Elementary Particles and the World of Planck Scale

Grand Unified Theory (GUT)

Although the Standard Model has been very successful in accounting for all experimental phenomena, it is not expected to be the ultimate theory because of its great complexity and the many questions it leaves unanswered. These objections seem to suggest that there may be deeper symmetries underlying the standard model, leading perhaps to the unification of the strong and electroweak interactions into a single "Grand Unified theory", or GUT. Such scheme is indeed possible if the internal rotation group is further generalized to SU(5).

		Similar to the symmetry group of sphere that contains circles as its subgroups, the SU(5) group includes the subgroup SU(3) X SU(2) X U(1). In SU(5) all the elementary particles can be assigned into two 5-multiplets and two 10-multiplets. Figure 15-10a shows one of the 5-multiplets with the 24 gauge bosons assignment arranged into a matrix. Of these, 12 are familiar (the photon, W+, W-, Z0 and 8 gluons). The remaining 12 are new bosons denoted by X; these carry new forces which can transform quarks into leptons and vice versa. The mass of the X bosons have been calculated under the Higgs mechanism, and turns out to be about 1015 Gev. These super-heavy particles lie many orders of magnitude beyond the energy ranges of any conceivable accelerator. However, they would be present in great abundance in the first 10-35 sec after the Big Bang.
Figure 15-10a SU(5) Symmetry [view large image]	Figure 15-10b Grand Unified Theory [view large image]

At energies well above 10¹⁵ Gev, all gauge bosons (including the Xs) can be produced freely and all interactions have the same strength and quarks can transform into leptons as easily as they change colours; and the grand SU(5) symmetry is manifest. At an energy of about 10¹⁵ Gev, the SU(5) symmetry breaks down to separate SU(3) and SU(2)XU(1) symmetries and the grand unified interaction separates into the strong and electroweak interactions. At about 10² Gev, the SU(2)XU(1) symmetry becomes broken, reflecting the separation of electroweak interaction into the distinct weak and electromagnetic interactions. This picture of the unification of interactions also incorporates the variation in the strengths of charges, depending on the distance from which they are acted upon as shown in

Figure 15-10b. The most dramatic consequence of grand unification is that the proton is no longer stable, it has a small probability for decay into neutral pion and a positron (with a half life of about 1032 years) as shown in Figure 15-11. No such decay has been detected so far. Thus after almost 20 years of futile attempts to detect proton decay, physicists now agree that the SU(5) GUT model can be ruled out, but the SO(10) model remains possible, it predicts a longer lifetime. SO(10) is a slightly larger symmetry group with 16-component multiplet. In SO(10) we can create a theory with left-right symmetry including a right-handed neutrino and introduce an "ultra-Higgs" particle

Figure 15-11 Proton Decay [view large image]

in such a way that spontaneous symmetry breaking happens twice - first, the underlying left-right symmetric theory breaks down to SU(3) X SU(2) X U(1), and then a second symmetry breaking happens, exactly as in the basic Standard Model.

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