Vanishing corrections on the intermediate scale and implications for unification of forces.pdf

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Vanishing corrections on the intermediate scale and implications for unification of forces.pdf

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Vanishing corrections on the intermediate scale and implications for unification of forces

a r X i v : h e p - p h / 9 7 1 0 2 4 6 v 1 5 O c t 1 9 9 7 VANISHING CORRECTIONS ON INTERMEDIATE SCALE AND IMPLICATIONS FOR UNIFICATION OF FORCES M.K.Parida High Energy Physics Group International Center for Theoretical Physics I-34100 Trieste,Italy and Physics Department North–Eastern Hill University P.O.Box 21, Laitumkhrah, Shillong 793 003 India (March 19, 1996) Abstract In two–step breaking of a class of grand unified theories including SO(10), we prove a theorem showing that the scale (MI) where the Pati–Salam gauge symmetry with parity breaks down to the standard gauge group, has vanish- ing corrections due to all sources emerging from higher scales (μ MI) such as the one–loop and all higher–loop effects, the GUT–threshold, gravitational smearing, and string threshold effects. Implications of such a scale for the unification of gauge couplings with small Majorana neutrino masses are dis- cussed. In string inspired SO(10), we show that MI ? 5× 10 12 GeV, needed for neutrino masses, with the GUT scale MU ? Mstr can be realized provided certain particle states in the predicted spectrum are light. 12.10.Dm, 12.60.Jv Typeset using REVTEX 1 I. INTRODUCTION Grand unified theories based upon SUSY SU(5), SO(10), nonSUSY SO(10) with inter- mediate symmetries, and those inspired by superstrings have been the subject of considerable interest over recent years. In order to solve the strong CP problem through Peccei–Quinn mechanism and achieve small neutrino masses [1] necessary to understand the solar neutrino flux [2] and/or the dark matter of the universe, an intermediate scale seems to be essential [3]. Such a scale might correspond to the spontaneous breaking of gauged B–L contained in intermediate gauge symmetries like SU(2)L × SU(2)R × U(1)B?L × SU(3)C(≡ G2213) and SU(2)L × SU(2)R × SU(4)C (≡ G224) with [3-6] or without [7] parity, or even others like SU(2)L × U(1)I3R × SU(4)C and SU(2)L × U(1)I3R × U(1)B?L × SU(3)C . But it is well known that the predictions