corresponding quanta have masses which are obtained from the initial mass by a discrete scale transformation. This suggests a certain type of democratic fermion mass matrices. Also extensions of the minimal Standard Model are investigated, obtained by including right-handed neutrions in the model. The Standard Model extended by two right-handed neutrinos gives rise to a mass spectrum with two massive and three massless (at tree level) neutrinos. No assumptions such as the see-saw assumption of a large mass scale are necessary, provided the neutrino mass matrix assumes a certain form. The phenomenological consequences of this model are discussed. The neutrino mass matrix in such a scheme has what is defined as a democratic texture. The democratic family mixing matrix, with only unit entries, is found to act as a projection matrix in the sense that multiplying any 3x3 matrix with the democratic matrix is the same as multiplying an appropriate diagonal 3x3 matrix with the democratic matrix. Neutrino mass matrices with a democratic texture are studied for the cases with two and three right-handed neutrinos, respectively. The chiral fields that we find in the Standard Model have certain similarities with self-dual fields. Among other things, both chiral and self-dual fields suffer species doubling on the lattice. Chiral p-forms are self-dual fields that appear in twice-odd dimensions. Chiral p-forms violet manifest covariance, in the same sense that manifest covariance is violated by non-covariant gauges in electrodynamics. It is shown that a covariant action can nevertheless be formulated for chiral p-forms, by introducing an infinite set of gauge fields in a carefully controlled way.