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For a concise review see R. Barloutaud, in TAUP '91, Proceedings of the Second International Workshop on Theoretical and Phenomenological Aspects of Underground Physics, Toledo, Spain, 1991, edited by A. Morales, J. Morales, and J. Villar
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(1992)
Nucl. Phys. B (Proc. Suppl.)
, vol.28 A
, pp. 437
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For a recent review see S. C. C. Ting, in Proceedings of the DPF 92 meeting, Fermilab, Batavia, Illinois, edited by C. Albright, P. H. Kasper, R. Raja, and J. Yoh (World Scientific, Singapore, 1992), Vol. 1, p. 53.
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It is interesting to note that at least the flavor-color sector of the model—i.e., the gauge symmetry G0= SU(2)Ltimes SU(2)Rtimes SU(4)c with six left-chiral and six right-chiral preonic superfields—can be unified within an SO(12) symmetry, where SO(4)times SO(8) sbset SO(12) with SO(4)=SU(2)timesL SU(2)R and SU(4)timesc U(1) sbset SO(8). The twelve preon superfields belonging to 12 of SO(12) transform under SU(2)timesL SU(2)Rtimes SU(4)ctimes U(1) as follows: Φ+a=x,yapp (2,1,1,0), ( Φ-a=x,y)starapp (1,2,1,0), Φ+a=r,y,bl app (1,1,4,1), ( Φ-a=r,y,b,l)starapp (1,1,4star, -1). In other words, these twelve superfields precisely fit the 12 of SO(12).
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While any other input value of αM at MPl/ 10 that is small compared to unity would still yield ΛM<< MPl, as long as N of SU(N) <= 10 (say), ΛM is determined within the model to be about 1011 GeV within a factor of 3 (say) because the model yields mWapp case 1 over 10 ΛM( ΛM/ MPl), which must equal 80 GeV (see Refs. [12,18]).
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These will be considered in a more detailed study with M. Parida.
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The ``effective'' threshold Λ tildeM denoting the transition from the spectrum of unconfined preons to that of the massive composites would, of course, differ from the confinement scale ΛM where α barM is of order 1. Consistent with our neglect of threshold effects, however, we ignore the differences between ΛM and Λ tildeM in this Rapid Communication [19].
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We have checked that small variations of ΛM in the range (1 – 3) times 1011 GeV (see Ref. [16]) and in α3approx (0.11 – 0.12) do not significantly alter this meeting.
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For instance, if we increase the number of preon flavors from the minimal number two to four (say), the number of chiral families must be even and thus at least four, so as to include the three observed families. The number of SU(2)L and likewise SU(2)R-doublet vector families must also be even, and, therefore, there must be at least two of each with a mass approx 1 TeV. Thus there must be at least 4+2+2=8 families and their superpartners contributing to the renormalization group equation in region II. In this case, QCD will become confining at about 107 GeV. Hence the increase from two to four in the number of flavors is simply not permitted. In other words, the preon content of Ref. [12] is not only the minimal choice, but also the maximal allowed one, and in fact the only possibility.
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