## samedi 18 avril 2015

### (Who is afraid of) the actual silence of these zetta/zepto-spaces (?)

after the SM Higgs discovery by ATLAS, CMS and then CDF and D0
The ATLAS and CMS Collaborations recently reported strong evidence for Higgs boson decays to fermions [25–30], with sensitivity dominated by the H → τ +τ − decay mode, though they have not yet performed spin and parity tests using fermionic decays. The particle decaying fermionically for which the Tevatron also found evidence might not be the same as the particle discovered through its bosonic decays at the LHC. Tests of the spin and parity [23] with Tevatron data therefore provide unique information on the identity and properties of the new particle or particles. The CDF and D0 Collaborations have re-optimized their SM Higgs boson searches to test the exotic Higgs boson models in the WH → ℓνb¯b [31, 32], ZH → ℓ +ℓ −b ¯b [33, 34], and WH + ZH → E/T b ¯b [35, 36] channels, where ℓ = e or µ and E/T is the missing transverse energy [37]...
...we combine CDF’s and D0’s tests for the presence of a pseudoscalar Higgs boson with J P = 0− and a graviton-like boson with J P = 2+ in the WX → ℓνb¯b, the ZX → ℓ +ℓ −b ¯b, and the VX → E/T b ¯b search channels using models described in Ref. [23]. The masses of the exotic bosons are assumed to be 125 GeV/c 2 . No evidence is seen for either exotic particle, either in place of the SM Higgs boson or produced in a mixture with a J P = 0+ Higgs boson. In both searches, the best-fit cross section times the decay branching ratio into a bottom-antibottom quark pair of a J P = 0+ signal component is consistent with the prediction of the SM Higgs boson.
(Submitted on 3 Feb 2015 (v1), last revised 24 Mar 2015 (this version, v2))

... and the last measurement of the astrophysical antiproton to proton ratio by Ams-02
Since decades, the antiproton component in cosmic rays has been recognized as an important messenger for energetic phenomena of astrophysical, cosmological and particle physics nature (see for instance [1, 2, 3]). In modern times, antiprotons have often been argued to be an important diagnostic tool for cosmic ray sources and propagation properties, and constitute one of the prime channels for indirect searches of Dark Matter (DM) [4, 5], which so far has only been detected gravitationally. In DM annihilation (or decay) modes, antiprotons can result either from the hadronization of the primary quarks or gauge bosons or through electroweak radiation for leptonic channels. The Alpha Magnetic Spectrometer (Ams-02) onboard the International Space Station (ISS), is the most advanced detector for such indirect DM searches via charged cosmic ray flux measurements. The positron fraction has been published earlier [6, 7], confirming the rise at energies above 10 GeV detected previously by Pamela [8, 9] and Fermi [10]. The sum of electrons and positrons [11] as well as they separate fluxes [12] have also been published, thus drawing a coherent and extremely precise picture of the lepton components of cosmic rays. Despite the fact that DM interpretations of the positron and, more generally, leptonic ‘excesses’ have been attempted (for a review see [13]), even before the advent of Ams-02 it had been recognized that explanations involving astrophysical sources were both viable and favoured (for a review see [14]), a conclusion reinforced by updated analyses (see [15, 16], and references therein, for recent assessments).
In this paper, we will instead focus on cosmic ray antiprotons. Up to now, the so-called secondary antiprotons (originating from collisions of cosmic ray primaries with the interstellar material) have been shown to account for the bulk of the measured flux [17], thus allowing to derive constraints on the DM parameter space and to compute expected sensitivities, respectively based on updated Pamela data [18] and projected Ams-02 data (see e.g. [19, 20, 21, 22, 23, 24]). Now that the Ams-02 Collaboration has presented its preliminary measurements of the ¯p/p ratio [25], with an improved statistical precision and energy range extending to 450 GeV, it is crucial and timely to re-examine the situation and update previous recent results.
...
In the light of the preliminary results recently presented by Ams-02 on proton and helium fluxes, as well as the antiproton to proton ratio, we have re-evaluated the secondary astrophysical predictions for the antiproton to proton ratio, accounting for the different sources of uncertainties: namely on the injection fluxes, on the production cross sections, on the propagation process and those connected to solar modulation. Our first and main result is that there is no unambiguous antiproton excess that can be identified in the first place, and thus, at this stage, no real need for primary sources of antiprotons. Within errors, secondary astrophysical production alone can account for the data.
(Submitted on 16 Apr 2015)

Poursuivant dans la veine du précédent billet (paraphrasant le même auteur), ce billet ci se voulait une illustration de ce que la physique expérimentale/phénoménologique se nourrit des données empiriques/contraintes qui s'imposent à elle pour lui éviter de délirer et de s'asservir à des ombres...
Puisqu'il est toujours bon d'expliciter ses sources d'inspiration, notons que la notion de zepto-espace qui fait référence à l'échelle caractéristique sondée par le LHC a été magnifiquement popularisée par Gian Francesco Giudice. Quant-à l'odyssée du zetta-espace, elle n'a pas encore été écrite à ma connaissance mais c'est pourtant celle que nous raconte les rayons cosmiques collectés sur Terre et qui ont traversé la Voie Lactée dont la dimension caractéristique est, heureux hasard, de l'ordre du zettamètre ...
La lectrice/le lecteur du jour aura aussi noté ce matin le clin d'oeil à une pensée de Blaise Pascal.

## vendredi 17 avril 2015

### Giving new momentum to the quantization of the spectral noncommutative standard model...

...removing the independent "masslessness of the photon" axiom ?

Noncommutative geometry (NCG) provides a particularly elegant way to derive and describe the structure and the Lagrangian of the Standard Model in curved spacetime and its coupling to gravitation [1]. The main ingredients of this approach is an algebra A=C(M)⊗AF (where M is a Riemann spin manifold M and AF=C⊕H⊕M3(C)) [1] a Hilbert space H=L2(M,S)⊗HF (where HF is 96-dimensional), and a Dirac operator D. The elements a of the algebra are represented by bounded operators π(a) over H. In this approach, the gauge bosons are described by gauge potentials (i.e. non- commutative one-forms) in Ω1DA, where DA is the differential graded algebra (DGA) constructed from A, whose differential is calculated by using the commutator with D.
From the physical point of view, a striking success of the noncommutative geometric approach is that the algebra, the Hilbert space and the Dirac operator of the Standard Model can be derived from a few simple axioms, including the condition of order zero, the condition of order one and the condition of massless photon [2,3,4]. Then, the Lagrangian of the Standard Model coupled to (Riemannian) gravity is obtained by counting the eigenvalues of the Dirac operator D [1].
Still, this approach is not completely physical because it is formulated in the Riemannian (instead of Lorentzian) signature and is not quantized. Therefore, the original NCG approach was variously modiﬁed, by using Lie algebras [5], twisted spectral triples [6] or Lie algebroids and derivation-based NCG [7], to deal with models that do not enter into the standard NCG framework (e.g. quantum groups or Grand Symmetry)[8] ...
Boyle and Farnsworth [9] recently used Eilenberg’s algebra extension method to build an algebra E where the universal differential graded algebra (DGA) Ω built on A (see section III) is extended by the Hilbert space H. This is physically more satisfactory because the gauge ﬁeld, the ﬁeld intensity, the curvature and the Lagrangian densities are noncommutative differential forms, which belong to Ω up to an ideal described below. They observed that the associativity of the algebra E imposes a new condition (of order two) which is satisﬁed by the ﬁnite part AF of the Standard Model and removes a somewhat arbitrary axiom in Chamseddine and Connes’ derivation [4]. This axiom requires the Dirac operator DF of the ﬁnite algebra to commute with a speciﬁc family of elements of AF. It is called the condition of massless photon because it ensures that the photon has no mass.
However, the approach proposed by Boyle and Farnsworth has two serious drawbacks: i) it is not valid for a spin manifold (i.e. the canonical spectral triple (C(M),L2(M,S),DM) does not satisfy the condition of order two); (ii) it uses the DGA algebra Ω in which gauge ﬁelds with vanishing representation (i.e. A ∈ Ω such that π(A)=0) can have non-zero ﬁeld intensity (i.e. π(dA)≠0). This makes the Yang-Mills action ill deﬁned [1]. A consistent substitute for Ω is the space ΩD of noncommutative differential forms which is a DGA built as the quotient of Ω by a differential ideal J usually called the junk. To solve both problems, we deﬁne an extension E of the physically meaningful algebra D of noncommutative differential forms by a representation space MD that we build explicitly. Since the algebra D is a DGA, we require the extension E to be also a DGA and we obtain that MD must be a differential graded bimodule over D (see below). The most conspicuous consequence of this construction is a modiﬁcation of the condition of order two proposed by Boyle and Farnsworth, which provides exactly the same constraints on the ﬁnite part of the spectral triple of the Standard Model, but which is now consistent with the spectral triple of a spin manifold. As a consequence, the full spectral triple of the Standard Model (and not only its ﬁnite part) now satisﬁes the condition of order two and enables us to remove the condition of massless photon.
...
To take into account the differential graded structure of D, we built a differential graded bimodule that takes the junk into account. The grading transforms the Boyle and Farnsworth condition on the commutator [π(δa),π(δb)◦] = 0 into a condition on the anticommutator {π(δa),π(δb)◦} ∈ K, which is now satisﬁed for the full Standard Model and not only for its ﬁnite part.

This indicates that, in a reinterpretation of the noncommutative geometric approach to ﬁeld theory, the differential graded structure of the boson ﬁelds must be accounted for. This is a good news for any future quantization and renormalization of NCG because the differential graded structure is also an essential ingredient of the Becchi-Rouet-Stora-Tyutinand Batalin-Vilkovisky approaches.

Our differential graded bimodule retains the advantages of the Boyle and Farnsworth approach: (i) it uniﬁes the conditions of order zero and one and the condition of massless photon into a single bimodule condition; (ii) it can be adapted to non-associative or Lie algebras.
We hope to use our construction for the quantization of a noncommutative geometric description of the Standard Model coupled with gravity.
(Submitted on 15 Apr 2015)

Voilà une belle illustration de ce que la physique théorique/mathématique (ne) vit (que) des hypothèses /axiomes dont elle se libère un peu comme l'art ne vit que des contraintes qu'il s'impose pour paraphraser Albert Camus (commentant André Gide).

Mise à jour : l'article de Brouder, Bizi et Besnard a reçu récemment un ajout très intéressant dans une seconde version datée du 5 juin que j'évoquerai bientôt.