dimanche 30 août 2015

(A less US-centric ;-) Mapping of the theories of everything

This summer the beautiful Quanta magazine has published online a very nice interactive mapping of candidate Theories of Everything:

Most comments to this work are well deserved dithyrambic with a relevant exception I think:
Adam Smith says:
The idea of the map is nice, but so far it is mostly a map of ideas promoted in the US. When US was the center of science, 20-30 years ago, a US-centric map would have been a good approximation. But now, after the failure of the SSC and of string theory, this is no longer the case.
To please(?) this anonymous commenter here is a personal addendum to the Theory Index:

I hope this may be informative and bring more data into the former index but of course such an addendum is strongly biased by the philosophy of this blog (and its geography as well)! 
I will try another day to make a simple summary for each new index entry.

//addendum December 1 2015

vendredi 28 août 2015

Listening to the little quantum music of the spectral model

... to find a path from general relativity to the standard theory?
I propose below a video of a conference at Institut Henri Poincaré recorded in November 2013. To paraphrase a famous author* one could say that it shows Alain Connes describing his current work on the problem of quantum gravity hoping to overcome the main difficulties with the help of a (some) local(or not) physicist(s**). Of course he does not claim to have a complete grand unified quantum theory. But one thing is certain, few mathematicians have worked as hard as him and have been injected with such a great awe of (flavour***) physics, which in some narrow materialist mind could be viewed as a pure mess in its more awkward forms! 

*The author is Einstein. Here are his words in a letter to Arnold Sommerfeld dated October 29, 1912:
At the moment I am working solely on the problem of gravitation and believe 1 will be able to overcome all difficulties with the help of a local, friendly mathematician. But one thing is certain, that I have never worked so hard in my life, and that I have been injected with a great awe of mathematics, which in my naiveté until now I only viewed as a pure luxury in its subtler forms!'
** I have particularly in mind Ali Chamseddine and Sacha Mukhanov but one should add Walter van Suijlekom and Matilde Marcolli.

We make no apology for this relatively high-brow approach to such an apparently simple matter.
***In the former video Connes explains briefly his geometric interpretation of the CKM matrix which is an important aspect of flavour physics. The interested reader may find below more information from a physicist's point of view:

vendredi 21 août 2015

Do all roads lead to a grand unification scale?

Experimental and phenomenological hints 
I continue my trip to a grand unified view of physics started this summer (see the Grand Loop of Physics). I have chosen to quote today an article that provides a simple summary about numerous experimental and phenomenological interesting facts pointing to the relevance of a grand unification energy scale close but below the Planck one:
What might the cosmological observations and particle physics being telling us ? It is interesting that the dark energy or cosmological constant scale 0.002 eV ... is of the same order that we expect for the light neutrino mass [15, 4649]. Light neutrino mass values ∼ 0.004-0.007eV are extracted from studies of neutrino oscillation data assuming normal hierarchy and values less than about 0.02 eV are obtained with inverted hierarchy [50, 51]. That is, one finds the phenomenological relation 
µvac∼mν∼Λ2ew/M   (10) 
where M∼3×1016 GeV is logarithmically close to the Planck mass MPl and typical of the scale that appears in Grand Unified Theories. There are also theoretical hints that this large mass scale might perhaps be associated with dynamical symmetry breaking, see below. The gauge bosons in the Standard Model which have a mass through the Higgs mechanism are also the gauge bosons which couple to the neutrino. Is this a clue? The non-perturbative structure of chiral gauge theories is not well understood. If taken literally Eq.(10) connects neutrino physics, Higgs phenomenon in electroweak symmetry breaking and dark energy to a new high mass scale which needs to be understood... 

Vacuum stability is very sensitive to the exact values of the Higgs and top-quark masses. For the measured value of mtmH is very close to the smallest value to give a stable vacuum with the vacuum being at the border of stable and metastable. With modest changes in mand mH (increased top mass and/or reduced Higgs mass) the Standard Model vacuum would be unstable [70,71,72,73,74]. If the vacuum is indeed stable up to the Planck mass, perhaps there is some new critical phenomena to be understood in the extreme ultraviolet?

Radiative corrections to the Higgs mass in the ultraviolet are very interesting. The running Higgs mass mH is related to the bare mass m0H through

mH2 = m0H2 − δmH2,    δmH2 = (MPl2/ 16πH2)C1    (16) 
where δmH2 is the mass counterterm and 
C1=6v2(MH2+MZ2+2MW2−4Mt2)=2λ+3/2g′2+9/2g2−12y2t    (17)  
Here v is the Higgs vacuum expectation value, λ is the Higgs self-interaction coupling, g′ and g are the electroweak couplings and yt is the top quark Yukawa coupling. The small value of mH2 relative to MPl2 is the hierarchy problem and connected to discussions [75] of naturalness. Taking the couplings in the formula for C1 to be renormalisation group scale dependent and the measured Higgs and top quark masses, Jegerlehner [74] has argued that Ccrosses zero at a scale ∼1016 GeV, logarithmically close to the Planck mass. He argues that the sign change in the Higgs bare mass squared triggers the Higgs mechanism with a first order phase transition if the Standard Model is understood as the low energy effective theory of some cutoff system residing at the Planck mass [74, 76, 77]. In this scenario the Higgs might act as the inflaton at higher mass scales in a symmetric phase characterised by a very large bare mass term [78, 79]. Note that the Higgs and top quark masses are taken to be time independent in these calculations. Further, the electroweak Higgs contribution to the vacuum energy density − λ/24v4 obeys a similar expression to Eq.(17) and crosses zero at a similar scale about 1016 GeV so the renormalised version of this quantity can be much less than the bare version at scales close to the Planck mass. 
It is interesting that the scale ∼1016 GeV found in this calculation also arises (modulo Yukawa couplings) in the see-saw mechanism for neutrino masses. The scale of inflation is related to the tensor to scalar ratio r in B modes in the cosmic microwave background through Vinflation ∼ (r/0.01)1/41016 GeV [80]. A finite value of r would be evidence of gravitational waves from the inflationary period. If ongoing and future measurements converge on a positive signal in the region 0.001<r<0.1, then this would point to a scale of inflation in the same region close to 1016 GeV.
What suppresses the very large vacuum energy contributions expected from particle physics? Is the accelerating expansion of the Universe really driven by a time independent cosmological constant or by new possibly time dependent dynamics? Experiments will push the high-energy and precision frontiers of subatomic particle physics. Is new physics “around the corner” or might the Standard Model work up to a very large scale, perhaps close to the Planck mass and perhaps hinting at critical new phenomena in the ultraviolet? Understanding the accelerating expansion of the Universe and the cosmological constant vacuum energy puzzle promises to teach us a great deal about the intersection of subatomic physics and dynamical symmetry breaking on the one hand, and gravitation on the other.
(Submitted on 18 Mar 2015)

Let's make the educated wish that the spectral noncommutative geometrization of physics has already taught us enough about the intersection of subatomic physics and dynamical symmetry breaking on the one hand, and gravitation on the other to start to investigate soon more thoroughly the accelerating expansion of the Universe and the cosmological constant vacuum energy puzzle...

Anyway a tentative coherent understanding of a connection between neutrino physics, Higgs phenomenon in electroweak symmetry breaking and dark energy (one can add dark matter as well) to a high mass scale ∼1016 GeV is available to the attentive reader of this blog!

There are more hopes in noncommutative geometry and spectral action, Wimplicio, than are thought of in our present phenomenology

In memoriam Daniel Kastler***, probably the first physicist prophet of noncommutative geometry

Hope(s) encouraged by science retrodiction (and recent progress)?
We feel that non-commutative geometry is as fundamental to physics as Minkowskian and Riemannian geometry. Let us try to explain this by comparing the standard model of particle physics and general relativity. From a chronological point of view, this comparison is difficult, because Riemannian geometry existed well before general relativity. However, the field theoretic approach allows to introduce general relativity in close analogy to classical electrodynamics without use of Riemannian geometry. Therefore this approach is well suited for our comparison. 
So let us imagine a world ignoring Riemannian geometry where physicists try to describe
gravity. They are inspired by Maxwell who takes a field A of spin 1, a second order differential operator DMaxand writes down his field equation

DMax A = (1/c2ε0) j,

where j is the source, charge density and currents, and ǫ0 is the proportionality constant from Coulomb’s law. After many ingenious and expensive experiments and theoretical trials and errors, the physicists agree on the standard model of gravity. It starts from a particular spin 2 field g, and a second order differential operator DEin. The field equation is
DEin g = −(8πG/c4)T,

where the source T is energy-momentum density and currents, and G is the proportionality constant from Newton’s universal law of gravity. Although in perfect agreement with experiment, this standard model has draw backs: who ordered spin 2? Maxwell’s differential operator DMax contains 8 summands, the gravitational one DEin results from brute force and contains roughly 80 000 summands. Some of these summands still are inaccessible to experiment. At this stage, Riemannian geometry is discovered, the spin 2 field is recognized as the metric and the differential operator DEin is recognized as the curvature if the unknown summands are chosen properly. Most physicists say: so what, just fancy mathematics. Some dream of a geometric unification of all forces. Later, even more expensive experiments will test the predictions of Riemannian geometry coming from the unknown summands. 

If, in the real world, we qualify general relativity as revolution, we have several criteria.
• Postdiction: the theory correctly reproduces experimental data, that remain unexplained in the old theories, e.g. the precession of perihelia of Mercury.
• Prediction: the theory can be in contradiction with future experimental data, e.g. deflection of light.
• New concepts, e.g. curved spacetimes, absence of universal time.
• Reticence of the majority.  
Our purpose is to explain that for non-commutative geometry the analogue of g in the imaginary world is the Higgs field, the analogue of DEin  is the Lagrangian of the standard model of electro-weak and strong interactions. Postdictions of the theory are that fermions sit in fundamental representations, that weak interactions violate parity... [that strong interactions preserve it, that photons and gluons are massless, that there is only one Higgs scalar with a mass of 125 GeV at the LHC scale.
Predictions of the most advanced spectral models are that there is a breaking of a Pati-Salam gauge symmetry at some high energy scale 1011 − 1013 GeV with a unification scale enforced by the spectral action principle where the three coupling constants meet around 1016Gev. The new particle spectrum is close to the minimal nonsupersymmetric SO(10) models with the notable lack of leptoquarks: namely three super-heavy right-handed neutrinos to complete the chiral family spinors and the minimum set of Higgs scalars to implement the see-saw mechanism and the spontaneous symmetry breaking to the standard model. Another important prediction might be there is no such thing like a dark matter particle as dark matter phenomenology could be gravitational signature of quantization of spacetime in front of our telescope so to speak.]*
(Submitted on 2 Nov 1995 (v1), last revised 9 Nov 1995 (this version, v3))
*added by the blogger as an educated tentative update.

With the benefit from history and (h)in(d)sight
A spectral triplet consists of an associative algebra A, a representation on a Hilbert space H classifying the fermions and a Dirac operator D. The invariance group is simply the automorphism group of A. The later is chosen to be a tensor product of the infinite dimensional, commutative algebra of differentiable functions on spacetime M by a matrix algebra A describing an internal space, A = C(M)⊗A. Then the automorphism group is the semi-direct product of diffeomorphisms and gauge transformations. The latter are inner automorphisms. In the commutative case, A=ℂ, there are only diffeomorphisms and the Dirac operator simply encodes the metric. If A is noncommutative, for instance A=⊕M3() for the standard model, then the metric 'fluctuates', that is, it picks up additional degrees of freedom from the internal space, the Yang-Mills connection and the Higgs scalarIn physicist's language, the spectral triplet is the Dirac action of a multiplet of dynamical fermions in a background field. This background field is a fluctuating metric, consisting of so far adynamical bosons of spin 0, 1 and 2. The remaining two action pieces are obtained exclusively from the spectrum of the covariant Dirac operator DA indexed by the quantum one-form A. These two pieces together are simply the number of eigenvalues of |DA| that are smaller than Λ, i.e. tr F(|DA|/Λ) with F the characteristic function of the unit interval. This function of Λ can be calculated conveniently from the heat kernel expansion [6] and if F was the logarithm then we would have an old physical interpretation of this action formula, the dynamics of the bosons would be induced from one-loop quantum corrections with fermions circulating in the loop. With the characteristic function instead, this action is essentially Klein-Gordon together with spontaneous symmetry breaking for spin 0, Yang-Mills for spin 1 and Einstein-Hilbert for spin 2. In this approach all coupling constants are fixed leading to the well known numerical problems, the Planck mass sets the scale. The hope is that these evaporate once the fuzziness of spacetime is properly taken into account. This hope is encouraged from history. Let us recall that Maxwell's relation c2=(ε0µ0)-1 relates a velocity to static coupling constants. At his time the speed of light was believed to be frame dependent. It was only by accepting the revolution of Minkowskian geometry on spacetime that this problem evaporated.
(Submitted on 18 Jul 1996)

One of the basic problems facing theoretical physics is to determine the nature of space-time. This is intimately related to the problem of unifying all the fundamental interactions including gravity, and thus is not independent of solving the problem of quantum gravity. In a series of papers we have made important understanding uncovering a first approximation of the hidden structure of space-time. Our assumption is that at energies below the planck scale, space-time can be approximated as a product of a continuous four-dimensional manifold by a finite space. We were able to show in [14] that finite spaces satisfying the axioms of noncommutative geometry are severely restricted, and the corresponding irreducible representations on Hilbert spaces can only have dimensions which are the square of integers, or the double of such a square. The second possibility is the only one allowed when the finite space has dimension 6 modulo 8 (in the sense of K-theory or more pragmatically of the periodicity of Clifford algebras) as imposed by the need to have the total dimension 2 = 4 + 6 modulo 8 in order to be able to write down the Fermionic part of the action. Together with the restriction of imposing a unitary–symplectic structure and grading on the finite noncommutative space, this singles out 42 = 16 as the number of physical fermions per generation. Then, in the same way as was shown in [13], this predicts the existence of right-handed neutrinos, and the see-saw mechanism. Our present framework ... is stronger [as a Pati-Salam gauge group with the proper Higgs scalar spectrum for spontaneous breaking down to]** the standard model emerge, rather than assumed and put in by hand. This construction, using the spectral action principle, predicts certain relations between the coupling constants, that can only hold at very high energies of the order of the unification scale. 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.
The compatibility between the values at low energy (obtained by integration over the fluctuations in the intermediate scales) and observation is a basic test of the general idea but in case this test is passed, one needs to go much further and develop a theory that takes over at higher scales... In [27] an analogy was developed between the phase transitions which occur in the number theoretic context and a scenario of spontaneous symmetry breaking involving the full gravitational sector. If substantiated, this could show how geometry would emerge from the computation of the KMS states of an operator theoretic system, closely related to a matrix model with basic variable the Dirac operator D. It is worthwhile to note, at this point, that, at the conceptual level, the spectral action is closely related to an entropy since it can be written as the logarithm of a number of states in the second quantized Fermionic Hilbert space.
(Submitted on 3 Apr 2010)

**added by the blogger as a definite update.

//addendum 12/09/15
Reading the nice art-book Radioactive : Pierre & Marie Curie, a tale of love and fallout by Lauren Redniss I was struck by a coïncidence : Daniel Kastler passed away a 4th of July just like Marie Curie (81 years before) and the very same day when the Higgs boson discovery at LHC were officially publicized (three years ago).

samedi 8 août 2015

Three caravels to sail towards the Cape of Grand Unification

The blogger is back and begins his first exploration of "spectral models" as announced just before his departure on holidays on July 19

Travelling light to go far enough
The very last post was about an interesting achievement by Babu and Khan consisting in the building of a minimal non-supersymmetric grand unification model with a Pati-Salam intermediate scale following the programmatic extension of the Standard Model in the orthodox line of quantum Yang-Mills-Higgs fields theory.  I have found this work interesting for different reasons, the most important one for today's post being it has freed from the burden of the pre-LHC ideology of the naturalness problem regarding the Higgs scalar (these days there is a more expert blogger raising this issue).
The naturalness principle strongly influenced high-energy physics in the past decades [1], leading to the belief that physics beyond the Standard Model (SM) must exist at a scale ΛNP such that quadratically divergent quantum corrections to the Higgs squared mass are made finite (presumably up to a log divergence) and not much larger than the Higgs mass Mh itself. This ideology started to conflict with data after TeVatron measured the top mass (which implies a sizeable order-one top Yukawa coupling λt) and after LEP excluded new charged particles below 100 GeV [2]...  
The most plausible new physics motivated by naturalness is supersymmetry. It adds new particles at the weak scale, with the lightest one possibly being Dark Matter (DM). Further support for this scenario come from gauge unification and from the fact that DM loosely around the weak scale is indicated by the hypothesis that DM is the thermal relic of a massive stable particle. Doubting that nature is natural seemed impossible. However, no new physics has been so far seen at LHC with √s=8TeV... While this is not conclusive evidence, while special models that minimise fine-tuning are being considered, while naturalness arguments can be weakened by allowing for a finer tuning, while various searches have not yet been performed, while LHC will run at higher energy, etc, it is fair to say that the most straightforward interpretation of present data is that the naturalness ideology is wrong.
(Submitted on 28 Mar 2013 (v1), last revised 29 Apr 2014 (this version, v3))

Skipping (for a while) naturalness requirements to progress in the understanding of physics at higher energy scale can sound hazardous but this is precisely the philosophy of this blog to follow a different shipping route...

Bringing gauge coupling running charts as modern Portolans
Let's report thus on the recently prepublished first proof of the Pati-Salam gauge couplings in the three spectral models compatible with the actual mathematical framework of noncommutative geometry and the physical principal of spectral action. We will comment afterwards on the common grounds and differences between these spectral models and the work of Babu and Khan.

This paper builds on ... recent discoveries in the noncommutative geometry approach to particle physics:... the original argument by classification [4] of finite geometries F that can provide the fine structure of Euclidean space-time as a product M×F (where M is a usual 4-dimensional Riemannian space) has now been replaced by a much stronger uniqueness statement [7, 8]. This new result shows that the algebra
 M2(H)⊕M4(C), (1) 
where H are the quaternions, appears uniquely when writing the higher analogue of the Heisenberg commutation relations. This analogue is written in terms of the basic ingredients of noncommutative geometry where one takes a spectral point of view, encoding geometry in terms of operators on a Hilbert space H. In this way, the inverse line element is an unbounded self-adjoint operator D. The operator D is the tensor sum of the usual Dirac operator on M and a ‘finite Dirac operator’ on F, which is simply a hermitian matrix DF. The usual Dirac operator involves γ matrices which allow one to combine the momenta into a single operator. The higher analogue of the Heisenberg relations puts the spatial variables on similar footing by combining them into a single operator Y using another set of γ matrices and it is in this process that the algebra (1) appears canonically and uniquely in dimension 4. We refer to [78] for a detailed account. What matters for the present paper is that the above process leads without arbitrariness to the Pati–Salam [19] gauge group SU(2)R×SU(2)L×SU(4), together with the corresponding gauge fields and a scalar sector, all derived as inner perturbations of D [9]. Note that the scalar sector can not be chosen freely, in contrast to the early work on Pati–Salam unification [110, 12, 13]. In fact, there are only a few possibilities for the precise scalar content, depending on the assumptions made on the finite Dirac operator. 

From the spectral action principle, the dynamics and interactions are described by the spectral action [2, 3], 

tr(f(DA/Λ)) (2) 

where Λ is a cutoff scale and f an even and positive function... This action is interpreted as an effective field theory for energies lower than Λ. 
One important feature of the spectral action is that it gives the usual Pati–Salam action with unification of the gauge couplings [9] ... This is very similar to the case of the spectral Standard Model [6] where there is unification of gauge couplings. Since it is well known that the SM gauge couplings do not meet exactly, it is crucial to investigate the running of the Pati–Salam gauge couplings beyond the Standard Model and to find a scale Λ where there is grand unification
gR(Λ) = gL(Λ) = g(Λ). (4) 
This would then be the scale at which the spectral action... is valid as an effective theory. There is a hierarchy of three energy scales: SM, an intermediate mass scale mR where symmetry breaking occurs and which is related to the neutrino Majorana masses (1011 − 1013Gev), and the GUT scale Λ.
For simplicity, we restrict our analysis to the running of the gauge couplings at one-loop. Indeed, at two loops, the gauge and scalar couplings are mixed and influence each other. Moreover, the running of the scalar mass terms can not be trusted at all because of quadratic divergences. 
... depending on the assumptions on DF , one may vary to a limited extent the scalar particle content, consisting of either composite or fundamental scalar fields... 
This is a general prediction of the spectral construction that there is 16 fundamental Weyl fermions per family, 4 leptons and 12 quarks ...

Running of coupling constants for the spectral Pati–Salam model with composite Higgs fields: g1, g2, g3 for µ < mR and gRgL, g for µ > mR with unification scale Λ ≈ 2.5×1015 GeV for mR=4.25×1013 GeV.

Running of coupling constants for the spectral Pati–Salam model with fundamental Higgs fields: g1, g2, g3 for  µ<mR and gRgL, g for µ > mR with unification scale Λ ≈ 6.3×1016 GeV for mR=1.5×1011 GeV.
Running of coupling constants for the left-right symmetric spectral Pati–Salam model: g1, g2, g3 for µ < mR and gRgL, g for µ > mR with unification scale Λ ≈ 2.7×1015 GeV for mR=5.1×1013 GeV. 
We have analyzed the running of the Pati–Salam gauge couplings for the spectral model, considering different scalar field contents corresponding to the assumptions made on the finite Dirac operator. We stress that the number of possible models is quite restrictive and that one can not freely choose the particle content. We have identified the three main models, although there exists small variations on them. The different possibilities correspond to restrictions on the geometry of the finite space F. In all the models considered here, we establish unification of the gauge couplings, with boundary conditions set by the usual Standard Model gauge couplings at an intermediate mass scale. Besides the direct physical interest of such grand unification, it also determines the scale at which the asymptotic expansion of  [the spectral action] is actually valid as an effective theory.
(Submitted on 29 Jul 2015)

//Additional material (25 August 2015)
Would the spectral action grand unification thrill the heart of James Bjørken?
It might be interesting to stress that these spectral models enjoy grand unification gauge coupling without proton decay, the most famous prediction of grand unification theories from the past:
I remember an occasion, in 1974, when I was visiting SLAC“Bj” Bjørken told me that he had recently read the article on SU(5) by Georgi and Glashow [99]. He said that, as he was reading it, his heart was pounding faster and faster at the beauty of the unification of QCD and the electroweak theory, the convincing explanation of the commensurate integer and fractional charges of quarks and leptons, etc., etc. But, Bj said, his heart sunk when he read that protons were not forever. At the time I thought his reaction was precisely the wrong one. Proton decay, I thought, was the best part of this Grand Unification: a candidate for the ultimate Yang-Mills (YM) theory, including such a fantastic prediction! With the benefit of thirty years of hindsight, I am beginning to wonder whether Bj was right... 
Grand unifications of YM theories and proton instability actually slightly preceded the work by Georgi and Glashow. Indeed, Jogesh Pati and Abdus Salam were the first to introduce the elegant idea of lepton number as a fourth colour [104]. I learned from Bram Pais, via Georgi [31], that their SU(2)⊗ SU(2)⊗ SU(4) group even contained the full SU(3)⊗SU(2)⊗U(1) gauge structure of the standard model! But they proceeded to break colour SU(3) into integrally-charged Han–Nambu quarks, thereby distantiating themselves from the current standard lore. The Harvard theorists were, this time, capable of immediately convincing experimentalists that proton decay was interesting to look for. Larry Sulak, in particular, was enthusiastic with the idea, and he was among those who developed the inverse-osmosis technique that proved to be crucial in making water —at a reasonable cost— sufficiently transparent to exploit a large water-Cerenkov detector. Larry ˇ deprived his colleagues at the University of Michigan of an elevator, to install in its shaft a sufficiently tall water container and test the technique. His colleagues may not have appreciated their extra stair-climbing efforts, but eventually this kind of detectors made great serendipitous discoveries: neutrinos from SN1987A, neutrino oscillations, ... Proton decay has not been observed to date, and who knows what future proton-decay detectors may uncover.

As one can read it, the proton decay hypothesis has not been confirmed but was a fantastic incentive to build better detectors making possible the neutrino oscillations detection, the only experimentally established physics beyond the Standard Model up to now!

lundi 3 août 2015

The beat particle physics' heart almost skipped

Non supersymmetric grand unification with Pati-Salam intermediate scale and minimal fermion spectrum
This spring and early summer 2015 have witnessed a blooming of beyond standard model speculations related to potential anomalies reported in data from LHC1 (see former posts).
Now the heart of sunny season can also be time for (re)visiting older and less fashionable pathways. This is precisely what Professor K. S. Babu and his student Saki Khan have courageously undertaken:
The crucial point about SO(10) Grand Unified Theories is that if we change our current attitude about fine-tuning, yet keep it at the minimal level by adopting philosophy like extended survival hypothesis, we realize that even without supersymmetry, SO(10) symmetry has the potential to be the gauge symmetry of nature on its own right, atleast upto the GUT scale (∼1016 GeV).
The absence of low energy supersymmetry might be the reality of our universe, taking away primary motivation to introduce supersymmetry. Thus it becomes mandatory to revisit the non-supersymmetric version of SO(10) GUTs with a more open attitude.

Evolution of gauge couplings using one-loop RGE with threshold corrections determined by the scalar mass spectrum given in Table 3. The unification scale determined here is compatible with the current experimental limit on proton lifetime. The small black circles correspond to the various scalar masses changing the β function coefficients and inflicting changes in the slope of the graphs. The vertical dashed lines correspond to gauge boson masses that stay at intermediate scale and unification scale
In this work, the philosophy of minimality was applied in the choice Higgs representation and that resulted in a breaking pattern with minimal number of intermediate scale (namely one) making the model truly minimal and predictive... 
Such a minimal model ended up relying on threshold corrections to escape from the wrath of experimental bounds on proton lifetime. The issue of threshold corrections deserves particular attention here. On one hand, one should not discard a model without taking into account the threshold corrections, on the other hand, one should not expect that threshold corrections can rescue any model before performing detailed calculation.

The non-SUSY SO(10) GUT presented here managed to unify the gauge couplings at a scale high enough to comply with the current experimental bound of proton lifetime. The Yukawa sector of the model provided a realistic description of fermion masses and mixings. The Peccei-Quinn-phase transition introduced axion as the dark matter candidate that can explain the dark matter abundance in the universe, while also solving the strong CP problem. Leptogenesis finds a natural place in SO(10) with seesaw mechanism and the Yukawa sector of the model has the potential to procure the right amount. Physics of inflation may reside outside the scope of the model or within the model where one (or more) SM singlets already present may provide the necessary ingredients.

One should emphasis the claim that the SM spectrum is completed by the recently discovered light Higgs and LHC should fail to find any other new physics, as the next scale of physics lies at the energy scale of 1010 GeV. 
Before getting demoralized one also needs to realize that the model generally predicts a proton lifetime less than a few times 1035 yrs. So Super-Kamiokande or next generation proton decay detectors and axion search experiments has the potential to discover the essential phenomenological proof of the model.
(Submitted on 24 Jul 2015)

/last new edition August 8, 2015: the graph has been added to underline the very precise work done to evaluate threshold corrections on the running of the gauge coupling constants; a work required to escape from the wrath of experimental bounds on proton lifetime!

//last update August 21 2015
Some critical questions from the past still pertinent today
I find it is very interesting to compare the last reported article on a tentative minimal nonsupersymmetric extension of the standard model with the very first published work (to my knowledge) which proposed a fit of the gauge couplings in a minimal susy grand unification model:

Is it not trivial for 3 lines to meet in one point with two free parameters?
In general one can always find a crossing point with two free parameters (MSUSY and MGUT), except for some exceptional cases... However, in case of SUSY the interesting aspect is the small SUSY scale and the unification scale well below the Planck mass, which does not violate proton decay bounds (see below). All of these are nontrivial constraints... 

Can non-supersymmetric models yield unification?

As shown, SUSY models yield unification consistent with the proton lifetime limit. It is easy to find other simple models which yield unification, like the SM with 6 or more Higgs doublets [3] or 2 Higgs doublets and two pairs of leptoquarks [11]. However, the obtained values lead to proton lifetimes 2 orders of magnitude or more below the present experimental limits. More extensive models can indeed yield unification consistent with the proton lifetime limits, as demonstrated by a systematic search of 800 extensions of the SM by adding split real representations (10+10b) and (5+5b) in SU(5)[12]. From the 800 possible models only about 60 yield unification and about 20 have GUT scales consistent with [13]. The real representations are split between the TeV and GUT scale. In all cases the new neutrinos and leptons are heavy (i.e. masses close to MGUT), while the quarks are partially light (i.e. TeV range) [13]. The physical motivation for such split representations is the fact that they lead to unification. In contrast, SUSY particles are predicted from the requirement of symmetry between fermions and bosons, a symmetry not related at all to unification...

Can one extrapolate the coupling constants reliably over 14 orders of magnitude in energy?

The answer is yes, since in first order the slopes are "quantized" by the known number of particles in a given theory. Especially, the slopes are of the values of the coupling constants, at least in first order and the second order contributions are small...

What is the meaning of MSUSY?  

Far above and below the threshold for the SUSY particles, the slopes of the inverse coupling constants are well known. Extrapolating them linear into the narrow threshold region defines an effective mass scale , defined as the energy where the SM and MSSM slopes cross. Clearly, a single parameter is inadequate to parametrize the SUSY mass spectrum, as emphasized in Ref. [8]; to do so one needs a minimum of 5 parameters. However, from the unification of the 3 coupling constants, one cannot determine so many parameters. What then is the meaning of MSUSY? One knows that within the MSSM the spread in sparticle masses is small compared with MGUT[7]. Therefore, MSUSY, being some effective mass in this rather narrow threshold region, is the best estimate of the sparticle masses we have. Unfortunately, even this single parameter has large errors, since MSUSY enters only logarithmically into the extrapolation of the coupling constants. The 68% C.L. error spans already one order of magnitude, so the 95% C.L. error spans two order of magnitudes, i.e. 102<MSUSY<105GeV, a result agreeing with our previous results[3] and obtained later also in Ref. [14]. Nevertheless, one knows that within the MSSM at least one of the Higgs particles will have a mass below 170 GeV [15], which should certainly be within reach of the next generation of accelerators. 

What is real significance of these fits? 

Several features could be considered. E.g. is it:
- the fact that no unification can be obtained within the SM, so new physics is required for the unifi cation of all three forces?
-the fact that it is the first fit of MSUSY ?
- the fact that MGUT is larger than 2×1015 as required by the lower limit on the proton lifetime and that MSUSY comes out to be much smaller than MGUT, as required by supersymmetry?
-the prediction of many new particles with masses "around the corner", so that new accelerators have to be built?
-the fact that one gets uni cation so easily in the minimal [supersymmetric extension of the] SM without invoking e.g. a complicated Higgs sector?
Probably none of them can be called most significant, but it is the combination of all these arguments, which provide such an amazingly and puzzlingly consistent picture...

Ugo Amaldi , Wim de Boer , Hermann Furstenau
5 November 1991