jeudi 27 mars 2014

Quelques commentaires autour des résultats de Bicep2 et du lien possible entre Higgs et inflaton

Echange réel avec Jester sur le blog Résonaances
Does it mean we have now some evidence for a second scalar field (not necesseraly fundamental) the inflaton, a big brother to the Higgs? How big (vev, mass) today (not just before Big Bang nucleosynthesis) by the way ? Could the inflaton talk to (interact with) the Higgs boson, could the big one helps the light one to cope with its quadratic divergences ... I stop here to avoid rhyme inflation with infatuation17 March 2014 20:33  
Jester said...
Yes, the hypothesis of a new scalar field to support inflation is getting more and more plausible. We don't know its properties, but the mass should not be larger than 10^16 GeV. We know nothing about its interactions with the Higgs, and we have no idea how it could help with the hierarchy problem.17 March 2014 21:18

Commentaire virtuel (proposé mais refusé) sur le blog Not Even Wrong
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A possibly relevant piece of information to know if the BICEP2 results (to be confirmed) could be useful to test simple models:
“[A Higgs inflaton scenario with the already known scalar boson mass close to the critical value for which the Standard Model is a self-consistent effective field theory up to inflationary scale] becomes a predictive theory for particle physics … It is amazing that a possible detection of large tensor-to-scalar ratio r … predicts the top quark and Higgs boson masses close to their experimental values. Another observation is that the running of the spectral index becomes relatively large and negative.”

dimanche 16 mars 2014

Bref échange (par blogs interposés) avec Matt Strassler ... et commentaires autour du boson de Higgs

What if the Large Hadron Collider Finds Nothing Else?

Thank you for speaking bluntly about this uncomfortable but interesting scenario of no physics beyond thenStandard Model at LHC and trying to draw prospects from such an alternative.
Your discussion about the Michelson experiment which more or less rejected the existence of a classical ether is on purpose from an epistemological point of view. But as far as heuristics is concerned, it is quite ironical to notice that the discovery of a pretty standard, fundamental scalar Higgs boson puts the existence of its quantum field and specific non zero vacuum expectation value on a firm basis, so it demonstates the existence of a very special quantum ether, some kind of “space condensate” so to speak (a wink to condensed matter phenomena which inspired the conception of the Higgs mechanism) ! So before looking for new fundamental particles may be high energy physicists definitely need to fully understand the Higgs at the TeV scale (with a Higgs factory accelerator) and extrapolate all the possible consequences of the associated “space condensate” up to Planck scale … and try to test them in a cosmological context (inflation model) with the measures of … the Planck sattelite!
  • Yes, there is some irony in that, I agree… but still, the “space-timecondensate” (not a space-condensate) that is the Higgs field fits right in with the odd story of an ether which is at rest with respect to everyone, no matter how they are moving. This is in contrast to the condensed matter physicists who had a space-condensate with respect to which you can be moving. 
  • There’s no question that we need to understand the Higgs thoroughly, and of course that is a major part of the LHC research program. But we already know enough about quantum field theory to know that there’s a conceptual problem if nothing else shows up at the LHC.
  • laboussoleestmonpays 
    Thanks for your addendum! The time dimension is very relevant indeed: what would be physics without causality and its “thermodynamic handmaiden” stability (another intriguing aspect of the Higgs vacuum by the way)?
    To carry on the fact that “ideas developed in the condensed matter field can prove useful in particle physics” (to quote more or less S. Weinberg :-), do you think the following line of reasoning : “stability conditions in solid state physics … are known, in certain cases, to cause UV divergences to sum automatically to zero” (quoted from has any chance to be relevant in the context of the quadratic divergences in the Higgs sector?
  • laboussoleestmonpays 
    To put equations (not mine!) behind “space condensate” (my awkward words) I precise that I have in mind the specific mathematical model patiently refined since twenty years by a mathematician A. Connes with severa theoretical physicsts like A. Chamseddine, M. Marcolli and P. van Suijlekom (, which does not pretend to solve the naturalness issue of the Higgs (it’s not their main strategy I would say) but try to give more conceptual meaning to the Standard Model Yang-Mills-Higgs gauge structure … may be like special relativity explained the hidden Lorentz symmetry of space-time ;-)

Dear Matt,
Didn’t mommy tell you never to mention the ether in company? Now look what you’ve done!
Dear Julian, I think Matt was right to mention the classical ether for the purpose of his argumentation. He makes a nice and courageous work of popularization and takes some “risks”. Of course the “ether” word is like a magic, pandora box and triggers wild speculations but for a condensed matter physicist working with low energy excitations over different kinds of electronic quantum liquids this is not necesseraly a dirty world, just a “meme” so to speak (of course Fermi sea or fractional quantum Hall liquid are more politically correct or fancy…).
To come back to the Higgs naturalness issue I think naively that it is interesting to notice that the “natural” solution for accelerator physicists is to look for new particles while the “natural” idea in a solid-state physics perspective is to think first about a new ether, a new vacuum state in order to make the scalar sector richer. Then its new phenomenology could be tricky to uncover with a collider but we can rely on astroparticle physics now since quantum cosmology has been born with Cobe, WMAP and Planck satellites.
Last but not least I wonder if, before thinking about new particles or new quantum vacuum, one would rather not look for a better or more subtle spacetime model to embed the Standard Model and its Higgs sector in a more generic or “natural” framework.

dimanche 9 mars 2014

Défense et illustration de l'intérêt de la géométrie non commutative dans le cadre de la physique du solide...

...celle de l'effet Hall Quantique entier hier
Dans ce billet, le blogueur retourne à ces premières amours, la physique du solide en l’occurrence, ne serait-ce que pour montrer au lecteur qu'il n'y a pas que le boson de Higgs et la physique des particules dans la vie!
In 1880, Hall undertook the classical experiment which led to the so-called Hall effect. A century later, von Klitzing and his co-workers showed that the Hall conductivity was quantized at very low temperatures as an integer multiple of the universal constant e2/h. Here e is the electron charge whereas h is Planck’s constant. This is the integer quantum Hall effect (IQHE). For this discovery, which led to a new accurate measurement of the fine structure constant and a new definition of the standard of resistance, von Klitzing was awarded the Nobel price in 1985. 
After the works by Laughlin and especially by Kohmoto, den Nijs, Nightingale, and Thouless’ (called TKN, below), it became clear that the quantization of the Hall conductance at low temperature had a geometric origin. The universality of this effect had then an explanation. Moreover, as proposed by Prange, Thouless, and Halperin, the plateaux of the Hall conductance which appear while changing the magnetic field or the charge-carrier density, are due to localization. Neither the original Laughlin paper nor the TKN one however could give a description of both properties in the same model. Developing a mathematical framework able to reconcile topological and localization properties at once was a challenging problem. Attempts were made by Avron et al. who exhibited quantization but were not able to prove that these quantum numbers were insensitive to disorder. In 1986, Kunz went further on and managed to prove this for disorder small enough to avoid filling the gaps between Landau levels. 
But ... [Bellissard] proposed to use noncommutative geometry to extend the TKN, argument to the case of arbitrary magnetic field and disordered crystal. It turned out that the condition under which plateaux occur was precisely the finiteness of the localization length near the Fermi level. This work was rephrased later on by Avron et aLI7 in terms of charge transport and relative index, filling the remaining gap between experimental observations, theoretical intuition and mathematical frame.
J. Bellissard, A. van Elst et H. Schulz- Baldest, The noncommutative geometry of the quantum Hall effect10/10/1994

...celle des isolants topologiques aujourd'hui
It is often said that the topological insulators (TI) are the equivalent of the Quantum Integer Hall Effect (IQHE), but without the need of an external magnetic field (or any other external field for that matter)...  the stability of topological phases under strong disorder should be placed among the key issues in an complete theory of important observation is the following simple but fundamental principle: If the bulk topological invariant, classifying the different phases of a TI, stays quantized and non-fluctuating as long as the Anderson localization length is finite, then the characteristics discussed above are necessarily present. Indeed, this property will ensure, on one hand, the stability of the topological phases in the presence of strong disorder and, on the other hand, that the only way to cross from one topological phase to another is via a divergence of the localization length. For IQHE, the Hall conductance as proven to posses this property using non-commutative geometry in the 1990’s [9]. This result represents one of the most important applications of the non-commutative geometry in condensed matter physics (cf [1] pg. 365). It was only recently that similar mathematically rigorous results start appearing for other topological phases [2, 3]. They gave a complete characterization of the entire complex classes (the A- and AIII-symmetry classes in any dimension) of the periodic table [5] of topological insulators and superconductors. As such, the methods of non-commutative geometry have been extended from the upper-left corner of this table to the entire rows of the complex classes. 
When discussing these results with his colleagues, the author is often asked how crucial is Alain Connes’ non-commutative geometry for the whole developmen? Of course, after understanding the arguments and seeing the final conclusions, one can reproduce them via  different methods. However, without the guidance from noncommutative geometry, searching for the correct form of the index theorems would have been like searching for a needle in a haystack. To convince the reader of this fact, the paper presents first some key elements of the noncommutative geometry program, which as we shall see lay down the basic principles and the guiding philosophyThen the paper gradually builds the specific structures needed for the problem at hand. The quantization and the homotopy stability of the topological invariants, together with the general conditions when these happen, will then naturally emerge... 
If the author is allowed to share some thoughts about his experience, then these will be his words for the noncommutative geometry as applied to materials science:
  • The framework provides guidance and intuitionWhen done inside this framework, the search for the correct invariants no longer feel like searching for a needle in a haystack.
  •  It provides the big picture so one can always know what he is computing. In the present context, the index theorems we just presented give morphisms from the K-groups of algebra of localized observables into the ℤ. 
  • Last but not the least, the framework provides some outstanding tools of calculus. It will be a true asset to the materials science if a wider acceptance is achieved among the physicists. Needles to say, the field of Topological Insulators is the perfect ground for applications.
 Emil Prodan , The Non-Commutative Geometry of the Complex Classes of Topological Insulators, 28/02/2014

samedi 8 mars 2014

La masse du boson de Higgs est une boussole (1er épisode)

Déconstruire le problème de la hiérarchie dans le secteur de Higgs?
Ce billet se veut le premier d'une série où on essaiera de collecter des informations sur les solutions possibles au problème de la hiérarchie et de la naturalité du boson de Higgs (merci encore à Jonathan Butterworth de nous avoir indiqué des références intéressantes :-).
Frequently, the hierarchy problem is formulated in a strong form, saying that if the Higgs mass is not  protected by a symmetry and hence we expect MH = O( ) and supposing all couplings are O(1) then MH = O(Λ) implies Mi = O(Λ) (i = H,W, Z, t, · · ·) for all masses. In other words, why is the electroweak scale v not just ? However, this type of argument is rather formal. According to this kind of interpretation, the term “spontaneous symmetry breaking” would become quite meaningless if the breaking would be naturally at the “hard” scale and not at a much lower “soft” one, as it is anticipated usually. It would mean that the symmetric phase is not recovered at the hard scale. In effective theories one has to distinguish between short range (e.g. lattice spacing a ∼ Λ−1) order and long range order quantities, the latter emerging from collective behavior as encountered in phase transitions. The fact that criticality requires the temperature to be tuned to its critical value does not mean that the critical temperature is Tc = O(1/a). Note that, in field theory language, the reduced temperature (T − Tc)/Tc is proportional to the renormalized mass square m2ren = m2bare −m2c bare, where m2c bare is the critical bare mass for which the renormalized mass is zero. The key point is that a limit Λ → ∞ need not exist as is a given physical quantity. The critical “fine tuning” T ∼ Tc is not a fine tuning problem giving an answer to why Tc ≪ 1/a. In typical cutoff systems encountered in condensed matter physics an order parameter associated with a first order phase transition, like the Higgs VEV v in our case, is by no means O(&Lamda;). Rather it is a matter of a collective phenomenon of the system with infinitely many degrees of freedom. Below the critical temperature, on the bare level, depending on the given effective short range interaction between the intrinsic degrees of freedom, the system is building up long range order and domain structures. The critical temperature Tc as well as an order parameter like the magnetization M are macroscopic quantities. Long range effective quantities emerging in critical phenomena, are effects we see when looking at a system from far away and do not simply reflect the microscopic structure. The emergence of long range collective patterns is what I called self-tuning or self-protection above. It is the natural case in critical or quasi-critical condensed matter systems. So it is natural to have v ≪ Λ and unnatural to expect v ∼ Λ. In the SM, in addition, stetting v = 0 enhances the symmetry in any case (the gauge- and chiral-one), in spite the Higgs mass square persists getting corrections O(Λ2), which in the symmetric phase boosts up the physical mH to an O(Λ) quantity.
Fred Jegerlehner, The hierarchy problem of the electroweak Standard Model revisited, 14/09/2013
Faire des divergences quadratiques le moteur de l'inflation?
Faire d'un obstacle l'axe d'un levier pour sinon soulever le monde du moins essayer de résoudre une grande énigme c'est ce que propose Fred jegerlehner dans un article tout récent qui prolonge les idées développées précédemment.
... the SM in the broken phase has no hierarchy problem. In contrast, in the unbroken phase (in the early universe) the quadratic enhancement of the mass term in the Higgs potential is what promotes the Higgs to be the inflaton scalar field. Thus the “quadratic divergences” provide the necessary condition for the explanation of the inflation profile as extracted from Cosmic Microwave Background (CMB) data [9].
Note that in the unbroken phase, which exists from the Planck scale down to the Higgs transition not very far below the Planck scale, the bare theory is the physical one and a hierarchy or fine-tuning problem is not an issue there. Standard Model Higgs vacuum stability bounds have been studied some time ago in Ref. [10,11], for example. Surprisingly, the Higgs mass determined by the LHC experiments revealed a value which just matched or very closely matched expectations from vacuum stability bounds.
Fred Jegerlehner, Higgs inflation and the cosmological constant, 16/02/2014

Ajouter un grain de sel non commutatif à l'équation Higgs = inflaton?
La spécificité de ce blog réside dans sa quête obstinée d'une trace de non commutatif dans le monde physique or cet aspect n'a pas encore été mentionné dans ce billet. Le texte qui suit a pour but de pallier ce défaut en présentant des travaux sur le lien entre boson de Higgs et inflaton dans la perspective de la physique spectrale non commutative. Il n'y a par contre a priori aucun lien entre les idées développées par Nelson et Sakellariadou ci dessous et celles de Jegerlehner.
Considering the product of ordinary Euclidean spacetime (i.e., space-time but with imaginary time) by a finite space (with the properties discussed above), a geometric interpretation of the experimentally confirmed effective low energy model of particle physics was given in Ref. [7]. Investigating cosmological consequnecs of this proposal, we have concluded that the Higgs field can play the rˆole of the inflaton field within the noncommutative approach to the standard model, provided inflation will take place at a scale higher than the strong weak unification scheme, 1017GeV. In order to find the precise value of this scale, a detailed analysis of the running of the couplings above unification would be required. However, let us emphasise that the aim of this paper is simply to note that within the noncommutative geometry approach to unifying gravity and the Standard Model, it is possible to have an epoch of inflation sourced by the dynamics of the Higgs field. In addition, this type of noncommutative inflation could have specific consequences that would discriminate it from alternative models. In particular, since the theory contains all of the Standard Model fields, along with their couplings to the Higgs field, which in this scenario plays the rôle of the inflaton, a quantitative investigation of reheating should be possible. More significantly, the cosmological evolution equations for inhomogeneous perturbations differs from those of the standard Friedmann-Lemaître-Robertson-Walker cosmology [10]. This raises the possibility that signatures of this noncommutative inflation could be contained within the cosmic microwave background power spectrum.
William Nelson et Mairi Sakellariadou, Natural inflation mechanism in asymptotic noncommutative geometry, 09/03/2009

mardi 4 mars 2014

Le champ de Higgs : de la matière condensée aux particules élémentaires ... en passant par un espace condensat ?

Trois points de vue sur un phénomène physique
  • Le boson de Higgs: c'est définitivement une nouvelle particule pour la physique expérimentale des hautes énergies;
  • Le modèle de Englert-Brout-Higgs-Guralnik-Hagen-Kible-Migdal-Polyakov: c'est peut-être la trace d'une structure fine de l'espacetemps pour une physique théorique inspirée par la géométrie non commutative;
  • Le mécanisme de brisure spontanée de la symétrie de jauge électrofaible à la Nambu-Goldstone-Anderson: c'est la manifestation d'un véritable éther quantique du point de vue de la physique phénoménologique de la matière condensée.

Brève histoire du mécanisme (NGA)EBHGHKMP ...
Following the introduction into particle physics of spontaneous global symmetry breaking into particle physics by Nambu [21] and the formulation of a simple field-theoretical model by Goldstone [22], as well as the interpretation by Anderson [23] of superconductivity in terms of a spontaneously-broken local U(1) symmetry, in 1964. several papers introduced spontaneously-broken local symmetry into particle physics.
The initial paper by Englert and Brout [24] was followed a few weeks later by two papers written independently by Higgs: the fi rst pointing out that a technical obstacle to a four-dimensional extension of Anderson's approach could be circumvented [25], and the second proposing a speci c four-dimensional model with a massive scalar boson [26]. The subsequent paper by Guralnik, Hagen and Kibble [27] referred explicitly to these earlier papers. Also of note is a relatively-unknown 1965 paper by Migdal and Polyakov [28], which discusses the partial breaking of a local non-Abelian symmetry, ahead of the influential paper of Kibble [29].
Of all these authors, Higgs was the only one who mentioned explicitly the existence of a massive scalar boson (see equation (2b) of his second paper [26]), and he went on to write a third paper in 1966 [30] that discusses the properties of this `Higgs boson' in surprising detail including, e.g., its decays into massive vector bosons.
John Ellis, Summary of the Nobel Symposium on LHC Results,13/09/2013

... par l'un de ceux à qui on doit la recherche effective et la découverte du boson de Higgs
For a decade, very few people took seriously Higgs' prediction of this boson, there being only a handful of papers about before the phenomenological pro le that Mary Gaillard, Dimitri Nanopoulos and I wrote in 1975 [31]. Fortunately, the LHC community did not pay attention to the caveat in the last sentence of our paper that \we do not want to encourage big experimental searches for the Higgs boson", and the ATLAS and CMS experiments announced the discovery of a candidate for a (the?) Higgs boson on July 4th 2012 [32].
Préhistoire du principe de brisure spontanée de symétrie ...
Landau introduced broken symmetry in condensed matter physics (simultaneously with Tisza...), making the simple observation that a symmetry change, being discrete, implies a thermodynamic phase transition. The higher-temperature and more entropic phase, he assumed, should always be averaging over a larger group and hence be more symmetric, though there are a number of cases where this tendency doesn't work.
... I believe it was I who, in 1952, first realised that a massless boson (Goldstone) excitation necesseraly accompanied a broken continuous symmetry, in connection with studying the ground state of an isotropic antiferromagnet. The reason is that the true symmetry must be restored by the zero-point motions, which must therefore have divergent amplitude, hence zero energy. ..
It was also Landau (and here his contribution is clear) who introduced the concept of elementary excitations into condensed matter physics. He pointed out that one could consider the ground state of an ordered solid (or quantum fluid) as analogous to the vacuum of a field theory, and the lowest-energy quantum excitations then would be like quanta of a field and could,, at low temperatures, behave like a rarefied gas of elementary particles. Thus he was generalizing Debye and Einstein's phonon theory of the specific heat of a solid. What Nambu did was to be the first to stand on its head Einstein's progression from light as a classical wave in a medium to light as a gas of photons in vacuum to quantized phonon vibrations in a solid; he proposed that the vacuum was not empty space but a condensed phase which broke some symmetry of space-time...
...the real value of broken symmetry concepts only became apparent when something new and deeply puzzling arrived on the scene. This was the new theory of superconductivity of Bardeen, Cooper and Schrieffer... a lot of discussion revolved around the peculiar fact that although the theory was manifestely neither Galilean nor gauge-invariant, it gave experimental answers which were right on the button.
...we [Nambu and I] both became "captured by the BCS theory".
Both of us realized that the solution to the problem of invariance was the same as it was in other broken symmetry situations: that one has to take into account the zero-point motions of the collective excitations.
...I think I even learned the words [broken symmetry] from him, if not the idea.
But soon he followed it up with something even more radical - the true originof the idea of a dynamical broken symmetry of the vacuum, namely the series of papers with Jona-Lasinio, of which the first was given in April 1960...
To me - and I suppose perhaps even more to his fellow particle theorists - this seemed like a fantastic stretch of the imagination. The vacuum ... had at least since Einstein got rid of the aether, been the epitome of emptiness, the space within which the quanta flew about. Momentarily, Dirac had disturbed us with his view of antiparticles as "holes" in a sea, but by redefining the symmetries of the system to include a new symmetry called charge conjugation, we made that seem to go away. I, at least, had my mind encumbered with the idea that if there was a condensate there was something there, with properties like superconductivity that you could measure. I eventually crudely reconciled myself by realizing that if you were observing from inside the superconductor and couldn't see out you wouldn't have anything observable except the spectrum.
Philip W. Anderson, More and Different, 2011

... par l'un de ces pères fondateurs
Motivated by his work in condensed matter physics, Philip Anderson showed that spontaneous symmetry breaking of gauge symmetry can give mass to the gauge bosons. His mechanism was essentially a nonrelativistic precursor to the Higgs Mechanism . The work was published in Physics Review rather than a condensed matter journal because Anderson thought it relevant to particle physics. The crucial observation was that the troublesome massless Goldstone boson mode is absorbed into the gauge boson field transforming it from the component field of a massless particle to the three component field of a massive one. He did not point out that a massive scalar boson would also be important.
Anderson was overlooked when the 2010 Sakurai prize was given to Higgs, Brout, Englert, Kibble, Guralnik and Hagen for the Higgs mechanism. Some people justify this by pointing out that the relativistic extension of his idea is non-trivial and an important part of the theory. Others say that there is bias against him from particle physicists because he is condensed-matter physicist and argued against funding the American SSC hadron collider. It is a difficult call, he certainly had some of the key elements, but the Nobel Prize is usually only given for more complete theories. In the form presented by Anderson the idea was described by Higgs as crucial but just speculation. At least Higgs cited Anderson’s paper. Brout, Englert, Guralnik, Hagen and Kibble all left the reference out despite being well aware of the prior work.
Anderson has the Nobel Prize from 1977 for work on superconductivity.
Philip Gibbs, There is a Nobel Prize for the Higgs Boson, but who will get it? 17/05/2012