Neutrino Masses and Mixing Angles in SUSY-GUT Theories with explicit R-Parity Breaking

In minimal SUSY GUT models the $R$-parity breaking terms are severely constrained by SU(5) gauge invariance. We consider the particular case where the explicit $R$-parity breaking occurs only via dimension 2 terms of the superpotential. This model possesses only three R-parity breaking parameters. We have studied the predictions of this model for the neutrino masses and mixing angles at the one-loop level within the framework of a radiatively broken unified supergravity model. We find that this model naturally yields masses and mixing angles that can explain the solar and atmospheric neutrino problems. In addition, there are regions in parameter space where the solution to the solar neutrino puzzle is compatible with either the LSND result or the existence of significant hot dark matter neutrinos.Comment: Revised version as published in Nucl. Phys. B; several typos correcte

On the fine-tuning problem in minimal SO(10) SUSY-GUT

In grand unified theories (GUT) based on SO(10) all fermions of one generation are embedded in a single representation. As a result, the top quark, the bottom quark, and the $\tau$ lepton have a universal Yukawa coupling at the GUT scale. This implies a very large ratio of Higgs vacuum expectation values, \tanb \simeq m_t/m_b. We analyze the naturalness of such a scenario quantitatively including all the relevant radiative corrections and find that in minimal unified supergravity models with universal soft supersymmetry breaking parameters at the GUT scale, the necessary amount of fine-tuning needed is excessive. GUT threshold correction to the universal Higgs mass parameter can significantly reduce the fine-tuning required for such large values of \tanb. We also point out that the top quark mass can play a crucial role in explaining the hierarchy between the SUSY breaking scale and the electro-weak scale and, hence, the naturalness of large values of \tanb.Comment: 20 pages, 10 figs, uses PHYZZX version to be published in Phys Rev.

Approximating the radiatively corrected Higgs mass in the Minimal Supersymmetric Model

To obtain the most accurate predictions for the Higgs masses in the minimal supersymmetric model (MSSM), one should compute the full set of one-loop radiative corrections, resum the large logarithms to all orders, and add the dominant two-loop effects. A complete computation following this procedure yields a complex set of formulae which must be analyzed numerically. We discuss a very simple approximation scheme which includes the most important terms from each of the three components mentioned above. We estimate that the Higgs masses computed using our scheme lie within 2 GeV of their theoretically predicted values over a very large fraction of MSSM parameter space.Comment: 31 pages, 10 embedded figures, latex with psfig.sty the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp95-09/ttp95-09.ps or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

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