During 2004, four divisions of the American Physical Society commissioned a study of neutrino physics to take stock of where the field is at the moment and where it is going in the near and far future. Several working groups looked at various aspects of this vast field. The summary was published as a main report entitled "The Neutrino Matrix" accompanied by short 50 page versions of the report of each working group. Theoretical research in this field has been quite extensive and touches many areas and the short 50 page report [1] provided only a brief summary and overview of few of the important points. The theory discussion group felt that it may be of value to the community to publish the entire study as a white paper and the result is the current article. After a brief overview of the present knowledge of neutrino masses and mixing and some popular ways to probe the new physics implied by recent data, the white paper summarizes what can be learned about physics beyond the Standard Model from the various proposed neutrino experiments. It also comments on the impact of the experiments on our understanding of the origin of the matter-antimatter asymmetry of the Universe and the basic nature of neutrino interactions as well as the existence of possible additional neutrinos. Extensive references to original literature are provided.2

We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in Grand Unified Theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture. *

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The usual see-saw formula is modified by the presence of two Higgs triplets in left-right symmetric theories. The contribution from the left-handed Higgs triplet to the see-saw formula can dominate over the conventional one when the neutrino Dirac mass matrix is identified with the charged lepton or down quark mass matrix. In this case an analytic calculation of the lepton asymmetry, generated by the decay of the lightest right-handed Majorana neutrino, is possible. For typical parameters, the out-of-equilibrium condition for the decay is automatically fulfilled. The baryon asymmetry has the correct order of magnitude, as long as the lightest mass eigenstate is not much lighter then 10 −6 to 10 −8 eV, depending on the solution of the solar neutrino problem. A sizable signal in neutrinoless double beta decay can be expected, as long as the smallest mass eigenstate is not much lighter than 10 −3 eV and the Dirac mass matrix is identified with the charged lepton mass matrix. *

A wide class of neutrino physics-motivated models are characterized by the spontaneous violation of a global U(1) lepton number symmetry at or below the electroweak scale by a n SU(2) U(1) singlet vacuum expectation value h i < O (1) TeV. In all these models the main Higgs decay c hannel is likely to be "invisible", e.g. h ! JJ, where J denotes the associated weakly interacting pseudoscalar Goldstone bosonthe majoron. This leads to events with large missing energy that could be observable at LEP and a ect the Higgs mass bounds obtained, as well as lead to novel ways to search for Higgs bosons at high energy supercolliders such as the LHC/SSC.