jeudi 31 juillet 2014

How many scalars for a quantum ladder to climb up the top of the Planck column ?

Dilaton, inflaton, majoron and darkon: the four Horsemen of the grand unification?

If cosmological inflation is due to a slowly rolling single inflation field taking trans-Planckian values as suggested by the BICEP2 measurement of primordial tensor modes in CMB, embedding inflation into the Standard Model challenges standard paradigm of effective field theories. Together with an apparent absence of Planck scale contributions to the Higgs mass and to the cosmological constant, BICEP2 provides further experimental evidence for the absence of large MPlanck induced operators. We show that classical scale invariance – the paradigm that all fundamental scales in Nature are induced by quantum effects – solves the problem and allows for a remarkably simple scale-free Standard Model extension with [two real singlet scalar fields φ and η and three heavy singlet right-handed neutrinos]... without extending the gauge group. Due to trans-Planckian inflaton values and vevs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio r in a large range, converging around the prediction of chaotic m²φ² inflation for a large trans-Planckian value of the inflaton vev. Precise determination of r in future experiments will single out a unique scale-free inflation potential, allowing to test the proposed field-theoretic framework. 
Embedding inflation into the Standard Model - more evidence for classical scale invariance, Kristjan Kannike, Antonio Racioppi, Martti Raidal (Submitted on 15 May 2014)

We propose that inflation and dark matter have a common origin, connected to the neutrino mass generation scheme. As a model we consider spontaneous breaking of global lepton number within the seesaw mechanism. We show that it provides an acceptable inflationary scenario consistent with the recent CMB B-mode observation by the BICEP2 experiment. The scheme may also account for the baryon asymmetry of the Universe through leptogenesis for reasonable parameter choices.
... Here we consider the simplest type-I seesaw scenario... of neutrino mass generation in which lepton number is promoted to a spontaneously broken symmetry, within the standard SU(3)c⊗SU(2)L⊗U(1)Y gauge framework... In order to consistently formu- late the spontaneous violation of lepton number within the SU(3)c⊗SU(2)L⊗U(1)Y model, one requires the presence of a lepton-number-carrying complex scalar singlet, σ, coupled to the singlet “right-handed” neutrinos νR. The real part of σ drives inflation through a Higgs potential... while the imaginary part, which is the associated Nambu-Goldstone boson, is assumed to pick up a mass due to the presence of small explicit soft lepton number violation terms in the scalar potential, whose origin we need not specify at this stage. For suitable masses such a majoron can account for the dark matter..., consistent with the CMB observations... 
(Submitted on 11 Apr 2014)

We revisit a single field inflationary model based on Coleman-Weinberg potentials. We show that in small field Coleman-Weinberg inflation, the observed amplitude of perturbations needs an extremely small quartic coupling of the inflaton, which might be a signature of radiative origin. However, the spectral index obtained in a standard cosmological scenario turns out to be outside the 2σ region of the Planck data. When a non-standard cosmological framework is invoked, such as brane-world cosmology in the Randall-Sundrum model, the spectral index can be made consistent with Planck data within 1σ, courtesy of the modification in the evolution of the Hubble parameter in such a scheme. We also show that the required inflaton quartic coupling as well as a phenomenologically viable B-L symmetry breaking together with a natural electroweak symmetry breaking can arise dynamically in a generalized B-L extension of the Standard Model where the full potential is assumed to vanish at a high scale.
Gabriela Barenboim, Eung Jin Chun, Hyun Min Lee (last revised 23 Jan 2014 (this version, v2))

mercredi 30 juillet 2014

A simple route far beyond the Cape of Grand Unification

... with just the Higgs compass...

We have studied the SM in its full perturbative validity range up to the Landau pole, assuming that the gravity does not significantly affect the SM predictions at energies above the Planck scale. The SM without gravity can be regarded as a consistent quantum field theory all the way between ΛQCD and the UV Landau pole of the U(1)Y gauge coupling. However, when viewed in isolation from any potential new physics, as we have assumed in this work, the SM suffers from a false vacuum problem at the EW scale, which is caused by the negative Higgs quartic coupling at an intermediate energy scale. We have proposed the most minimal extension of the SM by one complex singlet field that solves the wrong vacuum problem, generates EWSB dynamically via dimensional transmutation, provides the correct amount of DM, and is a candidate for the inflaton. Compared to previous such attempts to formulate the new SM, ours has less parameters as well as less new dynamical degrees of freedom. 
In this framework the false SM vacuum is avoided due to the modification of the SM Higgs boson quartic coupling RGE by the singlet couplings. The electroweak scale can be generated from a classically scale invariant Lagrangian through dimensional transmutation in the scalar sector, by letting the quartic coupling of the CP-even scalar run negative close to the EW scale. The VEV of this scalar then induces the standard model Higgs VEV through a portal coupling. We studied the perturbative validity range of this model and found that the scalar quartic Landau pole appears below the SM U(1)Y Landau pole. This happens because we demand EWSB to happen via dimensional transmutation. If more than one singlet is added to the model, this constraint can be avoided. Because dimensional transmutation depends only logarithmically on the energy scale, large hierarchies can be accommodated in our model.

...and a fair amount of fine-tuning?

Thus, obtaining the right EW scale form the high scale Landau pole is technically natural in our framework provided that the couplings have the right numerical values. Needless to say, we do not have any prediction why the fundamental Yukawa and scalar self-couplings must have the needed values. In order for our model to work, some of the scalar couplings at the EW scale have to be as small as 10−4 to provide the correct EW scale. We here simply remind the reader that couplings of this order are already present in the SM in the form of Yukawa couplings. Anthropic selection might be a possibility to explain the smallness of those couplings, if a suitable measure on the space of couplings can be defined. For a recent discussion of fine-tuning in a similar model framework we refer the reader to [42].  
The model also naturally provides a DM candidate in the form of the CP-odd scalar that is stable due to the CP-invariance of the scalar potential. We demonstrated that this model allows the DM particle to be produced with the correct relic density while fulfilling all experimental constraints on Higgs boson and DM phenomenology. Detecting the DM directly at colliders is very challenging due to the small mixing between the Higgs dou- blet and the singlet. However, this framework is potentially testable in the planned DM direct detection experiments.  
We also demonstrated that inflation can be accommodated in this model without introducing additional degrees of freedom. In this case the scalar couplings must be very finely tuned. Our framework does not differ from generic large scale inflation models in that respect 

 A first shot in the unknown, waiting for more tools...  
Our SM model extension does not provide a complete solution to the known open questions in particle physics. Obviously, there is no model of gravity in our framework that could support our initial assumptions and explain the observed cosmological constant value. We simply assume that the presently unknown UV theory of gravity does not spoil our assumptions. Recent theoretical developments may support this view on gravity. The baryon asymmetry of the universe also requires additional dynamics, which we do not discuss. Leptogenesis remains the favourite candidate mechanism and can easily be incorporated in our framework together with neutrino masses. In the context of particle physics, the strong CP problem remains unexplained, and likely requires additional degrees of freedom to be added to this minimal model. Clearly our results and conclusions remain valid under the assumption that these new degrees of freedom somehow decouple from the relevant degrees of freedoms that contribute to our scalar sector. 
Finally we want to remark that even if the Planck scale is indeed a physical cutoff for the validity of the Standard Model, our conclusions remain mostly valid. The extra scalars would still avert the metastability problem of the EW vacuum, and the low energy phenomenology of the model, including the dynamical generation of the EW scale and the DM model, remains intact. If our framework turns out to be the right approach for extending the validity of the SM above the Planck scale, there are concrete predictions of our model that could be tested by future DM and collider experiments.

mardi 29 juillet 2014

What does Dark matter look like in non-susy SO(10) models?

A theoretical answer: a scalar 16 

The existence of Dark Matter (DM) of the Universe is now established without doubt [1]. However, the fundamental physics behind it is unknown at present. In the most popular new physics scenario containing DM – supersymmetry – discrete R-parity is imposed by hand to prevent phenomenological disasters such as fast proton decay [2]. Similarly, in dedicated DM extensions of the standard model (SM) with new singlet [3], doublet [4] or higher multiplet scalars [5], ad hoc Z2 symmetry must be added to ensure the stability of DM. These phenomenological models cannot answer the two most fundamental questions related to DM: (i) why this particular multiplet or particle constitutes the DM of the Universe?; (ii) what is the origin of the imposed Z2 symmetry? Therefore the underlying physics principles related to the existence of DM remain obscured. In this work we argue that the existence of DM of the Universe can be a consequence of Grand Unification (GUT). The GUT framework not only explains the origin of DM but also determines the type of the DM particle and constrains its properties. In this scenario the existence of DM, non-zero neutrino masses via seesaw [6] and baryon asymmetry of the Universe via leptogenesis [7] all point to the same GUT framework. We show that the Z2 symmetry needed for DM stability could be a discrete remnant of GUT symmetry group, such as SO(10) [8] that we choose to work with in the following. When breaking SO(10) down to the SM gauge group SU(2)L×U(1)Y, the SO(10) embedded U(1)X, where X is orthogonal to the SM hypercharge Y, leaves unbroken Z2 [9, 10]
PX = PM = (−1)3(B−L), (1)
which is the well known matter parity PM. Due to its gauge origin PM is a symmetry of any SM extension including non-SUSY ones. In the latter case group theory predicts uniquely, without any detailed model building, that the only possible Z2-odd multiplet under Eq. (1) is the 16 of SO(10) [11]. As inclusion of the fourth fermion generation 164 to the SM is not supported by experimental data, the non-SUSY SO(10) GUT predicts that the DM is a mixture of SU(2)L×U(1)Y  PM-odd complex scalar singlet S and neutral component of doublet H2 belonging to a new scalar 16 of SO(10). Thus the DM of the Universe corresponds to the scalar analogues of the fermionic neutral matter fields, the right-handed neutrino NR and the left-handed neutrino νL, respectively. Preserving PM requires SO(10) breaking by an order parameter carrying even charge of B − L [910]. Therefore SO(10) breaking also generates heavy Majorana masses which induce the seesaw mechanism as well as leptogenesis. 
To test the proposed DM scenario we study the scalar potential of a minimal SO(10) GUT model containing one scalar 16 for the DM and one scalar 10 for the SM Higgs double...

 DM direct detection cross-section per nucleon vs. MDM. Color shows SM Higgs masses from 115 GeV (red) to 170 GeV (violet). The points shown encompass the whole parameter space allowed by theoretical and experimental constraints. [Since 2009 all the region above Xenon100 has been excluded, see next paragraph]
The direct DM interaction with nuclei occurs via the SM Higgs boson exchange...  If MDM<∼300 GeV, cancellation between different terms in [the DM-Higgs effective coupling] is possible and the spin independent direct detection cross section can be accidentally small, cf. Fig [above]
Based on SO(10) GUT, we have presented a minimal DM model, calculated the full set of its RGEs and studied its predictions. We find that the EWSB occurs radiatively due to SM Higgs boson couplings to the DM, analogously to SUSY models. The thermal relic DM mass is predicted to be MDM<∼O(0.1−1) TeV by the requirement of perturbativity of model parameters up to the GUT scale.
(last revised 14 Dec 2009 (this version, v3))

A phenomenological comment

The red line is the previous best limit from Xenon100. The blue line is the current 90% CL limit from LUX, which puts them at the pole position in the entire mass range above GeV. They are the first to break the 10^-45 cm^2 cross section barrier: the limit goes down to 7.6*10^-46 cm^2 for dark matter mass of 33 GeV. To put it into perspective, the LHC can currently study processes with a cross section down to 10^-39 cm^2 (1 femtobarn). The inlay shows the low mass region where positive signals were claimed by CDMS-Si (green), CoGeNT (orange), CRESST (yellow) and DAMA (grey). All of these regions are now comfortably excluded, at least in the context of simple models of dark matter.

So, the light dark matter signal that has been hanging around for several years is basically dead now. Of course, theorists will try to reconcile the existing positive and negative results, just because it's their job. For example, by playing with the relative couplings of dark matter to protons and neutrons one can cook up xenophobic models where dark matter couples much more strongly to silicon and germanium than to xenon. But seriously, there's now little reason to believe that we are on the verge of a discovery. Next time, maybe.
Fiat LUX, Jester, 30 October 2013

More about the race to detect DM wimps here.

More about scalar dark matter model building
Contrary to what Jester says half kidding, theorists can make their job to escape the direct phenomenological constraints in a little less opportunistic way than just building xenophobic models, but in extending the philosophy developed in the former paragraph in a recent article from 2014 for instance which reads in its conclusion:

We have explored the phenomenology of an inert doublet and complex scalar dark matter model stabilized by ZN symmetries, with explicit investigation of the Z3 and Z4 cases. The new feature of these models as compared to the Z2 case is the possibility of semi-annihilation and dark matter conversion. This has important consequences for all dark matter observables.
In the Z3 model, semi-annihilation processes, e.g. x1x1 → x1h, can give the dominant contribution to the relic abundance through the cubic (µ00 SS3) or quartic (λS12S2H† 1H2) terms in the scalar potential. This means that the λS1 parameter which sets the coupling of DM to the Higgs and thus the direct detection cross section is not uniquely determined by the relic density constraint as occurs in the Z2 model. Large semi-annihilation is therefore associated with suppressed direct detection rate. While the bulk of the points will be testable by ton-scale detectors, it is possible to satisfy the constraints from vacuum stability and globality of the minimum of the potential with very small values of λS1 – hence to escape all future searches, in particular when the DM is near the TeV range. The direct detection limits from LUX almost completely rule out the region where dark matter masses are below 120 GeV since for kinematic reasons the semi-annihilation does not play an important rôle (the Higgs cannot be produced in the final state)... Furthermore we have shown that the model can be perturbative up to the GUT scale even with a large fraction of semi-annihilation. Enlarging the symmetry to Z4 entails two dark sectors, hence two dark matter candidates: a singlet and a doublet. In this case both semi-annihilation and dark matter conversion significantly affects the dark matter phenomenology of the model. While this model shares many characteristics of the inert doublet model especially when interactions between the two dark sectors can be ignored, the presence of the singlet dark matter candidate means that the doublet DM could only contribute to a fraction of the relic density (and vice versa). This means in particular that the doublet DM can have any mass instead of being confined to be at the electroweak scale or heavier than 500 GeV as in the inert doublet model. We found that for the sub-dominant dark matter component, it is possible to have a detectable signal in future direct detection experiments even after taking into account the fraction of each component in the DM density. This occurs in particular when the sub-dominant component is the doublet since it typically has a large direct detection rate. Furthermore in some cases a detectable signal in future ton-scale experiments is predicted for each DM component, opening up the exciting possibility of discovering two DM particles.
(Submitted on 19 Mar 2014)


lundi 28 juillet 2014

Brainwashed by Pythagoras and Descartes?

Are extra metric dimensions really an illusion coming from Pythagoras theorem?
The idea to write this post comes from the following sentence :
Illusion of extra-dimension come from Pythagoras theorem, which is a particular case of Pythagoras-1.
 Pierre Martinetti, (The standard model from the metric point of view: how noncommutative geometry provides extra-dimensions from Pythagoras theorem)
This sentence is extracted from the following slide...

and has to be associated with this other slide...

P. Martinetti, May 2008

... where the mysterious Pythagoras-1 mentioned in the last sentence of the first slide refers in fact to a formula from noncommutative geometry, the mathematical framework envisioned by Alain Connes where a Riemannian-like line element is the inverse of a generalized Dirac Operator D.  In this context a simple relation between three squared Dirac operators ∂, DI and D - defined respectively on a continuous 4D space, a discrete 0-dimensional one and the noncommutative tensor product of both - appears naturally as an "inverse Pythagorean equality" (third line of the first slide). This kind of relation has been first discussed by Connes here (in French) and more informally in a post there. It was extended in another article by F. d'Andrea and P. Martinetti in 2012.

Is the Higgs doublet the fifth column which undermines the Descartes commutative geometry?
To get a full understanding of the claim presented above one has to read an older article by Martinetti and Wulkenhaar which reads in part:
In the noncommutative approach to the standard model of elementary particles [10], spacetime appears as the product (in the sense of fibre bundles) of a continuous manifold by a discrete space... within the framework of noncommutative geometry, we investigate how the distance in the continuum evolves when the space-time of euclidean general relativity is tensorised by an internal space. We find that in many cases the relevant picture is the two sheets model [8]... Indeed, under precise conditions, the metric aspect of ”continuum × discrete” spaces reduces to the simple picture of two copies of the manifold. It was known [11,5] that the distance on each copy is the geodesic distance while the distance between the copies – the distance on the fibre – is a constant. But this does not give a complete description of the geometry, in particular the distance between different points on different copies. In this paper we show that this distance coincides with the geodesic distance within a (4+1)-dimensional manifold whose fifth component comes from the internal part of the geometry. This component is a constant in the simplest cases and becomes a function of the manifold when the metric fluctuates. Restricting ourselves to scalar fluctuations of the metric, which correspond to the Higgs sector in the standard model, it appears that the Higgs field describes the internal part of the metric in terms of a discrete Kaluza-Klein model...
The finite part of the geometry of the standard model with scalar fluctuations of the metric consists of a two-sheets model labelled by the single states of C and H. Each of the sheets is a copy of the Riemannian four-dimensional space-time endowed with its metric. The fifth component of the metric, corresponding to the discrete dimension, is

where (h1,h2) is the Higgs doublet and mt the mass of the quark top... 
Noncommutative geometry intrinsically links the Higgs field with the metric structure of space-time. We have not considered the gauge field Aµ so it is not clear whether or not the interpretation of the Higgs as an extra metric component has a direct physical meaning. It is important to study the influence of the gauge fluctuation and, particularly, how it probably makes the metric of the strong interaction part finite.
P. Martinetti, R. Wulkenhaar (last revised 17 Apr 2001 (this version, v2))

Replacing the Pythagorean knotted rope by a spin-half fermionic Dirac propagator for the quantum surveyor
Let us now recap the information already gained on the notion of dimension in a generalized spacetime viewed as a "product" of a continuous and a discrete space with the abstract distance concept forged by Connes in his real spectral triple paradigm:
  • Notion of dimension is subtle: from the distance point of view, illusion of extra-dimension, that comes from the line elements satisfying Pythagore relation.
  • But the metric dimension (defined as the rate of decrease of the eigenvalues of D) is still m=dim M.
  • Still another dimension (KO dimension), important for massive neutrinos (see Chamseddine, Connes, Marcolli and Barrett)
P. Martinetti, May 2008

Of course, no disrespect is implied by the title of the post. It is a pale remake of the title of an informative article by Z. K. Silagadze "Brainwashed by Newton" which was already a remake by Anderson’s famous article ”Brainwashed by Feynman?” (do not miss Feynman Brainwashed? either by Nathan Isgur ;-)

vendredi 25 juillet 2014

Looking for a proper reference frame to navigate in an ambiguous quantum flow

A metaphor
Infinities of perturbative quantum field theories are blessing stars in the dark sky of the renormalizable physical world for the noncommutative navigator drawing a cosmic map from the miraculous catches of the spectral physicist fishing now in the roaring "Tera eVs". 

An explanation
We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain “ motivic Galois group” U∗, which is uniquely determined and universal with respect to the set of physical theories. The renormalization group can be identified canonically with a one parameter subgroup of U∗. The group U∗ arises through a Riemann–Hilbert correspondence. Its representations classify equisingular flat vector bundles, where the equisingularity condition is a geometric formulation of the fact that in quantum field theory the counterterms are independent of the choice of a unit of mass. As an algebraic group scheme, U∗ is a semi-direct product by the multiplicative group Gm of a pro-unipotent group scheme whose Lie algebra is freely generated by one generator in each positive integer degree. There is a universal singular frame in which all divergences disappear. When computed as iterated integrals, its coefficients are certain rational numbers that appear in the local index formula of Connes–Moscovici [12] ... 
The natural appearance of the “motivic Galois group” U∗ in the context of renormalization confirms a suggestion made by Cartier in [4], that in the Connes–Kreimer theory of perturbative renormalization one should find a hidden “cosmic Galois group” closely related in structure to the Grothendieck–Teichmüller group. The question of relations between the work of Connes–Kreimer, motivic Galois theory, and deformation quantization was further emphasized by Kontsevich in [16]. At the level of the Hopf algebra of rooted trees, relations between renormalization and motivic Galois theory were also investigated by Goncharov in [15]. The “motivic Galois group” U acts on the set of dimensionless coupling constants of physical theories, through the map of the corresponding group G to formal diffeomorphisms constructed in [10]. This also realizes the hope formulated in [6] of relating concretely the renormalization group to a Galois group... 
These facts altogether indicate that the divergences of Quantum Field Theory, far from just being an unwanted nuisance, are a clear sign of the presence of totally unexpected symmetries of geometric origin. This shows, in particular, that one should understand how the universal singular frame “renormalizes” the geometry of space-time using the Dim-Reg scheme and the universal counterterms
Alain Connes, Matilde Marcolli (Submitted on 17 Sep 2004)
A vision
Let us immerse once more in the last 23.16 minutes of this conference:
KITP Program: Mathematical Structures in String Theory
Alain Connes, (Nov 17, 2005)

jeudi 24 juillet 2014

What could a hint of non-supersymmetric physics beyond the standard model look like at the LHC?

A putative fluke in an experimental exclusion limit study looking for right-handed bosons arising in the minimal left-right symmetric extension of the Standard Model

 A search for right-handed bosons (WR) and heavy right-handed neutrinos (Nl) in the left-right symmetric extension of the standard model has been presented. The data sample is in agreement with expectations from standard model processes in the µµjj final state. An excess is observed in the electron channel with a local significance of 2.8σ at Meejj ≈ 2.1 TeV. The excess does not appear to be consistent with expectations from left-right symmetric theory. Considering WR → e Ne and WR → µNµ searches separately, regions in the (MWR, MNl) mass space are excluded at 95% confidence level that extend up to MWR < 3.0 TeV for both channels. Assuming Wregion in the two-dimensional (MWR, MNl) mass plane compared to previous searches, and for the first time this search has excluded MWvalues beyond the theoretical lower mass limit of MWR > 2.5 TeV.

... turning into a speculative smoking-gun for a left-right symmetry model with a spontaneous D-parity breaking motivated by a non-SUSY SO(10) with a Pati-Salam subgroup

The CMS analysis compares the experimental result with the theoretically predicted cross section in the minimal left right symmetric model (LRSM) using  gL=gR. In this case, the ee excess cannot be explained by the theoretical prediction since the predicted cross section is too large by a factor of ≈3−4. This discrepancy could be reconciled in our model with a smaller gR. In the following we assume that the excess is due to the production of a WR which decays to a heavy neutrino N that dominantly couples to electrons with a large right-handed current mixing matrix element VNe≤1. We also assume that there is a negligible mixing between the heavy and light neutrinos as well as the left and right W bosons. In this case, both WR and N couple only through right-handed currents and the total cross section of the process under consider where σCMS(pp→eejj) corresponds to the scenario with gL=gR and  VNe=1 as used in the CMS analysis. Instead, using the value derived in the LRSM with spontaneous symmetry breaking and SO(10) unification, the predicted cross section is suppressed by a factor of ≈0.4. This is already sufficient to allow the excess to be interpreted as a signal. In addition, even a small deviation in VNe will lead to a sizable further suppression. This is shown in Fig. 2 where we compare our calculated process cross section with the CMS result.

We have shown that a TeV scale left-right symmetric model can naturally arise via spontaneous D-parity breaking. The asymmetry between the gauge couplings near the electroweak symmetry breaking scale is then a consequence of gauge coupling unification. Assuming that the Pati-Salam symmetry SU(2)L×SU(2)R×SU(4)C is the largest sub-group of a non-supersymmetric SO(10) grand unified theory we obtain gR/gL≈0.6. This gives rise to an extra suppression in the production of WR in proton-proton collisions. As a result we could reconcile our prediction for WR → eejj events at the LHC with the recent 2.8σ excess within the mass range 1.9 TeV < MWR < 2.4 TeV, reported recently by the CMS collaboration. If this result is confirmed by future data, it would be the first direct evidence for physics beyond the standard model from LHC, which will rule out the SU(5) GUT. Moreover, a TeV scale WR would imply B − L violation at the TeV scale (which will also be the first evidence for baryon or lepton number violation), which has strong implication on the generation of baryon asymmetry of the Universe as well as the mechanism of neutrino mass generation. For example, if the excess were to be confirmed for the same sign lepton events, sizable contributions to neutrinoless double beta decay are possible and high scale models of Leptogenesis would be strongly disfavoured [13]. While the excess cannot be considered a significant deviation from the SM as of now, the model we discussed here demonstrates that the excess can be explained in well-motivated extensions of the minimal left-right symmetric model.
Frank F. Deppisch et al, (Submitted on 21 Jul 2014)

... en route to a long march from TeV scale partial unification to YeV scale grand unification?

We embed [our] model in a SO(10) grand unified theory, in which the symmetry breaking pattern goes through the Pati-Salam group G224≡SU(2)L×SU(2)R×SU(4)C  as 
SO(10) → G224D→ G224→ G2213→ G2113→ GSM→ G13 
The symmetry breaking of SO(10) to the SM is achieved by the Higgs multiplets 10H126H, 54H and 210H. However, we have introduced two extra Higgs multiplets 16H and 210H in the renormalization group evolution to achieve the unification of gauge couplings. This is shown in Fig. 1. From the gauge coupling unification, the intermediate mass scales are found to be MB-L=(3−6)TeV, M=10TeV, MC=105-6GeV, MD=109.6GeV and MU=1015.89GeV. The most desirable prediction of the model is that the values of gL and gR at TeV scale, consistent with gauge coupling unification, are given by gL ≈0.632 and gR≈0.367. As a result the ratio of right- and left-handed SU(2) gauge couplings around the TeV scale is found to be gR/gL ≈0.58...  
It is interesting that this particular ratio of the gauge coupling strengths allows us to interpret the excess of events at CMS [3] as the signature of right handed charged gauge boson.

Some reminders...

We cannot exclude the presence of the SM Higgs boson below 127GeV because of a modest excess of events in the region between 115 and 127GeV.
Speaker: Guido Tonelli (13 december 2011)

As one can see in december 2011 the excess of events compatible with a Higgs boson reported by CMS had the same 2.8σ siginificance  as the excess of events compatible with a TeV scale right handed gauge boson reported nowadays! A big difference nevertheless is that ATLAS had seen a similarly significant excess of events in the same mass range for the Higgs boson at the time while - as far as the blogger knows - ATLAS has not (pre)published anything similar to the CMS observation for the right handed boson and its last report in the search for this kind of particle beyond the Standard Model is two-year-old!
A dedicated search for hypothetical heavy Majorana and Dirac neutrinos N, and Wbosons in final states with two high pT same-sign or opposite-sign leptons and hadronic jets has been presented. In a data sample corresponding to an integrated pp luminosity of 2.1 fb-1 at √s = 7 TeV, no signifcant deviations from the SM expectations are observed, and 95% C.L. limits are set on the contributions of new physics. Excluded mass regions for Majorana and Dirac neutrinos are presented for various operators of an effective lagrangian framework and for the LRSM. The latter interpretation was used to extract a lower limit on the mass of the gauge boson WR. For both no-mixing and maximal-mixing scenarios, WR bosons with masses below ≈1.8 TeV (≈ 2.3 TeV) are excluded for mass differences between the WR and N masses larger than 0.3 TeV (0.9 TeV).
ATLAS Collaboration (last revised 20 Jun 2012 (this version, v2))

The blogger thanks Lubos Motl for his report on the subject!

Update 30/07/2014
The search gets more momentum! Check this up:
Recent searches for a first-generation leptoquark by the CMS collaboration have shown around 2.5σ deviations from Standard Model predictions in both the eejj and eνjj channels. Furthermore, the eejj invariant mass distribution has another 2.8σ excess from the CMS right-handed W plus heavy neutrino search. We point out that additional leptoquark production from a heavy coloron decay can provide a good explanation for all three excesses. The coloron has a mass around 2.1 TeV and the leptoquark mass can vary from 550 GeV to 650 GeV. A key prediction of this model is an edge in the total mT distribution of eνjj events at around 2.1 TeV.
Yang Bai, Joshua Berger (Submitted on 16 Jul 2014)

The CMS Collaboration has published two different searches for new physics that contain possible hints for excesses in eejj and eνjj final states. Interpreting those hints as a possible signal of a right handed gauge boson WR with mass 2-2.5 TeV may have profound implications for our understanding of the gauge structure of nature and Grand Unification, the scalar sector accessible at the LHC, neutrino physics, and the baryon asymmetry of the Universe. We show that this interpretation is, indeed, consistent with all existing constraints. However, before making premature claims we propose a number of cross-checks at the LHC14 that could confirm or falsify this scenario. Those include searches for a ZR resonance and the related new scalar sector around 6-7 TeV. Additionally, large effects in top-quark spin-asymmetries in single top production are possible.
Matti Heikinheimo, Martti Raidal, Christian Spethmann (Submitted on 25 Jul 2014)


mercredi 23 juillet 2014

A 40 year-old complex quest looking for a principle of minimality

The past of SO(10) grand unification quest

Blue: number of papers per year with the keyword "SO(10)" in the title as a function of the years. Red: subset of papers with the keyword "supersymmetry" either in the title or in the abstract. (Source: inSPIRE)
By looking at the plot above it is possible to reconstruct the following historical phases:
• 1974 ÷ 1986: Golden age of grand unification. These are the years of the foundation in which the fundamental aspects of the theory are worked out. The first estimate of the proton lifetime yields τp ∼ 1031 yr [37], amazingly close to the experimental bound τp > 1030 yr [38]. Hence the great hope that proton decay is behind the corner. 
• 1987 ÷ 1990: Great depression. Neither proton decay nor magnetic monopoles are observed so far. Emblematically the last workshop on grand unification is held in 1989 [39]. 
•> 1991: SUSY-GUTs. The new data of the Large Electron-Positron collider (LEP) seem to favor low-energy supersymmetry as a candidate for gauge coupling unification. From now on almost all the attention is caught by supersymmetry 
•> 1998: Neutrino revolution. Starting from 1998 experiments begin to show that atmospheric [40] and solar [41] neutrinos change flavor. SO(10) comes back with a rationale for the origin of the sub-eV neutrino mass scale.
•> 2010: LHC era. Has supersymmetry something to do with the electroweak scale? The lack of evidence for supersymmetry at the LHC would undermine SUSY-GUT scenarios. Back to nonsupersymmetric GUTs? 
•> 2019: Next generation of proton decay experiments sensitive to τp∼1034-35yr [42]. The future of grand unification relies heavily on that.
Luca Di Luzio (Submitted on 14 Oct 2011)

A stumbling block for future development
Despite the huge amount of work done so far, the situation does not seem very clear at the moment. Especially from a theoretical point of view no model of grand unification emerged as "the" theory. The reason can be clearly attributed to the lack of experimental evidence on proton decay. 
In such a situation a good guiding principle in order to discriminate among models and eventually falsify them is given by minimality, where minimality deals interchangeably with simplicity, tractability and predictivity. It goes without saying that minimality could have nothing to do with our world, but it is anyway the best we can do at the moment. It is enough to say that if one wants to have under control all the aspects of the theory the degree of complexity of some minimal GUT is already at the edge of the tractability.
Quite surprisingly after 37 years there is still no consensus on which is the minimal theory. Maybe the reason is also that minimality is not a universal and uniquely defined concept, admitting a number of interpretations. For instance it can be understood as a mere simplicity related to the minimum rank of the gauge group... if we stick to the SO(10) case, minimality is closely related to the complexity of the symmetry breaking sector. Usually this is the most challenging and arbitrary aspect of grand unified models. While the SM matter nicely fit in three SO(10) spinorial families, this synthetic feature has no counterpart in the Higgs sector where higher dimensional representations are usually needed in order to spontaneously break the enhanced gauge symmetry down to the SM. Establishing the minimal Higgs content needed for the GUT breaking is a basic question which has been addressed since the early days of the GUT program. Let us stress that the quest for the simplest Higgs sector is driven not only by aesthetic criteria but it is also a phenomenologically relevant issue related to the tractability and the predictivity of the models. Indeed, the details of the symmetry breaking pattern, sometimes overlooked in the phenomenological analysis, give further constraints on the low-energy observables such as the proton decay and the effective SM flavor structure. For instance in order to assess quantitatively the constraints imposed by gauge coupling unification on the mass of the lepto-quarks responsible for proton decay it is crucial to have the scalar spectrum under control. Even in that case some degree of arbitrariness can still persist due to the fact that the spectrum can never be fixed completely but lives on a manifold defined by the vacuum conditions. This also means that if we aim to a falsifiable (predictive) GUT scenario, better we start by considering a minimal Higgs sector.
A possible noncommutative breakthrough with geometric unification
The freedom in the choice of the gauge group and the fermionic representations have led to any attempts to unify all the gauge interactions in one group, and the fermions in one irreducible representation. The most notable among the unification schemes are models based on the SO (10) gauge group and groups containing it such as E6, E7 and E8. The most attractive feature of SO (10) is that all the fermions in one family fit into the 16 spinor representation and the above delicate hypercharge assignments result naturally after the breakdown of symmetry. However, what is gained in the simplicity of the spinor representation and the unification of the three gauge coupling constants into one SO (10) gauge coupling is lost in the complexity of the Higgs sector. To break the SO (10) symmetry into SU(3)c×U(1)em one needs to employ many Higgs fields in representations such as 10, 120, 126 [1]. The arbitrariness in the Higgs sector reduces the predictivity of all these models and introduces many arbitrary parameters, in addition to the unobserved proton decay... 
[The noncommutative geometric] approach predicts a unique fermionic representation of dimension 16 [with gauge couplings unification in a Pati-Salam type model at a high energy somewhere between 6.5×1012−1.4×1017GeV]... The main advantage of our approach over the grand unification approach is that the reduction to the Standard Model gauge group is not due to plethora of Higgs fields [but to a minimal scalar spectrum (the Higgs fields are fixed and belong to the 16 × 16 and 16 × 16bar products with respect to the Pati-Salam group) with a specific dynamics which are outputs from noncommutative geometry axioms and the spectral action principle with the input of the fermion spectrum]... The spectral action is the pure gravitational sector of the noncommutative space. This is similar in spirit to the Kaluza-Klein approach, but with the advantage of having a finite spectrum, and not the infinite tower of states. Thus the noncommutative geometric approach manages to combine the advantages of both grand unification and Kaluza Klein without paying the price of introducing many unwanted states. 
We still have few delicate points which require further understanding... [one] is to determine the number of generations. From the physics point, because of CP violation, we know that we need to take N ≥ 3, but there is no corresponding convincing mathematical principle. 
We would like to stress that the spectral action of the standard model comes out almost uniquely, predicting the number of fermions, their representations and the Higgs breaking mechanisms, with very little input. [It predicts a real singlet scalar field beyond the minimal Standard Model whose large vev sets the scale of right handed Majorana neutrino mass providing a natural see-saw mechanism. This new scalar also gets mixed in a non-trivial way with the Higgs field of the Standard Model so that the renormalization group equations of the combined Higgs-singlet system solves the stabilization problem faced with a light Higgs field of the order of 125 GeV avoiding making the Higgs quartic coupling negative at very high energies. Remarkably, the form of the Higgs-singlet potential derived before from the spectral action [2] agrees with the one proposed recently by different groups [3], [4], [5], [6]. The quartic couplings are determined at unification scale in terms of the gauge and Yukawa couplings. Running these relations down with the scale, give values consistent with the present data for the Higgs and top quark mass]
[+ update adapted from Resilience of the Spectral Standard Model, 2012 

Last editing work on 25th July 2014

samedi 19 juillet 2014

(How) to grow an oasis in the desert (?)

Exploring some potential phenomenology of non-SUSY SO(10) model with Pati-Salam and other symmetries breaking at intermediate scales.

It is well-known that in physics beyond the Standard Model (SM) very often one has to think about the violation of two SM symmetries, Baryon (B) and Lepton (L) numbers, and postulate the existence of a large desert between the low and high scales. It was pointed out by S. Weinberg [1] long time ago that one can write down operators such as, O5=cνLLHH/Λ, and O6=cBLQQQL/Λ², where the first one breaks total lepton number and the second operator violates both symmetries. Typically, one can compute the coefficient in front of these operators in a grand unified theory defined at the high scale. The scale Λ in O6 has to be very large, i.e. Λ>1014−16GeV, in order to satisfy the bounds on the proton decay lifetime. 
Pavel Fileviez Perez (Submitted on 23 Sep 2012)

 Interactions which violate baryon number (B) are not present in the renormalizable part of the SM Lagrangian, but can arise through effective higher dimensional operators... [which] arise naturally when SM is embedded in grand unified theories (GUTs) such as SU(5) and SO(10). They lead to nucleon decay modes such as p→e+π0 and p→νK+, which conserve baryon number minus lepton number (B − L) symmetry. Experimental searches to date have primarily focused on these modes with the latest limits on proton lifetime constraining the masses of the heavy mediators to be larger than about 1015GeV. This is in accord with the scale inferred from the unification of gauge couplings. Going beyond the d = 6 baryon number violating operators, the next–to–leading ones have d = 7, and obey the selection rule ∆(B − L) = −2 for nucleon decay [2]. These operators lead to novel nucleon decay modes such as n→e−K+,e−π+, and p→νπ+, which have received less attention. In this Letter we show that these d = 7 operators arise naturally in unified theories based on SO(10), upon the spontaneous breaking of (B−L), which is part of the gauge symmetry. In particular, we find that in non–supersymmetric SO(10) models with an intermediate scale so that gauge couplings unify, the partial lifetime to these decay modes can be within reach of ongoing and proposed experiments. Furthermore, we show that these new modes provides a novel way to understand the origin of matter in the universe. This mechanism relies on the fact that, owing to their (B − L) breaking nature, a GUT scale induced baryon asymmetry would not be affected by the electroweak sphalerons [3] and would survive down to low temperatures. Observed baryon number of the universe then carries the direct imprint of GUT scale physics. This is unlike the (B −L)–preserving baryon asymmetry induced in the decays of GUT mass particles such as in SU(5), which is however washed out by the sphaleron interactions, leaving no trace of GUT physics. We show that in minimal SO(10) models [4] which have been highly successful in predicting large neutrino oscillation angles, including a relatively large value of sin²(2θ13)≃(0.085−0.095), consistent with recent results [5], the baryon asymmetry of the right magnitude is generated by the new (B−L)–violating mechanism. The results of this paper should provide motivations to search for (B−L)–violating semi-leptonic decay modes of the nucleon in the ongoing and the next round of searches. Their observation would furnish evidence against the simple one–step breaking of GUT symmetry, and could also resolve the mystery behind the origin of matter in the universe.
K. S. Babu, R. N. Mohapatra (Submitted on 24 Jul 2012) 

A detail study of the literatures... gives an idea about many intriguing features of the SO(10) grand unified theory (including both non-SUSY and SUSY). One of these features is that when left-right gauge symmetry appears as an intermediate symmetry breaking step in a novel symmetry breaking chain, then seesaw mechanism can be naturally incorporated into it. In conventional seesaw models associated with thermal leptogenesis the mass scale for heavy Right Handed Majorana neutrino is at 1010GeV which makes it unsuitable for direct detectability at current accelerator experiments like LHC. Therefore, it is necessary to construct a theory having SU(2)L×SU(2)R×U(1)B-L×SU(3)and SU(2)L×SU(2)R×SU(4)C gauge groups as intermediate symmetry breaking steps which results in low mass right-handed Majorana neutrinos along with WR, Z′ gauge bosons at TeV scale. At the same time it should be capable of explaining post-sphaleron baryogenesis elegantly along with other derivable predictions like proton decay and neutron-antineutron oscillation. 
We intend to discuss TeV scale post-sphaleron baryogenesis, neutron-antineutron oscillation having mixing time close to the experimental limit with the Pati-Salam symmetry or SO(10) GUT as mentioned in a recent work [19] slightly modifying the Higgs content where non-zero light neutrino masses can be accommodated via gauged extended inverse seesaw mechanism along with TeV scale WR, Z′ gauge bosons. The Dirac neutrino mass and hence, the corresponding Yukawa coupling (≃ 10-1-10-2) found in this work can be much larger than the Yukawa coupling values (10-6) in the conventional type-I seesaw mechanism with TeV scale RH Majorana neutrinos.
Sudhanwa Patra, Prativa Pritimita (Submitted on 27 May 2014)

 Recent developments in particle physics have had profound impact on cosmology. One of the most far–reaching consequences has been the possibility that new interactions beyond the standard model can explain the origin of matter–antimatter asymmetry of the universe as a dynamical phenomenon. There are currently several attractive scenarios which achieve this, the two most widely discussed ones being (i) baryogenesis via leptogenesis [1], which is connected to the seesaw mechanism and neutrino masses, and (ii) weak scale baryogenesis [2], which involves supersymmetric or multi–Higgs extensions of the standard model. Both these proposals depend crucially on the properties of the electroweak sphaleron [3] which serves as the source of B violation. Since the nature of new physics beyond the standard model remains unknown presently, it is important to explore alternative mechanisms that can explain the matter–antimatter asymmetry while yielding testable consequences. In this letter we suggest and explore one such alternative.

The salient feature of our proposal is that baryogenesis occurs via the direct decay of a scalar boson Sr having a weak scale mass and a high dimensional baryon violating coupling. Sr is the real part of a baryon number carrying complex scalar S, which acquires a vacuum expectation value (vev). The decays Sr → 6q... will then be allowed, providing the source for B asymmetry. These decays occur when the temperature of the universe is T ∼ 0.1 − 100 GeV. By this time the electroweak sphalerons have gone out of thermal equilibrium, and thus play no role in the B asymmetry generation. We call this mechanism “post–sphaleron baryogenesis”. The three Sakharov conditions for successful baryogenesis [4] are satisfied rather easily in our scheme. The high dimensionality of the B violating coupling of Sr to the quark fields allows the ∆B 6= 0 decays to go out of equilibrium at weak scale temperatures. CP violation occurs in the decay via loop diagrams involving the exchange of the standard model W± gauge bosons. This amplitude has sufficient light quark mass  suppression to explain naturally the observed (small) value of the baryon to photon ratio ηB ∼ 10−10. The simplest realization of our mechanism involves interactions that violate B by two units and therefore gives rise to neutron–antineutron oscillations. We find that the successful implementation of our mechanism sets an upper limit on the transition time for N ↔ N¯ oscillation bringing it to within the realm of observability. This connection provides a strong motivation for improved searches for N ↔ N¯ oscillation [5]
Post-Sphaleron Baryogenesis K.S. BabuR.N. MohapatraS. Nasri (last revised 27 Jun 2006 (this version, v2))

vendredi 18 juillet 2014

Out of the mouth of neutrino comes wisdom...

... wisdom of particle physics beyond the standard model 
Decades of experimental and observational scrutiny have revealed less than a handful of phenomena outside the standard model, among them evidence for dark energy and dark matter, and the existence of nonzero neutrino masses... 
Massive neutrinos are special. Among all known fermions, neutrinos are the only ones not charged under the two unbroken gauge symmetries: electromagnetism and color. This implies that, unlike all known particles, neutrinos may be Majorana fermions. Majorana neutrinos would imply, for example, that neutrino masses are a consequence of a new fundamental energy scale in physics, potentially completely unrelated to the electroweak scale. Dirac neutrinos, on the other hand, would imply that U(1)B−L, or some subgroup, is a fundamental symmetry of nature, with deep consequences for our understanding of the laws of physics. If neutrinos are Majorana fermions, lepton number cannot be a conserved quantum number. Conversely, lepton number-violation indicates that massive neutrinos are Majorana fermions. Hence, the best (perhaps only) probes for the hypothesis that neutrinos are Majorana fermions are searches for lepton-number violation. By far, the most sensitive probe of lepton-number conservation is the pursuit of neutrinoless double-beta decay 0νββ 
Neutrinos (authors not shown) submitted on 16 Oct 2013 
... wisdom of the spectral noncommutative paradigm 
... the Kamiokande experiments on solar neutrinos showed around 1998 that, because of neutrino oscillations, one needed a modification of the Standard Model incorporating in the leptonic sector of the model the same type of mixing matrix already present in the quark sector... At first our reaction to this modification of the Standard Model was that it would certainly not fit with the noncommutative geometry framework and hence that the previous agreement with noncommutative geometry was a mere coincidence. After about 8 years it was shown... that the only needed change (besides incorporating a right handed neutrino per generation) was to make a very simple change of sign in the grading for the anti-particle sector of the model... This not only delivered naturally the neutrino mixing, but also gave the see-saw mechanism and settled the above Fermion doubling problem. Besides yielding the Standard Model with neutrino mixing and making testable predictions..., this allowed one to hope that, instead of taking the finite geometry F from experiment, one should in fact be able to derive it from first principles. The main intrinsic reason for crossing by a finite geometry F has to do with the value of the dimension of space-time modulo 8. We would like this KO-dimension to be 2 modulo 8 (or equivalently 10) to define the Fermionic action, since this eliminates the doubling of fermions in the Euclidean framework. In other words the need for crossing by F is to shift the KO-dimension from 4 to 2 (modulo 8).
This suggested to us to classify the simplest possibilities for the finite geometry F of KO-dimension 6 (modulo 8) with the hope that the finite geometry F corresponding to the Standard Model would be one of the simplest and most natural ones. This was finally done recently ([14], [15]).
Ali H. Chamseddine, Alain Connes (Submitted on 5 Aug 2010)
Wisdom of silence
We are now in the very interesting situation that experimental physics may give us deep insights into the internal geometry of space time. If the neutrinoless double beta-decay would be experimentally confirmed, i.e. the electron-neutrino would possess a Majorana mass, one would have to consider one of the... spectral geometries as internal space. This would exclude the case of KO-dimension zero, where Majorana masses may not exist...
Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6, Christoph A. Stephan, October 9th 2006

Neutrinoless double beta decay experiments constrain one combination of neutrino parameters, while cosmic surveys constrain another. This complementarity opens up an exciting range of possibilities. If neutrinos are Majorana particles, and the neutrino masses follow an inverted hierarchy, then the upcoming sets of both experiments will detect signals. The combined constraints will pin down not only the neutrino masses but also constrain one of the Majorana phases. If the hierarchy is normal, then a beta decay detection with the upcoming generation of experiments is unlikely, but cosmic surveys could constrain the sum of the masses to be relatively heavy, thereby producing a lower bound for the neutrinoless double beta decay rate, and therefore an argument for a next generation beta decay experiment. In this case as well, a combination of the phases will be constrained...  In the absence of this lower ... [bound], we will never be guaranteed an answer to the question of whether neutrinos are Majorana or Dirac particles.
Scott Dodelson, Joseph Lykken (Submitted on 20 Mar 2014)

//last edition 30/09/2014

jeudi 17 juillet 2014

(Why) Saving Pati-Salam (?)

Seven empirically driven reasons for a partial (or grand) unification model
The symmetry G(224) = SU(2)L×SU(2)R×SU(4)C... supplemented by Left–Right discrete symmetry which is natural to G(224), brings a host of desirable features. Including some of those mentioned above which served as motivations for grand unification, they are:
(i) Unification of all sixteen members of a family within one left-right self-conjugate multiplet with a neat explanation of their quantum numbers; 
(ii) Quantization of electric charge 
(iii) Qe−/Qp = −1;
(iv) Quark-lepton unification through SU(4)-color; 
(v) Conservation of parity at a fundamental level... (It appears aesthetically attractive to assume that symmetries like Parity (P), Charge Conjugation (C), CP and Time Reversal (T) break only spontaneously like the gauge symmetries. While such a preference a priori is clearly subjective... observations of neutrino oscillations and the likely need for leptogenesis, suggesting the existence of νR’s à la SU(4)-color and SU(2)L× SU(2)R, seem to go well with the notion of exact conservation of parity at a fundamental level); 
(vi) RH neutrino as a compelling member of each family that is now needed for seesaw and leptogenesis;
(vii) B–L as a local symmetry. It has been realized eventually that this is needed to protect νR’s from acquiring Planck scale masses and to set (for reasons noted above) M(νiR) ∝ MB−L ∼ MGUT, both crucial to seesaw and leptogenesis; ...
These... features constitute the hallmark of G(224). Historically, all the ingredients underlying these features, and explicitly (i)–(vii), including the RH ν’s, B–L and SU(4)-color, were introduced into the literature only through the symmetry G(224) [6]; this was well before SO(10) or (even) SU(5) appeared. Any simple or semi-simple group that contains G(224) would of course naturally possess these features. So does therefore SO(10), which is the smallest simple group containing G(224). In fact, all the advantages of SO(10), which distinguish it from SU(5) and are now needed to understand neutrino oscillations as well as baryogenesis via leptogenesis, arise entirely through the symmetry G(224). SO(10) being the smallest extension preserves even the family-multiplet structure of G(224) without needing additional fermion... 
I have... implicitly assumed the existence of an underlying unified theory including gravity—be it string/M theory or something yet unknown—that would describe nature in a predictive manner and explain some of its presently unexplainable features, of the type mentioned above. Such a theory inevitably would operate at very short distances... and very likely in higher dimensions. It then becomes imperative, for reasons stated above, that such a theory, as and when it evolves to be predictive, should lead to an effective grand unification-like symmetry (possessing SU(4)-color) in 4D near the string/GUT-scale, rather than the SM symmetry. If such a symmetry does emerge from the underlying theory as a preferred solution in 4D... it would explain observations in the real world, beyond those encompassed by grand unification.  
The picture depicted above is of course clearly a wish and a goal, yet to be realized. Entertaining such a wish amounts to hoping that the current difficulties of string/M theory as regards the large multiplicity of string vacua... and lack of selectivity... would eventually be overcome possibly through a better understanding and/or formulation of the theory, and most likely through the introduction of some radically new ingredients (Perhaps as radical as Bohr’s quantization rule that selected out a discrete set of orbits from an unstable continuum, which in turn found its proper interpretation within quantum mechanics). Entertaining such a hope no doubt runs counter to the recently evolved view of landscape..., combined with anthropism... Such a hope is nevertheless inspired... by the striking successes we have had over the last 400 years in our attempts at an understanding of nature at a fundamental level. To mention only a few that occurred in the last 100 years, they include first and foremost the insights provided by the two theories of relativity and quantum mechanics. In the present context they include also the successes of the ideas of the standard model, grand unification and inflation. Each of these have aided in varying degrees to our understanding of nature.
Jogesh C. Pati, June 7 2006

Reading more extensively Pati's article, one will notice his emphasis on another symmetry not quoted in this excerpt: SUSY of course! It is important to underline nevertheless that - as far as the blogger can understand - SUSY is important for consistency of string theory and it gives a spectrum compatible with gauge coupling unification but it is not necessary for the part of the Pati's argumentation shown above. 

A spectral noncommutative inspired heuristic incentive for non-SUSY GUTs 
The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and their representations. A strong restriction on the noncommutative space results from the first order condition which came from the requirement that the Dirac operator is a differential operator of order one. Without this restriction, invariance under inner automorphisms requires the inner fluctuations of the Dirac operator to contain a quadratic piece expressed in terms of the linear part. We apply the classification of product noncommutative spaces without the first order condition and show that this leads immediately to a Pati-Salam  SU(2)R×SU(2)L×SU(4)C type model which unifies leptons and quarks in four colors. Besides the gauge fields, there are 16 fermions in the (2,2,4) representation, fundamental Higgs fields in the (2,2,1), (2,1,4) and (1,1,1+15) representations. Depending on the precise form of the initial Dirac operator there are additional Higgs fields which are either composite depending on the fundamental Higgs fields listed above, or are fundamental themselves [in the (2,2,1+15) and (3,1,10) and (1,1,6) representations]. These additional Higgs fields break spontaneously the Pati-Salam symmetries at high energies to those of the Standard Model... 
Remarkably, we note that a very close model to the [case with a generic initial Dirac operator]... is the one considered by Marshak and Mohapatra where the U (1) of the left-right model is identified with the B−L symmetry... Although the broken generators of the SU(4) gauge fields can mediate lepto-quark interactions leading to proton decay, it was shown that in all such types of models with partial unification, the proton is stable. In addition this type of model arises in the first phase of breaking of SO(10) to SU(2)R×SU(2)L×SU(4)C and these have been extensively studied [1].
It remains to minimize the potential to determine all possible minima as well as studying the unified model and check whether it allows for unification of coupling constants gR=gL=g in addition to determining the top quark mass and Higgs mass. Obviously, this model deserves careful analysis, which will be the subject of future work.

One has learnt then that - beyond the Standard Model - only a non-SUSY partial unification scenario with a Pati-Salam model and possibly a Marshak and Mohapatra version of an SO(10) grand unification theory could fit in the noncommutative framework. One can then hope that the spectral paradigm and the almost commutative fine structure of spacetime at the attoscale are good and radical enough ingredients to help to grant the wish and pursue the goal of Pati: building partial or grand unification models which symmetries prove to be preferred solutions in 4D of an underlying theory!