A MINIMAL SO(10) GRAND UNIFIED THEORY

DAVID COLEMAN TERRY, Purdue University

Abstract

We propose a viable SO(10) model which is minimal in the Higgs content, needing only three representations to perform the necessary symmetry breaking and to give the fermions their masses. We show that exactly one 10 and one 126 will produce a phenomenologically acceptable fermion mass spectrum from a general analysis of their Yukawa couplings, and that the initial symmetry breaking at the grand unified mass scale of (TURN) 10('15) GeV may be achieved with one 45 representation. In doing this, we find that the main contribution to the weak SU(2)(,L) symmetry breaking arises from the vacuum expectation value (VEV) given to the 10, rather than the one attributed to the 126, so that the 126 essentially breaks the residual symmetry from the initially broken SO(10) into an approximate QCD-Weinberg-Salam group SU(3)(,C) x SU(2)(,L) x U(1)(,Y). From there, the 10 reduces the remaining symmetry into the observed low-energy group, SU(3)(,C) x U(1)(,Q). We further examine an interesting variant of the standard model: by choosing the 45 and 126 VEVs appropriately, we have the possibility of an intermediate mass scale between 10('2) and 10('15) GeV. Included in the fermion mass matrix are massive neutrinos. We calculate the physical neutrino eigenmasses, and find that of (nu)(,(tau)) perhaps as high as (TURN) .1 eV, just below current experimental thresholds. The resulting neutrino oscillations, which should currently be visible only in solar lengths, are allowed to be quite significant. The fact the (e(--->)e) diagonal flavor-change probability can be lower than 60% offers a solution to the solar neutrino problem: why neutrinos are apparently lost in coming from the sun, yet reactors and accelerators show no hard evidence for neutrino oscillations at this time. Extensive computer modeling is used in support of all predictions for the fermion masses and neutrino oscillations.

Degree

Ph.D.

Subject Area

Particle physics

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