Back to the sources of Grand Unification

The first two guys who wrote down the full gauge structure of the standard model ...
... but did not get the rationality of the quarks electric charges:

Jogesh Pati and Abdus Salam... discovered a very beautiful thing — lepton number as a fourth color, the Pati-Salam SU(4). .. they were the first people to actually write down a model with charge quantization that incorporated the fractionally charged quarks in their beautiful SU(2)×SU(2)×SU(4) model. In fact, ironically, they were the first people to write down the full gauge structure of the standard model, which is contained in SU(2) × SU(2) × SU(4). I say that this is ironic, because having written down the right gauge structure, they proceeded to do something absolutely disgusting to it — they spontaneously broke the color SU(3) and electroweak U(1) down to a subgroup that left the quarks with integral, Han-Nambu charges. I think that Salam had some philosophical problem with fractionally charged quarks. Anyway, this model was a disaster. It was not consistent with the picture of fractionally charged quarks emerging from deep inelastic lepton-hadron scattering experiments. Nevertheless, they stuck to it long after people almost everywhere had gotten used to confinement. Salam used to wear Quark Liberation Front buttons. It is worth noting that Pati and Salam also talk about proton decay, but they were actually talking about the decay of their silly, integrally charged quarks. Their model had no proton decay if color was not broken. Their insistence on breaking the color symmetry was particularly unfortunate because it kept many people from appreciating the beauty of Pati-Salam SU(4)... 

I knew from my adventures in group theory that the algebra of SU(2)× SU(2) is the same as SO(4) and SU(4) is SO(6). So the Pati-Salam SU(2)×SU(2)×SU(4), now that I understood it, immediately suggested SO(10). The nice thing about SO(10) was that I did not have to guess what representation to look at. From my work on anomalies, I knew that the complex spinor representation was the obvious, and in fact only, choice, even though I did not see in detail how it was going to work, just because it was the only complex representation that was plausible. So I wrote down the representation of SO(10) for the 16L... This was tremendously exciting, because I now understood that the reason why we had been having such difficulty in constructing interesting models was that we had not thought of putting quarks and antiquarks into the same representation. In fact, I had not thought of it this time. This is what I like about the story — the group theory had done this for me!... 

Discussions  

Question to Howard Georgi : GUT is very beautiful for the unification of the matter sector, but for the Higgs sector, the unification is incomplete. Due to the incompleteness, there is some fine tuning in some models. What do you think about that? 

Answer from H. Georgi : Well, I haven’t thought about that as much as the people that have made a business of trying to construct GUT models. There are a whole host of issues, the biggest one being may be that you have to make the triplet Higgs very heavy in some way without doing anything too hideous. My feeling there I guess is that there is so much going on in supersymmetry and supersymmetry breaking that I find it difficult to keep up frankly. It has been a few years since I taught a graduate course on supersymmetry, and so I think three new mechanisms for SUSY breaking have been discovered since the last time. I need to do it again. Nothing compelling, as far as I know, has appeared. What one would like is a mechanism that is somehow as unique as the GUT groups themselves are, and so far that hasn’t appeared. 

The Future of Grand Unification

Howard Georgi (December 2006)

The story by one of the two guys himself

The collaborative research of Salam and myself started during my short visit to Trieste in the summer of 1972. At this time, the electroweak SU(2) × U(1)-theory existed [4], but there was no clear idea of the origin of the fundamental strong interaction. The latter was thought to be generated, for example, by the vector bosons (ρ,ω,K∗ and φ), or even the spin-o mesons (π,K,η,η′,σ), assumed to be elementary, or a neutral U(1) vector gluon coupled universally to all the quarks [5]. Even the existence of the SU(3)-color degree of freedom [6, 7] as a global symmetry was not commonly accepted, because many thought that this would require an undue proliferation of elementary entities. And, of course, asymptotic freedom had not yet been discovered. 

In the context of this background, the SU(2)×U(1) theory itself appeared (to us) as grossly incomplete, even in its gauge-sector (not to mention the Higgs sector), because it possessed a set of scattered multiplets, involving quark and lepton fields, with rather peculiar assignment of their weak hypercharge quantum numbers. To remove these shortcomings, we wished: (a) to find a higher symmetry-structure that would organize the scattered multiplets together, and explain the seemingly arbitrary assignment of their weak hypercharges; (b) to provide a rationale for the co-existence of quarks and leptons; further (c) to find a reason for the existence of the weak, electromagnetic as well as strong interactions, by generating the three forces together by a unifying gauge principle; and finally (d) to understand the quantization of electric charge, regardless of the choice of the multiplets, in a way which should also explain why Q_electron=−Q_proton.

We realized that in order to meet these four aesthetic demands, the following rather unconventional ideas would have to be introduced: 

(i) First, one must place quarks and leptons within the same multiplet and gauge the symmetry group of this multiplet to generate simultaneously weak, electromagnetic and strong interactions.... 

(ii) Second, the most attractive manner of placing quarks and leptons in the same multiplet, it appeared to us ... was to assume that quarks do possess the SU(3)-color degree of freedom, and to extend SU(3)-color to the symmetry SU(4)- color, interpreting lepton number as the fourth color. A dynamical unification of quarks and leptons is thus provided by gauging the full symmetry SU(4)-color. The spontaneous breaking of SU(4)-color to SU(3)c×U(1)B−L at a sufficiently high mass-scale, which makes leptoquark gauge bosons superheavy, was then suggested to explain the apparent distinction between quarks and leptons, as regards their response to strong interactions at low energies. Such a distinction should then disappear at appropriately high energies. Within this picture, one had no choice but to view fundamental strong interactions of quarks as having their origin entirely in the octet of gluons associated with the SU(3)-color gauge symmetry In short, as a by-product of our attempts to achieve a higher unification through SU(4)-color, we were led to conclude that low energy electroweak and fundamental strong interactions must be generated by the combined gauge symmetry SU(2)L×U(1)Y×SU(3)C, which now constitutes the symmetry of the standard model... It of course contains the electroweak symmetry SU(2)L×U(1)Y... The idea of the SU(3)-color gauge force became even more compelling with the discovery of asymptotic freedom about nine months later... which explained approximate scaling in deep inelastic ep-scattering, observed at SLAC. 

(iii) Third, it became clear that together with SU(4)-color one must gauge the commuting left-right symmetric gauge structure SU(2)L ×SU(2)R, rather than SU(2)L×U(1)I3R, so that electric charge is quantized. In short the route to higher unification should include minimally the gauge symmetry... G(224) = SU(2)L×SU(2)R ×SU(4)C with respect to which all members of the electron-family fall into... [a] neat pattern... 

Viewed against the background of particle physics of 1972, as mentioned above the symmetry structure G(224) brought some attractive features to particle physics for the first time. They are: 

(i) Organization of all members of a family (8L +8R) within one left-right self-conjugate multiplet, with their peculiar hypercharges fully explained. 

(ii) Quantization of electric charge, explaining why Q_electron=−Q_proton. 

(iii) Quark-lepton unification through SU(4)-color. 

(iv) Left-Right and Particle-Antiparticle Symmetries in the Fundamental Laws: With the left-right symmetric gauge structure SU(2)L×SU(2)R, as opposed to SU(2)L×U(1)Y, it was natural to postulate that at the deepest level nature respects parity and charge conjugation, which are violated only spontaneously [9, 13]. Thus, within the symmetry-structure G(224), quark-lepton distinction and parity violation may be viewed as low-energy phenomena which should disappear at sufficiently high energies. 

(v) Existence of Right-Handed Neutrinos: Within G(224), there must exist the right- handed (RH) neutrino (νR), accompanying the left-handed one (νL), for each family, because νR is the fourth color - partner of the corresponding RH up- quarks. It is also the SU(2)R -doublet partner of the associated RH charged lepton (see eq. (2)). The RH neutrinos seem to be essential now (see later discussions) for understanding the non- vanishing light masses of the neutrinos, as suggested by the recent observations of neutrino-oscillations. 

(vi) B-L as a local Gauge Symmetry: SU(4)-color introduces B-L as a local gauge symmetry. Thus, following the limits from Eötvos experiments, one can argue that B-L must be violated spontaneously. It has been realized, in the light of recent works on electroweak sphaleron effects, that such spontaneous violation of B-L may well be needed to implement baryogenesis via leptogenesis... 

(vii) Proton Decay: The Hall-Mark of Quark-Lepton Unification: We recognized that the spontaneous violation of B-L, mentioned above, is a reflection of a more general feature of non-conservations of baryon and lepton numbers in unified gauge theories, including those going beyond G(224), which group quarks and leptons in the same multiplet... Depending upon the nature of the gauge symmetry and the multiplet- structure, the violations of B and/or L could be either spontaneous 6 , as is the case for the non-conservation of B-L in SU(4) color, and those of B and L in the maximal one-family symmetry like SU(16)...; alternatively, the violations could be explicit, which is what happens for the subgroups of SU(16), like SU(5) ... or SO(10)... One way or another baryon and/or lepton-conservation laws cannot be absolute, in the context of such higher unification. The simplest manifestation of this non-conservation is proton decay (△B≠0,△L≠0); the other is the Majorana mass of the RH neutrinos (△B=0,△L≠0), as is encountered in the context of G(224) or SO(10). An unstable proton thus emerges as the crucial prediction of quark-lepton unification... Its decay rate would of course depend upon more details including the scale of such higher unification.

With Neutrino Masses Revealed, Proton Decay is the Missing Link

J. C. Pati

(Submitted on 23 Nov 1998)

//the second paragraph was added on 8 October 2014.