jeudi 30 juin 2016

Now is the winter (of our discontent)

The threat of the long night over Tera eV scale?
The absence of new physics at the electroweak scale scale appears as a paradox to most of us. But possibly Nature has a way, hidden to us, to realize a deeper form of naturalness at a more fundamental level. Indeed the picture suggested by the last 20 years of data is simple and clear: just take the standard model (SM), extended to include Majorana neutrinos, as the theory valid up to very high energy. It is impressive to me that, if one forgets the fine tuning problem, the SM can stand up well beyond the LHC range with only a few additional ingredients. The most compelling evidence for new physics is Dark Matter. But a minimal explanation for Dark Matter could be provided by axions, introduced originally to solve the strong CP problem {45}, which only need a modest enlargement of the SM with some heavy new particles and a Peccei-Quinn additional global symmetry [46, 47, 48]. The Majorana neutrino sector with violation of B-L and new sources of CP violation offers an attractive explanation of baryogenesis through leptogenesis [49]. Coupling unification and the explanation of the quantum numbers of fermions in each generation in a non SUSY context can be maintained in SO(10) with two (or more ) steps of symmetry breaking at MGUT and at an intermediate scale MI. We have recently discussed an explicit example of a non-SUSY SO(10) model [43], with a single intermediate breaking scale MI between MGUT and the electroweak scale, compatible with the following requirements: unification of couplings at a large enough scale MGUT compatible with the existing bounds on the proton life-time; a Yukawa sector in agreement with all data on flavour physics, fermion masses and mixings, also including neutrinos, as well as with leptogenesis as the origin of the baryon asymmetry of the Universe; an axion, which arises from the Higgs sector of the model, suitable to solve the strong CP problem and to account for the observed amount of Dark Matter. It turns out that imposing all these requirements is very constraining, so that most of the possible breaking chains of SO(10) must be discarded and the Pati Salam symmetry at the intermediate scale emerges as the optimal solution. We show that all these different phenomena can be satisfied in this fully specified, although schematic, GUT model, with a single intermediate scale at MI∼1011 GeV. In fact, within this breaking chain, the seesaw and leptogenesis mechanisms can both be made compatible with MI1011 GeV, which is consistent with the theoretical lower limit on the lightest heavy right-handed neutrino for sufficient leptogenesis [50] given by MI109 GeV. The same intermediate scale MI is also suitable for the axion to reproduce the correct Dark Matter abundance. If this scenario is realized in nature one should one day observe proton decay and neutrinoless beta decay. In addition, none of the alleged indications for new physics at colliders should survive (in particular even the claimed muon (g-2) [32] discrepancy should be attributed, if not to an experimental problem, to an underestimate of the theoretical errors or, otherwise, to some specific addition to the above model [51]). This model is in line with the non observation of µ→eγ at MEG [52], of the electric dipole moment of the neutron [53] etc. It is a very important challenge to experiment to falsify this scenario by establishing a firm evidence of new physics at the LHC or at another ”low energy” experiment.
(Submitted on 2 Aug 2013 (v1), last revised 4 Dec 2013 (this version, v2))

A long time ago, there came a night that lasted a generation. Experimenters froze to death in their laboratories, same as the phenomenologists in their nontenured positions; and theorists smothered their speculations rather than see them starve, and wept, and felt the tears freeze on their cheeks...
 Fashionable Game  

samedi 25 juin 2016

Thinking one more (six? ;-) time(s) about the Higgs mass

A farewell to low energy susy
We think that there is one clue, perhaps, provided by the latest result from the Large Hadron Collider:[5,6] the mass, 125 GeV, found for the Higgs particle, is a very special value. The Higgs mass has been the one unknown parameter in the Standard Model, but, since the vacuum value of the Higgs field is precisely known from the W and Z mass and Fermi’s interaction constant for the weak force, having the Higgs mass now also yields the Higgs self-interaction parameter, λH. The value of λH, following from the given value of the Higgs mass, appears to be very special. One can compute how λH changes as we look at different energy scales. It is a running coupling parameter. If mH ≈ 125 GeV, the Higgs self-coupling parameter runs almost to zero at very high energies [8]
This means that the renormalization group β function rapidly runs to zero at high energies, a property it will have in common with the other β functions that describe how the gauge field forces run to zero. Apparently, our field theory of the subatomic particles, at sufficiently high energies, becomes scale-invariant 
Why is this? What do we have to infer from that?  
If there is scale invariance at higher energies, the masses of heavy particles would be at odds with this, and this could explain why we have not seen them, and also the massive superpartners of the SM particles, expected by many investigators, would be at odds with this symmetry. Is this why we see no heavy particles at all? Then, what about the preferred explanation of ‘dark matter’? It was always assumed to consist of WIMPs, ‘Weakly Interacting Massive Particles’. WIMPs would also have to be forbidden. So, perhaps LHC gave us a hint, but the hint is difficult for us to understand. It is more likely that the role played by scaling transformations will be a more subtle one, [9] and that it will not forbid the occurrence of heavier masses in the system, if the particles associated with these heavy masses, interact sufficiently weakly, as, indeed, is likely to be the case with the dark matter particles.
It is also the case with gravity. In units where = c = 1, Newton’s constant GN has dimension length-squared, or inverse mass-squared. The associated length, called Planck length, is very small, and accordingly, the associated mass, the Planck mass, is very large... This length unit is very tiny, even at the scale of subatomic particles, and the mass is very large compared to subatomic particles. Nevertheless, one can elegantly restore exact scale invariance in perturbative quantum gravity. This, we do by observing that only the truly constant quantities in a theory, such as interaction constants, must be dimensionless if we want scale invariance. In contrast, the metric tensor gµν, which determines the distance scales between neighboring points in space–time in terms of metres, is actually a dynamical variable. Like many other dynamical variables of a theory, it may have nontrivial dimensions even if the theory itself is scale invariant. 


gµν (x, t) ≡  ω2(x, t)gµν(x, t) , (7)
we can take the field ω2(x, t) to have dimension of a length — just like all other fields in the Standard Model — while all components of the tensor gµν(x, t) are kept dimensionless. 
In perturbative quantum gravity, we now keep gµν close to the identity matrix ηµν ≡diag(−1,1,1,1). In that case, however, we must postulate that ω stays close to one in the geometrically flat vacuum, while in general it may fluctuate. Or, 
we say:
<∅|ω(x, t)|∅> = 1 . (8)
This means that scale invariance is a gauge symmetry that is spontaneously broken, a situation that one often encounters in quantum field systems. 
Actually, in gravity, we also have general coordinate transformations, so we can also say that the theory has local conformal invariance, which is spontaneously broken. In that case, Eq. (8) expresses the fact that we have a BEH mechanism here. We can choose the gauge such that ω2(x, t)=1, or we can fix the gauge constraint in some other way. In either case, we have a new local gauge symmetry, and this is a very important observation shedding a different light on quantum gravity. 
One can even argue that gravity herewith becomes a renormalizable theory [15], but before arriving at such a conclusion, one would have to add kinetic terms for the gµν field [10,11,12]. Such terms can be written down (the Weyl action), but that ruins positivity: the Weyl action adds a negative metric massive spin-2 particle to the system, something that will be difficult to accept, as this is believed to make our theory internally inconsistent. 
The Weyl action, however, seems to be such a fundamental interaction, that some of us suspect it can be used anyway, inviting us to think again about stability of theories and the exact role of indefinite metric particles...  in a local conformally invariant theory.
Gerard ’t Hooft
published 9 June 2016

Sur un air de géometrie spectrale
Thanks to David Broadhurst for stressing the following point during my lecture at a summer school in Les Houches. 
Whilst introducing gauge fields from noncommutative spin manifolds (aka spectral triples) I first explained how the Dirac operator can be seen as a metric on a (possibly noncommutative) space described via Connes’ distance formula. Then the action of a unitary in the algebra of coordinates was given as a gauge transformation on the Dirac operator, generating a pure gauge field. 
What David noticed was that this is in compelling agreement with Weyl’s old idea of gauge invariance. Indeed, the term Eichinvarianz was preceded by Maβstabinvarianzin the original work (see Yang’s review ...). This is precisely the notion captured by noncommutative geometry: a gauge transformation actually acts on the metric (the Dirac operator) but leaves the distance function invariant.
Perturbations of the metric and Weyl’s Eichinvarianz
posted in Blog on June 19, 2014 by Walter van Suijlekom

A long Hello again to Weyl invariance
In this note we will show the intimate relationships between Weyl anomalies, the dilaton and the Higgs field in the framework of spectral physics. The framework is the expression of a field theory in terms of the spectral properties of a (generalized) Dirac operator. In this respect this work can be seen in the framework of the noncommutative geometry approach to the standard model of Connes and collaborators..., as well as of Sakharov induced gravity [5] (for a modern review see [6]).  
We start with a generic action for a chiral theory of fermions coupled to gauge fields and gravity. The considerations here apply to the standard model, but we will not need the details of the particular theory under consideration. It is known, and this is the essence of the noncommutative geometry approach to the standard model, that the theory is described by a fermionic action and a bosonic action, both of which can be expressed in terms of the spectrum of the Dirac operator. In [7] two of us have shown that if one starts from the classic fermionic action and proceeds to quantize the theory with a regularization based on the spectrum, an anomaly appears. it is possible that the full quantum theory is still invariant by correcting the path integral measure. This is tantamount to the addition of a term to the action, which renders the bosonic background interacting to the dilaton field. The main result of that paper is that this term is a modification of the bosonic spectral action [3]. In this case the theory is still invariant. 
In this paper we have a shift of the point of view. We still consider the theory to be regularized in the presence of a cutoff scale, but we consider this scale to have a physical meaning, that of the breaking of Weyl invariance. We then consider the flow of the theory at a renormalization scale, which is not necessarily the scale which breaks the invariance. The theory has a dilaton, and the Higgs field. 
The dilaton may involve a collective scalar mode of all fermions accumulated in a Weyl-non-invariant dilaton action. Accordingly the spectral action arises as a part of the fermion effective action divided into the Weyl non-invariant and Weyl invariant parts. 
We calculate the dilaton effective potential and we discuss how it relates to the transition from the radiation phase with zero vacuum expectation value of Higgs fields and massless particles to the electroweak broken phase via condensation of Higgs fields. The collective field of dilaton can provide the above mentioned phase transition with EW symmetry breaking during the evolution of the universe.
(Submitted on 16 Jun 2011)

samedi 18 juin 2016

The adventures of AC2

The year is 4 AH (after the Higgs boson discovery). High energy physics is still mostly dominated by superstring theoreticians. Well, not entirely... One pair of indomitable mathematician and physicist still holds out against the superstring trust. And experimental facts are not compelling for the superstring advocates who garrison the fortified camps of  Kontsevium, Pestum, Rabinovicium and Shatashvilium...

The blogger has no affiliation to the IHES of course (or any research institution). 

mercredi 15 juin 2016

Are binary black holes the best model for the source of detected transient gravitational waves?

Taking the exciting announcement about GW151226 with a grain of salt?

... we have observed that the neutron star radii (in the sense of the end of the matter distribution, where the pressure drops to zero) are smaller in f(R) theories than in their Einsteinian counterparts. This is due to much of the apparent or effective mass-energy being distributed in the outer gravitational field in f(R) theories, and thus not needing additional matter shells in the star. While current measurements of neutron star radii [42] in quiescent X-ray binary systems do point to radii smaller than preferred in General Relativity (9-11 km versus 12- 13 km for typical masses), more accurate measurements are eagerly awaited.  
Finally, because the calculated neutron star masses can be much larger than in General Relativity, the energy available for gravitational-wave emission as well as the total system mass can well exceed what is assumed in Einsteinian gravity. We have provided the basic reasoning and performed a qualitative analysis on this issue. Thus, the conclusion of the LIGO collaboration [28] that the merging objects must be black holes because the measured total mass seems to be 70M and the mass loss about 3M is restricted to standard General Relativity. If gravity is significantly modified at neutron star scale (which certainly remains to be seen) then f(R) theory may accommodate an emission of 3−4M in the merger of neutron stars. This is being investigated.
(Submitted on 11 Feb 2016 (v1), last revised 16 Feb 2016 (this version, v2))

Waiting for electromagnetic counterparts... 

Mergers of binary neutron stars and black hole-neutron star binaries produce gravitational-wave (GW) emission and outflows with significant kinetic energies. These outflows result in radio emissions through synchrotron radiation of accelerated electrons in shocks formed with the circum-merger medium. We explore the detectability of these synchrotron generated radio signals by follow-up observations of GW merger events lacking a detection of electromagnetic counterparts in other wavelengths. We model radio light curves arising from (i) sub-relativistic merger ejecta and (ii) ultra-relativistic jets. The former produces radio remnants on timescales of a few years and the latter produces γ-ray bursts in the direction of the jet and orphan radio afterglows extending over wider angles on timescales of a week to a month. The intensity and duration of these radio counterparts depend on the kinetic energies of the outflows and on circum-merger densities. We estimate the detectability of the radio counterparts of simulated GW merger events to be detected by advanced LIGO and Virgo by current and future radio facilities. The maximum detectable distances for these GW merger events could be as high as 1 Gpc. 20–60% of the long-lasting radio remnants arising from the merger ejecta will be detectable in the case of the moderate kinetic energy of 3 · 1050 erg and a circum-merger density of 0.1 cm-3 or larger, while 5–20% of the orphan radio afterglows with kinetic energy of 1048 erg will be detectable. The detection likelihood increases if one focuses only on the well-localizable GW events.
(Submitted on 30 May 2016)

... or correlated PeV to EeV neutrino signals

As the technology of gravitational-wave and neutrino detectors becomes increasingly mature, a multi-messenger era of astronomy is ushered in. Advanced gravitational wave detectors are close to making a ground-breaking discovery of gravitational wave bursts (GWBs) associated with mergers of double neutron stars (NS-NS). It is essential to study the possible electromagnetic (EM) and neutrino emission counterparts of these GWBs. Recent observations and numerical simulations suggest that at least a fraction of NS-NS mergers may leave behind a massive millisecond magnetar as the merger product. Here we show that protons accelerated in the forward shock powered by a magnetar wind pushing the ejecta launched during the merger process would interact with photons generated in the dissipating magnetar wind and emit high energy neutrinos and photons. We estimate the typical energy and fluence of the neutrinos from such a scenario. We find that ∼PeV neutrinos could be emitted from the shock front as long as the ejecta could be accelerated to a relativistic speed. The diffuse neutrino flux from these events, even under the most optimistic scenarios, is too low to account for the two events announced by the IceCube Collaboration, but it is only slightly lower than the diffuse flux of GRBs, making it an important candidate for the diffuse background of ∼PeV neutrinos. The neutron-pion decay of these events make them a moderate contributor to the sub-TeV gamma-ray diffuse background.
(Submitted on 13 Jun 2013 (v1), last revised 4 Aug 2013 (this version, v2))

The existence of fast radio bursts (FRBs), a new type of extragalatic transients, has been established recently and quite a few models have been proposed. In this work we discuss the possible connection between the FRB sources and ultra-high energy (> 1018 eV) cosmic rays. We show that in the blitzar model and the model of merging binary neutron stars, the huge energy release of each FRB central engine together with the rather high rate of FRBs, the accelerated EeV cosmic rays may contribute significantly to the observed ones. In other FRB models including for example the merger of double white dwarfs and the energetic magnetar radio flares, no significant EeV cosmic ray is expected. We also suggest that the mergers of double neutron stars, even if they are irrelevant to FRBs, may play a non-ignorable role in producing EeV cosmic ray protons if supramassive neutron stars were formed in a good fraction of mergers and the merger rate is & 103 yr-1 Gpc-3 . Such a possibility will be unambiguously tested in the era of gravitational wave astronomy.
(Submitted on 19 Dec 2013 (v1), last revised 23 Nov 2014 (this version, v2))

lundi 6 juin 2016

SO(20) : twenty years of spectral obstinacy

Have A. Chamseddines and A. Connes opened the way of a new wisdom for physics towards quantum gravity since 1996?
The spectral action principle that epitomizes the geometric unification of the electroweak and strong interactions with the gravitational one in a noncommutative formalism was put forward for the first time in an article submitted the 3rd of June 1996. Exactly 20 years later, its first author Ali Chamseddine, a former Ph. D. student of Abdus Salam choses to celebrate the memory of his mentor with a synthetic summary of the last developments of this joint program. Here are a few extracts:
The work I am reporting in this presentation is the result of a long-term collaboration with Alain Connes over a span of twenty years starting in 1996 [3] [4] [5] [6] [7] [8]. In the latest work on volume quantization we were joined by Slava Mukhanov [9] [10]. On the inner fluctuations of the Dirac operator over automorphisms of the noncommutative algebra times its opposite, we were joined by Walter van Suijlekom [11] [12] [13]...

In this setting, the four dimensional manifold emerges as a composite of the inverse maps of the product of two spheres of Planck size. The manifold M4 which is folded many times in the product, unfolds to macroscopic size. The two different spheres, associated with the two Clifford algebras can be considered as quanta of geometry which are the building blocks to generate an arbitrary oriented four dimensional spin-manifold. We can show that the manifold M4, the two spheres with their maps Y, Y' and their associated Clifford algebras define a noncommutative space which is the basis of unification of all fundamental interactions, including gravity...

The phase space of coordinates and Dirac operator defines a noncommutative space of KO dimension 10. The symmetries of the algebras defining the noncommutative space turn out to be those of SU(2)R×SU(2)L×SU(4)C known as the Pati-Salam models. Connections along discrete directions are the Higgs fields... The action has a very simple form given by a Dirac action for fermions and a spectral action for bosons. The 16 fermions (per family) are in the correct representations with respect to Pati-Salam symmetries or the Standard Model symmetries. There are many consequences of the volume quantization condition which could be investigated. For example imposing the quantization condition through a Lagrange multiplier would imply that the cosmological constant will arise as an integrating constant in the equations of motion. One can also look at the possibility that only the three volume (space-like) is quantized. This can be achieved provided that the four-dimensional manifold arise due to the motion of three dimensional hypersurfaces, which is equivalent to the 3+1 splitting of a four-dimensional Lorentzian manifold. Then three dimensional space volume will be quantized, provided that the field X that maps the real line have a gradient of unit norm gµνµX∂νX=1. It is known that this condition when satisfied gives a modified version of Einstein gravity with integrating functions giving rise to mimetic dark matter [21] [22]. 
(Submitted on 3 Jun 2016)

//addition on June 8, 2016:

A Salam's student slow drift from superstring theory to  noncommutative geometry ...
... and a roughly 40 year old cyclic unfolding time from one paper to another:
In 1973 I got a scholarship from government of Lebanon to pursue my graduate studies at Imperial College, London. Shortly after I arrived, I was walking through the corridor of the theoretical physics group, I saw the name Abdus Salam on a door. At that time my information about research in theoretical physics was zero, and since Salam is an Arabic name, and the prime minister in Lebanon at that time was also called Salam, I knocked at his door and asked him whether he is Lebanese. He laughed and explained to me that he is from Pakistan. He then asked me why I wanted to study theoretical physics. I said the reason is that I love mathematics. He smiled and told me that I am in the wrong department. In June 1974, having finished the Diploma exams I asked Salam to be my Ph.D. advisor and he immediately accepted and gave me two preprints to read and to chose one of them as my research topic. The first paper was with Strathdee [1] on the newly established field of supersymmetry (a word he coined), and the other is his paper with Pati [2] on the first Grand Unification model, now known as the Pati-Salam model. Few days later I came back and told Salam that I have chosen supersymmetry which I thought to be new and promising. Little I knew that the second project will come back to me forty years later from studying the geometric structure of space-time, as will be explained in what follows. In this respect, Salam was blessed with amazing foresight.

Grand unified theories provide an attractive mechanism to unify the weak, strong and electromagnetic interactions and put order into the representations of quarks and leptons. At present, the simplest models are based on SU(5)[1] and SO(10) gauge theories [2]. The second class of models has the advantage of including all the fermions (plus a right handed neutrino) in one representation. This advantage does not translate itself into a more predictive theory, because there are many possibilities to break SO(10) down to SU(3)×U(1)em requiring many different and often complicated Higgs representations [3]. What is clearly needed in grand unified theories is a principle to put order into the Higgs sector. During the last few years, much effort has been directed towards this problem by studying unified theories as low-energy limits of the heterotic string . Although this is an attractive strategy, it has proven to be a difficult one, due to the fact that one must search for good models among the very large number of string vacua. We shall follow, instead, a different strategy.
It has been shown by Connes [4-5] and Connes and Lott [6-7] that the ideas of non-commutative geometry can be applied to, among other things, model building in particle physics. In particular, the Dirac operator, defined on the one-particle Hilbert space of quarks and leptons, is used to construct the standard SU(3)×SU(2)×U(1) model with the Higgs field unified with the gauge fields. The space-time used in this construction is a product of a Euclidean four-dimensional manifold by a discrete two-point space. If, in coming years, an elementary Higgs field is observed experimentally, one can turn the argument around and view it as an indication that space-time has the product structure proposed by Connes.