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Grand Unification H GRAND UNIFICATION H. Georgi To cite this version: H. Georgi. GRAND UNIFICATION. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-705-C3- 721. 10.1051/jphyscol:1982384. jpa-00221940 HAL Id: jpa-00221940 https://hal.archives-ouvertes.fr/jpa-00221940 Submitted on 1 Jan 1982 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque C3, suppzdrnent au no 12, Tome 43, ddcernbre 1982 page C3-705 GRAND UNIFICATION H. Georgi Department of Physics, Lyman Laboratory of Physics, Harvard University, hl.4 02138, U.S.A. Today I will talk about the progress that has been made in the last year or two in unifying the interactions of physics. The short summary is that there hasn't been any. This is a field which is strangling for want of experimental input. But some things have happened. If we haven't made progress, we have at least learned a thing or two. And who knows, they may turn out to be useful when experiment does finally point us in the right direction. UNIFICATION OF OBSERVED INTERACTIONS Let me begin by briefly discussing the unification of the observed (or almost observed) SU(3) xSU(2) xU(1) gauge interactions. Nothing revolutionary has happened lately,which is not surprising since the main theoretical ideas have been in place for 8 But there has been some evolution in our ideas. The most 2 interesting recent developments have been in the predictions of sin OW and of the 2 proton decay rate. The prediction of sin eW in the simplest SU(5) model has now been refined about as far as it is worth refining it.2 And it agrees perfectly with the data. At this point, improvement in the data would be most welcome. The situation with respect to proton decay is more interesting. On the theoretical side, two things have happened. One is that the experimental deter- mination of A has evolved. As David Politzer will discuss in the next talk, the QCD best (or at least the current favorite) value of A is something like 150 MeV, down a factor of two or more from earlier estimates. The second development is an improvement in the quark model estimates of the strong interaction matrix elements involved in the proton decay process. It has been found3 that the three-quark fusion process, or the pole diagram cannot be ignored. The inclusion of this effect brings the quark model results into agree- ment with results from complementary approaches (such as current algebra). But both the change in A and the extra diagram have the effect of increasing QCD the predicted proton decay rate in any given model. In the simplest SU(5) model, this brings the prediction to the very edge of disagreement with the present experi- mental bound. On the other hand, there are "candidate" nucleon decay events from the Kolar Gold Field and NUSEX group^.^ This is very exciting. Either we will see more soon, or the simplest (and thus one of the most attractive) GUTS will be ruled Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982384 JOURNAL DE PHYSIQUE out. SU(5) VERSUS SO(10) Alas, it doesn't take much of a modification of the simplest GUT to drasti- cally increase the uncertainty in the prediction of the proton decay rate. In SU(5), many more light fermions would increase the lifetime (although one extra family doesn't do,much). After SU(5), the next simplest GUT is based on an SO(10) gauge group. In SU(5), the unification scale is unique, because there is no larger subgroup of SU(5) that contains SU(3) xSU(2) xU(1). But in S0(10), there are many possible routes from the full SO(10) symmetry to SU(3) xSU(2) xU(1). Some of them involve several different scales and many more parameters than in SU(5) (see Table 1). In this theory (or perhaps I should say "set of theories") it is easy to change the proton decay rate prediction by a factor of almost 103 . Let's hope that Nature is Simple. TABLE 1 SO(10) Breakdown Schemes Ref. T -P + SU(3) x SU(2) x U(1) = H + SU(5) + H + SU(5)' x U(l)(anti SU(5)) + H -.SO(6) x SU(2) x U(1) + H There has'also been a development in technical quantum field theory which has potentially extremely important application to GUTS. This is the suggestion by Rubakov and Callan (and the related work by Wilczek) that SU(5) monopoles may catalyze baryon number violating processes with a typical strong interaction cross section.* I say "potentially important" only because I do not fully understand the argument. If it is correct, it is certainly one of the most exciting ideas to come along in some time. THE GRAND MYSTERIES There may be good reasons to embellish the simple SU(5) GUT. Although the SU(3) xSU(2) xU(1) interactions of quarks and leptons fit into SU(5) like the proverbial hand into a (fivc fingered) glove, this unification does little to demystify two old puzzles: hierarchy and flavor. The large scales, the Planck H. Georgi mass % and the grand unification scale MG are so much larger than the small scales Mu, AQCD and quark and lepton masses--the hand is at the end of a very, very long arm. And why is ttgere more than one generation of quarks and leptons? Isn't one hand enough? Some things get less mysterious with time, simply because we get used to them. We have grown accustomed to renormalization, confinement, even income tax laws. But hierarchy and flavor seem more mysterious as time passes, because our attempts to understand them don't seem to lead anywhere. UNIFICATION OF IMAGINED INTERACTIONS Here I will discuss three types of unobserved interactions which, if they exist, might help unravel these puzzles: Technicolor, Supersymmetry and Family Symmetry. All of these subjects go far beyond grand unification, but I will talk only about those aspects which impinge on GUTS and the hierarchy and flavor puzzles. Technicolor and Supersymmetry might address the hierarchy puzzle while Family Symmetry may have something to do with flavor. TECHNICOLOR It is easy to understand why M >>%if the W mass is due to dynamical breaking of the SU(2) xU(1) symmetry. If there is a technicolor (TC) interaction of (as yet unobserved) technifermions. weak at MG, MW may be -eATC/sin8 where ATC is the analog of A for the technicolor intera~tion.~This is automatically exponen- OCD tially small compared to MG. This kind of dynamical mechanism for breaking SU(2)xU(l) almost surely makes sense, because it is based on a simple and direct analogy with chiral symmetry breaking in QCD. It is very simple and elegant. And it requires no fundamental Higgs mesons with masses less than M This is impor- G' cant, because in ordinary quantum field theories, it takes one unnatural finetuning for each Higgs multiplet that must be kept light. The trouble with TC is that by itself, it cannot give quark and lepton masses. There must be other interactions, called extended technicolor, ETC, which couple quarks and leptons to techni- fermions.1° Of course, if TC is embedded in a GUT, there are other interactions. But since these are interactions with particles of mass "M if TC is asymptotically G' free (AF), they don't do much. It would seem that there are four possibilities for implementing ETC: Have spinless bosons with a mass *METC not much larger than A ' (a) TC' (b) Have gauge bosons with a mass -M ETC .' (c) Give up the asymptotic freedom of TC and push up METC; (d) Rely on interactions at MG. It is easy to construct realistic models in (a), but this possibility is very unattractive because it requires fine tunings to keep the spinless bosons light. The most of the motivation for TC is lost. JOURNAL DE PHYSIQUE (b) is the classic ETC idea. It requires no light scalars. It is very ambitious. A successful grand unified ETC scheme would describe all of low energy particle physics in terns of a small number of gauge coupling constants. The problem is that it is hard, and perhaps impossible, to get enough structure. And there are phenomenological difficulties. General arguments (supported by toy examples) suggest that these ETC models will have potentially serious flavor changing neutral current interactions. l1 Not much has happened recently to suggest that these difficulties can be overcome with AF TC. (c) has its roots in Holdom's comment that if the TC theory were a confining phase of a non AF theory with a nontrivial ultraviolet fixed point (UVFP), the %TC scale could be raised and the phenomenological problems with ETC correspondingly allayed.12 But it is still hard to build realistic models. (d) is the suggestion by Glashow and me.that if we could raise M to MG, we wouldn't need ETC in the ETC usual sense at all, but could use the heavy spinless mesons which always appear in GUTS to produce quark and lepton mass.13 Ian MacArthur and I then found a plausible 14 dynamical scheme that could give the right physics.
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