lundi 20 octobre 2014

Patience in the noncommutative garden

Patience of a gardener
... the very fact that noncommutative examples are hard to find but nonetheless exist is rather encouraging: it indicates that our set of axioms is just constraining enough to be consistent but not trivial.
(Submitted on 9 Dec 2013 (v1), last revised 24 Dec 2013)

Patience of a bee
The Higgs boson is a spectral flower blooming from the seed of non-commutative spacetime sown in the electroweak field  / Le boson de Higgs est une fleur spectrale qui nait d'une graîne d'espacetemps non commutatif semée dans le champ électrofaible.
a spectral noncommutative geometry enthousiast blogger dreaming of himself as a pollinator ;-)

Patience of a physicist waiting for LHC run 2
Patience, patience,
Patience in the zeptospace,
Each null result
is the chance of a new symmetry!
The glad surprise may come,
A signal, not a statistical fluke,
The faintest track,
A missing energy
could bring hope
When LHC will run again
...
(October 19, 2014)


This comment is loosely based on the penultimate stanza of "Charmes" from the French poet Paul Valéry. It is secretly dedicated to the physicists waiting for SUSY and/or low scale left-right extensions of the Standard Model; to others who could apprehend a nightmare scenario at LHC run 2, I suggest to take comfort in listening the genuine words of the poet :
Ces jours qui te semblent vides
Et perdus pour l’univers
Ont des racines avides
Qui travaillent les déserts
[...]
Patience, patience,
Patience dans l’azur!
Chaque atome de silence
Est la chance d’un fruit mûr!
[...]

Paul Valéry, Charmes (1922)

Time will say if the noncommutative garden stores a harvest of ripe fruits for physicists   

dimanche 19 octobre 2014

Strong CP problem and the spectral noncommutative geometric paradigm

Is the spectral standard model free of the strong CP problem ?
Last week, the twitto/blogo/media-spheres were abuzz over a potential detection of axions from X-ray astrophysics. From axion to the strong CP problem there is essentially a hypothetical dynamical variable coming out from a theta parameter of quantum chromodynamics thus the blogger jumps on this opportunity to have a look on this problem in the spectral noncommutative geometric framework:
The spectral action principle is the simple statement that the physical action is determined by the spectrum of the Dirac operator D. This has now been tested in many interesting models including Superstring theory [6], noncommutative tori [30], Moyal planes [34], 4D-Moyal space [37], manifolds with boundary [12], in the presence of dilatons [10], for supersymmetric models [5] and torsion cases [38]. The additivity of the action forces it to be of the form Trace f(D/Λ). In the approximation where the spectral function f is a cut-off function, the relations given by the spectral action are used as boundary conditions and the couplings are then allowed to run from unification scale to low energy using the renormalization group equations. The equations show, when fitted to the low energy boundary conditions, that the three gauge coupling constants and the Newton constant nearly meet (within few percent) at very high energies, two or three orders from the Planck scale. This might be a coincidence but it can also be an indication that a more fundamental theory exists at unification scale and manifests itself at low scale through integration of the intermediate modes, as in the Wilson understanding of renormalization...
 It is possible to add to the spectral action terms that will violate parity such as the gravitational term εµνρσRµνabRρσab and the non-abelian θ term εµνρσVμνmVρσm. These arise by allowing for the spectral action to include the term Tr(γG(D22)) where G is a [test] function [, Λ a cut-off scale]... and γ=γ5⊗γF is the total grading. In this case it is easy to see that there are no contributions coming from a0 and a2 [the first De Witt–Seeley–Gilkey terms in the asymptotic expansion of the spectral action] and the first new term occurs in a4 where there are only two contributions... Thus the additional terms to the spectral action, up to orders 1/Λ2, are 
(3G0/8π2µνρσ(2g12BµνBρσ - 2g22WμναWρσα) 
where G0 [is the Newton constant]. The BµνBρσ is a surface term, while WμναWρσα is topological, and both violate [CP] invariance. The surprising thing is the vanishing of both the gravitational [CP] violating term εµνρσRµνabRρσab and the θ QCD term εµνρσVμνmVρσm. In this way the θ parameter is naturally zero, and can only be generated by the higher order interactions. The reason behind the vanishing of both terms is that in these two sectors there is a left-right symmetry graded with the matrix γF giving an exact cancellation between the left-handed sectors and the right-handed ones. In other words the trace of γF vanishes and this implies that the index of the full Dirac operator, using the total grading, vanishes. There is one more condition to solve the strong CP problem which is to have the following condition on the mass matrices of the up quark and down quark
det ku det kd = real.  
At present, it is not clear what condition must be imposed on the quarks Dirac operator, in order to obtain such relation. If this condition can be imposed naturally, then it will be possible to show that ([49]) θQTQCD=0 at the tree level, and loop corrections can only change this by orders of less than 10-9.
Ali H. Chamseddine (July 15, 2014 Frontiers of Fundamental Physics 14)

Axion free Left-Right symmetric extensions of the standard model
In this letter we show that in left-right symmetric gauge models, that conserve P and T prior to spontaneous symmetry breakdown the problem of strong CP-non-invariance can be solved without the need for axions or massless quarks. First let us notice that the requirement of left-right symmetry of the entire Lagrangian before symmetry breaking implies that there is no strong CP-violation at this level. Subsequent to the symmetry breakdown, the complex mixings between the different quark flavors introduces weak CP-violation into the theory. But if quarks matrices at the tree level satisfy the condition
 (det M(+/-))=(det M(+/-))*                                                   (2) 
where M+(M -) stand for mass matrices for Q=+2/3 (Q=-1/3) quarks, then the unitary matrices that diagonalize the quark mass matrices obviously will not induce θ. As a result, after the diagonalization of the fermion mass matrices, no strong CP-violationg phase is introduced. Thus, at the tree level θ=0 naturally. We then compute the one loop contribution to the mass including the one loop effects continues to satisfy the relation in eqn. (2). As a result, any non-zero contribution to θ can only arise at two or higher loop level, thus providing a natural suppression of strong CP-non-invariance.

dimanche 12 octobre 2014

A tentative noncommutative geometric superconnection approach for beyond Standard Model phenomenology

Superconnection 
...we have investigated the possibility of reviving the superconnection formalism first discussed in 1979 by Ne’eman [4], Fairlie [5, 6], and others [7,8,9]. The original observation of Ne’eman was that the SU(2)L×U(1)Y gauge fields and the Higgs doublet in the SM could be embedded into a single su(2/1) superconnection [10, 11] with the SU(2)L×U(1)Y gauge fields constituting the even part of the superconnection and the Higgs doublet φ constituting the odd part... This embedding predicts sin2 θW = 1/4 as well as the Higgs quartic coupling, the latter leading to a prediction of the Higgs mass [12,13,14]. The leptons and quarks could also be embedded into irreducible representations of su(2/1) [15,16,17,18], thereby fixing their electroweak quantum numbers in a natural fashion. Subsequently, suggestions have been made to incorporate QCD into the formalism by extending the superalgebra to su(5/1) [20,21,22]. Though the appearance of the su(2/1) superconnection suggested an underlying ‘internal’ SU(2/1) supersymmetry, gauging this supersymmetry to obtain the superconnection proved problematic as discussed in Refs. [23, 24]... Due to these, and various other problems, interest in the approach waned. 
(Submitted on 26 Sep 2014)

Noncommutative geometry 
It was subsequently recognized, however, that the appearance of a superconnection does not necessarily require the involvement of the familiar boson↔fermion supersymmetry. This development follows the 1990 paper of Connes and Lott [29] who constructed a new description of the SM using the framework of noncommutative geometry (NCG) in which the Higgs doublet appears as part of the Yang-Mills field (i.e. connection) in a space-time with a modified geometry. The full Yang-Mills field in this approach was described by a superconnection, the off-diagonal elements of which were required to be bosonic. The NGC-superconnection approach to the SM was studied by many authors and a vast literature on the subject exists, e.g. Refs. [3055] to give just a representative list. Though these works differ from each other in detail, the basic premise is the same. The models are all of the Kaluza-Klein type in which the extra dimension is discrete and consists of only two points. In other words, the model spacetime consists of two 3 + 1 dimensional ‘branes.’ In such a setup, the connection must be generalized to connect not just points within each brane, but also to bridge the gap between the two. If the left-handed fermions live on one brane and the right-handed fermions on the other, then the connections within each brane, i.e. the even part of the superconnection, will involve the usual SM gauge fields which couple to fermions of that chirality. In contrast, the connection across the gap, i.e. the odd part of the superconnection, connects fermions of opposite chirality and can be identified with the Higgs doublet. In this approach, both the even and odd parts of the superconnection are bosonic, the Z2-grading of the super- algebra resulting not from fermionic degrees of freedom but from the existence of the two ‘branes’ (on which the chirality γ5 provides the Z2 grading operator), and the definition of the generalized exterior derivative d in the discrete direction. That is, the superconnection emerges from the ‘geometry’ of the discrete extra dimension...  
Id.
A left-right symmetric or a Pati-Salam patch to fix a refuted Higgs mass prediction
The extra-discrete-dimension interpretation of the superconnection model also solves the problem that the prediction sin2θW=1/4 is not stable under renormalization group running and can only be imposed at one scale [64, 65]. That scale can be interpreted as the scale at which the SM with sin2θW=1/4 emerges from the underlying discrete extra dimension model... Given the current experimental knowledge of the SM, this scale turns out to be ∼ 4 TeV [3], suggesting a phenomenology that could potentially be explored at the LHC, as well as the existence of a new fundamental scale of nature at those energies... These developments notwithstanding, a definitive recipe for constructing a NCG Kaluza-Klein model for a given algebra still seems to be in the works. Different authors use different definitions of the exterior derivative d, which, naturally, lead to different Higgs sectors and different predictions. In the Spectral SM of Connes et al. [5963], for instance, the prediction for the U(1)×SU(2)×SU(3) gauge couplings are of the SO(10) GUT type, pushing up the scale of emergence to the GUT scale. The Spectral SM is not particularly predictive either: the fermionic masses and mixings must all be put in by hand into the operator D. Thus, the NCG- superconnection approach still has much to be desired and further development is called for.  
The su(2/1) superconnection also predicts the Higgs quartic coupling at that scale, from which in turn one can predict the Higgs boson mass to be ∼170 GeV. As discussed in Ref. [3], lowering this prediction down to ∼126 GeV requires the introduction of extra scalar degrees of freedom which modify the renormalization group equations (RGE) of the Higgs couplings. Those degrees of freedom would be available, for instance, if the su(2/1) superconnection were extended to su(2/2). The extra-discrete-dimensional su(2/2) model shares the same prediction for sin2θW as the su(2/1) version, and therefore the same scale (∼4 TeV) at which an effective SU(2)L×SU(2)R×U(1)B−L gauge theory can be expected to emerge. Thus, explaining the Higgs mass within the NCG-superconnection formalism seems to demand an extension of the SM gauge group.
Curiously, Connes et al.’s Spectral SM with a GUT emergence scale also predicts the Higgs mass to be ∼170 GeV. Lowering this to ∼126 GeV requires the introduction of extra scalar degrees of freedom as discussed above [62, 63]. See also Refs. [66, 67]. Here too, the Higgs mass seems to suggest that the SM gauge group needs to be extended to SU(2)L×SU(2)R×U(1)B−L, or including the QCD sector, to SU(2)L×SU(2)R×SU(4). 
Thus, the NCG-superconnection formalism already requires the extension of the SM gauge group to that of the left-right symmetric model (LRSM), or that of Pati-Salam... 
Id.
Do only right handed neutrinos know if LHC run 2  will see new gauge bosons?
Based on ... conventional phenomenological analyses, we conclude that the TeV scale LRSM predicted by the su(2/2) superconnection formalism, possibly with an underlying NCG, provides a wealth of new particles and predictions within reach of LHC and other experiments. The fact that the current experimental bounds on the LRSM and the corresponding predictions of the superconnection formalism are suspiciously close may be a sign that LHC is on the brink of discovering something new and exciting. With the center of mass energy of √s = 13 TeV for its second run, the LHC is well capable of observing the new particles of the model among which the most important are the right-handed gauge bosons (W±R, Z0 whose masses are fixed by the formalism and range within the TeV scale. With the scale of 4 TeV, selected by the formalism itself, these masses will be within reach of the LHC, provided that the right handed neutrinos (NR) are light enough to make the corresponding channels accessible [There is nothing in the model which constraints the right-handed neutrinos NR to be light. With NR heavier than W±R , the Drell-Yan interactions will be highly suppressed and thus, although theoretically the TeV scale LRSM could still be viable, it will be very difficult for the LHC to detect its signature through the W±R channels].   
A number of relevant and important observations could be delivered in the lepton flavor violation branch as well, especially in µ→e conversion in nuclei, which we briefly discussed in an earlier section. With the next generation of machines, COMET [166] and Mu2e [167] collaborations target to increase their sensitivity for this process from 10-13 to 10-17, which will significantly improve the limits on new physics including LRSM. Moreover, the next generation of super B factories aim to increase the limit on LFV τ decays to a level of 10-9 [164, 165], which will also provide useful information on the nature of new physics.
Id.

UV/IR mixing : a conjectural quantum (or noncommutative spectral geometry/ field theory and strings) syncretism (?)
... we would like to comment on the observation made in Ref. [168] regarding the violation of decoupling in the Higgs sector, and how this violation may point to the more fundamental possibility of mixing of UV and IR degrees of freedom, given our view that a NCG underlies the Higgs sector. Such UV/IR mixing is known in the simpler context of non-commutative field theory [169a,169b]...
At the moment we are not aware of an explicit UV/IR relation in the context of the NCG of Connes that underlies the superconnection formalism and the new view- point on the SM and the physics beyond it, as advocated in this paper. However, there exists a very specific toy model of non-commutative field theory in which such UV/IR mixing has been explicitly demonstrated. The nice feature of this toy model is that it can be realized in a fundamental short distance theory, such as string theory [169a,169b]The UV/IR mixing, characteristic of this type of non-commutative field theory leads to the question of the existence of the proper continuum limit for non-commutative field theory. This question can be examined from the point of view of non-perturbative Renormalization Group (RG). The proper Wilsonian analysis of this type of non-commutative theory has been done in Ref. [170]. The UV/IR mixing leads to a new kind of the RG flow: a double RG flow, in which one flows from the UV to IR and the IR to the UV and ends up, generically, at a self-dual fixed point. It would be tantalizing if the NCG set- up associated with the SM, and in particular, the LRSM generalization discussed in this paper, would lead to the phenomenon of the UV/IR mixing and the double RG flow with a self-dual fixed point. Finally, we remark that it has been argued in a recent work on quantum gravity and string theory that such UV/IR mixing and the double RG might be a generic feature of quantum gravity coupled to matter [171, 172].  
... we might reasonably expect that the the Higgs scale is mixed with the UV cut-off defined by some more fundamental theory. Needless to say, at the moment this is only an exciting conjecture. 
If this conjecture is true, given the results presented in this paper one could expect that the appearance of the LRSM degrees of freedom (as well as the embedded SM degrees of freedom) at low energy is essentially a direct manifestation of some effective UV/IR mixing, and thus that on one hand the remnants of the UV physics can be expected at a low energy scale of 4 TeV, and conversely that the LRSM structure point to some unique features of the high energy physics of quantum gravity. In this context we recall the observations made in Ref. [69] about the special nature of the Pati-Salam model, which unifies the LRSM with QCD, in certain constructions of string vacua. Even though this observation is mainly based on “groupology” and it is not deeply understood, this observation might be indicative that the Pati-Salam model is the natural completion of the SM, as suggested in this paper, in which the infrared physics associated with the Higgs sector is mixed with the ultraviolet physics of some more fundamental physics, such as string theory.
Id.

lundi 6 octobre 2014

P.Minkowski, P. Ramond, T. Yanagida, G. Senjanovićin and R. Mohapatra will not get the Nobel prize 2014 for the discovery of the see-saw mechanism...

... but may be another day, only right-handed neutrinos know 
A nod to the famous event expected for tomorrow. The  ZapperZ's physics blog informed us that some predictions (based on some computations?*) favor for 2014 a prize for condensed matter physics rather than high energy physics, well this is just a fair return of the pendulum (or see-saw ;-) I guess.
The discovery of neutrino masses and mixings has been an important milestone in the history of particle physics and rightly qualifies as the first evidence for new physics beyond the standard model. The amount of new information on neutrinos already established from various neutrino oscillation searches has provided very strong clues to new symmetries of particles and new directions for unification. Enough puzzles have emerged making this field a hotbed for theory research with implications ranging all the way from supersymmetry and grand unification to cosmology and astrophysics. A major cornerstone for the theory research in this field has been the seesaw mechanism introduced 25 years ago in four independently written papers [1] to understand why neutrino masses are so much smaller than the masses of other fermions of the standard model. Even though there was no solid evidence for neutrino masses then, there were very well motivated extensions of the standard models that led to nonzero masses for neutrinos. It was therefore incumbent on those models that they have a mechanism for understanding why upper limits on neutrino masses known at that time were so small and the seesaw mechanism was introduced in the context of specific such models in the year 1979 e.g. horizontal, left-right and SO(10) models to achieve this goal. A general operator description of small neutrino mass without any specific model was written down the same year [2]. A very minimal non supersymmetric SO(10) model was constructed soon after as an application [3]. It was clear from this early enthusiasm about the idea that if the experimental evidence for neutrino masses ever appeared then, seesaw mechanism would be a major tool in understanding its various ramifications. As we see below, this has indeed turned out to be the case...  
In summary, the seesaw mechanism is by far the simplest and most appealing way to understand neutrino masses. It not only improves the aesthetic appeal of the standard model by restoring quark-lepton symmetry but it also makes weak interactions asymptotically parity conserving. Furthermore it connects neutrino masses with the hypothesis of grand unification.
(Submitted on 24 Dec 2004)

The prediction of small neutrino masses through the Seesaw Mechanism and their subsequent measurement suggests that the natural cut-off of the Standard Model is very high indeed. The recent neutrino data must be interpreted as a reflection of physics at very high energy...  
We are beginning to read the new lepton data, but there is much work to do before a credible theory of flavor is proposed. The Seesaw Mechanism links static neutrino to physics that can never be reached by accelerators, creating a new era of the physics which centers around right-handed neutrinos. With no electroweak quantum numbers, they could hold the key to the flavor puzzles. The second large neutrino mixing angle suggests that hierarchy is independent of electroweak breaking, and occurs at grand-unified scales
I became aware ... of a prescient paper by P. Minkowski, Phys. Lett. B67, 421(1977), in which the seesaw matrix is proposed. It predates our contribution, but is presented in a limited context that does not establish the link to Planck scale physics, the heart of the seesaw mechanism as we know it.
(Submitted on 31 Oct 2004)



(source)


*the predictions failed for the physiology or medicine  prize.

jeudi 2 octobre 2014

Expecting the end of alchemy and astrology in Standard Model extensions

 The Standard Model is sowing the seeds of its own destruction
Because we have forbidden higher dimension operators by hand, the Standard Model has no explicit cutoff dependence. However, if the Higgs self-coupling is too large – corresponding to a physical Higgs boson mass greater than about 180 GeV – then the SM generates its own ultraviolet cutoff ΛLP. This is because λ runs logarithmically with energy scale, and if λ is large enough at the electroweak scale the sign of the effect is to increase λ at higher energies. At some energy scale ΛLP the coupling hits a Landau pole and the electroweak sector of the Standard Model breaks down. If the Higgs self-coupling at the electroweak scale is too small – corre- sponding to a physical Higgs boson mass less than about 130 GeV – then the running goes the other way, and at some high energy scale the sign of this quartic coupling goes negative. At best, this destabilizes the vacuum; at worst, theories with this kind of disease are unphysical. One could attempt to compensate by invoking dimension 6 Higgs self–couplings, but this would violate one of our defining theoretical inputs.
(Submitted on 26 Sep 2006)

The Standard Model is sowing the seeds of its own extension
If a right-handed neutrino exists, the group-theoretic evidence for grand unification is ... compelling: the fermions of each generation transform as the 16-dimensional representation of SO(10) ... and the three gauge groups are unified into one [irreducible representation]. We assume the existence of a right-handed neutrino for the remainder of the discussion. SO(10) has a subgroup SU(3)×SU(2)×U(1)×U(1). When SO(10) is spontaneously broken to SU(3)c×SU(2)L×U(1)Y, the hypercharge subgroup [by definition, the unbroken U(1) subgroup, which does not correspond in general to the usual hypercharge subgroup of the standard model] is a linear combination of the two U(1) subgroups of SO(10). Thus the hypercharges of the fermions are not uniquely determined in SO(10) grand unification ... but rather depend upon which linear combination of the two U(1) subgroups is unbroken. The SU(3)c×SU(2)L×U(1)Y quantum numbers of the left-handed fields which make up the 16-dimensional representation of SO(10) are given in Table 1.

The hypercharge is normalized such that the left-handed positron has unit hypercharge. The parameter a depends upon which linear combination of the two U(1) subgroups is unbroken. It is a rational number because the hypercharges are “quantized”, i.e., commensurate, since a U(1) subgroup of a non-Abelian group is necessarily compact ... [1]. 
The value of the parameter a depends upon the Higgs representation employed to break SO(10) to SU(3)c×SU(2)L×U(1)Y . The Higgs field may be either fundamental or com- posite; only its group-theoretic properties are relevant to the considerations of this pa- per. The candidate values of a for a given irreducible representation correspond to the SU(3)×SU(2)×U(1) singlets contained in that representation [9]. Usually this representa- tion must be accompanied by at least one additional Higgs irreducible representation in order to break SO(10) down to SU(3)×SU(2)×U(1), because the latter is generally not a maximal little group of the former for a single irreducible representation [9]. To generate fermion masses, the SU(2)L×U(1)Y symmetry must be broken by yet one or more additional Higgs irreducible representation, chosen from the 10-, 120-, and 126-dimensional representa- tions (since 16 × 16 = 10 + 120 + 126). The SU(2)L×U(1)Y symmetry is broken to U(1)EM when any of the color-singlet, SU(2) doublets contained in these representations acquires a vacuum-expectation value, leading to the electric charges listed in the last column of Table 1. The standard model evidently corresponds to a = 1/6. 
We have shown by construction that any rational value of a can be obtained by an appro- priate choice of the Higgs irreducible representation. However, a given value of a generally requires a very large Higgs irreducible representation. In practice, the smallest Higgs irre- ducible representations yield only a few values of a ...
It is satisfying that the standard model (a=1/6) is obtained with several small Higgs irreducible representations,6 the 16-, 126-, and 144-dimensional representations, as is well known [11a, 11b]. If we lived in a world in which the ratio of the hypercharges of the quark doublet and the positron were, say, 1/8 rather than 1/6, we could still embed the fermions in the 16-dimensional representation of SO(10), but we would need a 9504-dimensional Higgs representation to obtain the desired symmetry breaking. While there is (perhaps) nothing fundamentally wrong with this, it is less palatable than a model which requires only Higgs fields in low-dimensional irreducible representations ...
We believe that the economy of the Higgs representation in SO(10) grand unification, while well known, has not been fully appreciated. We regard it as further evidence for SO(10) grand unification.
(Submitted on 28 Oct 1997)


mercredi 1 octobre 2014

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. 
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 Qelectron=−Qproton.
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 Qelectron=−Qproton. 
(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,△L0); the other is the Majorana mass of the RH neutrinos (△B=0,△L0), 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.
(Submitted on 23 Nov 1998)

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