samedi 31 octobre 2015

One SM gauge singlet scalar for dark matter and the inflaton? Ask Xenon1T!

How physics might be simpler after LHC1 and Planck results
The most studied proposal is that dark matter (DM) is a thermal relic weakly-interacting massive particle (WIMP). WIMPs typically have annihilation cross-sections comparable to the value required to reproduce the observed density of DM, the so-called “WIMP miracle”. Nevertheless, the non-observation of any new weak-scale particles at the LHC beyond the Standard Model (SM) places strong constraints on many models for WIMPs, such as in supersymmetric extensions of the SM. The absence of new particles may indeed indicate that any extension of the SM to include WIMP DM should be rather minimal. In the present work we therefore focus on a particularly simple extension of the SM, namely an additional gauge singlet scalar, which is arguably one of the most minimal models of DM [2–4].  
A similar issue arises from recent constraints on inflation. In fact, the non-observation of non-Gaussianity by Planck [5] suggests that the inflation model should also be minimal, in the sense of being due to a single scalar field. The absence of evidence for new physics then raises the question of whether the inflaton scalar can be part of the SM or a minimal extension of the SM. The former possibility is realized by Higgs Inflation [6], which is a version of the non-minimally coupled scalar field inflation model of Salopek, Bond and Bardeen (SBB) [7] with the scalar field identified with the Higgs boson. A good example for the latter option are gauge singlet scalar extensions of the SM, because the DM particle can also provide a well-motivated candidate for the scalar of the SBB model. In other words, in these models the same scalar particle drives inflation and later freezes out to become cold DM. 
The resulting gauge singlet inflation model was first considered in [8], where it was called S-inflation (see also [9]).[The case of singlet DM added to Higgs Inflation was considered in [10]] All non-minimally coupled scalar field inflation models based on the SBB model are identical at the classical level but differ once quantum corrections to the inflaton potential are included. These result in characteristic deviations of the spectral index from its classical value, which have been extensively studied in both Higgs Inflation [6, 11–15] and S-inflation [16]. Since the original studies were performed, the mass of the Higgs boson [17] and the Planck results for the inflation observables [1] have become known. In addition, direct DM detection experiments, such as LUX [18], have imposed stronger bounds on gauge singlet scalar DM [19–25]. This new data has important implications for these models, in particular for S-inflation, which can be tested in Higgs physics and DM searches. The main objective of the present paper is to compare the S-inflation model with the latest results from CMB observations and direct DM detection experiments. We will demonstrate that — in spite of its simplicity — the model still has a large viable parameter space, where the predictions for inflation are consistent with all current constraints and the observed DM relic abundance can be reproduced. In addition, we observe that this model can solve the potential problem that the electroweak vacuum may be metastable, because the singlet gives a positive contribution to the running of the quartic Higgs coupling. Intriguingly, the relevant parameter range can be almost completely tested by XENON1T.  
Another important aspect of our study is perturbative unitarity-violation, which may be a significant problem for Higgs Inflation. Since Higgs boson scattering via graviton exchange violates unitarity at high energies [26, 27], one might be worried that the theory is either incomplete or that perturbation theory breaks down so that unitarity is only conserved non-perturbatively [28–31]. In both cases there can be important modification of the inflaton potential due to new physics or strong-coupling effects. Indeed, in conventional Higgs Inflation, the unitarity-violation scale is of the same magnitude as the Higgs field during inflation [14, 32], placing in doubt the predictions of the model or even its viability. In contrast, we will show that S-inflation has sufficient freedom to evade this problem, provided that the DM scalar is specifically a real singlet. By choosing suitable values for the non-minimal couplings at the Planck scale, it is possible for the unitarity-violation scale to be much larger than the inflaton field throughout inflation, so that the predictions of the model are robust. Therefore, in addition to providing a minimal candidate for WIMP DM, the extension of the SM by a non-minimally coupled real gauge singlet scalar can also account for inflation while having a consistent scale of unitarity-violation...
We find two distinct mass regions where the model is consistent with experimental constraints from LUX, LHC searches for invisible Higgs decays and Fermi-LAT: the low-mass region, 53 GeV <ms< 62.4 GeV, where DM annihilation via Higgs exchange receives a resonant enhancement, and the high-mass region, ms > 93 GeV, where a large number of annihilation channels are allowed. In both mass regions it is possible without problems to fix the non-minimal couplings ξs and ξh in such a way that inflation proceeds in agreement with all present constraints. In particular, the tensor-to-scalar ratio and the running of the spectral index are expected to be unobservably small. On the other hand, radiative corrections to the spectral index typically lead to a value of ns slightly larger than the classical estimate, i.e. ns > 0.965. This effect is largest for large values of ms and λhs and current Planck constraints already require ms<2 TeV. The entire high-mass region compatible with Planck constraints will therefore be tested by XENON1T, which can constrain gauge singlet scalar DM up to ms ∼ 4 TeV
Felix Kahlhoefer (DESY), John McDonald (Lancaster University)
(Submitted on 13 Jul 2015 (v1), last revised 14 Oct 2015 (this version, v2))

vendredi 30 octobre 2015

Quel Nouveau Mond(e) nous attend à l'échelle de la Voie Lactée et au delà ?

A flash review on the Dark Matter versus Mond debate in cosmology and astrophysics
The achievements of both the standard model (or theory) of particle physics and of the standard (or concordance) model of cosmology ranging from yocto to hundreds of yotta meters must not make us forget that our understanding of physics is still patchy - particularly at intermediate astrophysical scales. Here is a brief but informative summary:
The Dark Matter (DM) paradigm has been remarkably successful at explaining various large-scale observations. The expansion history, the detailed shape of the peaks in the cosmic microwave background (CMB) anisotropy power spectrum, the growth history of linear perturbations and the shape of the matter power spectrum are all consistent with a non-baryonic, clustering component making up ∼ 25% of the total energy budget. Although this is usually hailed as evidence for weakly interacting particles, one should keep in mind that these large-scale observations only rely on the hydrodynamical limit of the dark component. Any perfect fluid with small equation of state (w ' 0) and sound speed (cs ' 0), and with negligible interactions with ordinary matter, would do equally well at fitting cosmological observations on linear scales. 
On non-linear scales, the evidence for DM particles is somewhat less convincing. N-body simulations reveal that DM particles self-assemble into halos with a universal density profile, the NFW profile [1]: ρNFW(r) = ρS/[(r/rS)(1+ r/rS2]. (1)
The density thus scales as ∼r-1 in the interior, and asymptotes to ∼r-3 on the outskirts. The regularity of DM self-assembly is certainly a welcome feature. Unfortunately, the NFW profile does not naturally account for flat rotation curves of spiral galaxies and the isothermality of galaxy clusters, both of which require ρ∼r-2The cold dark matter paradigm also faces challenges on small scales, for instance the cuspiness of galactic cores [2], the mass [4] and phase-space distributions [5–8] of satellite galaxies, and the internal dynamics of tidal dwarfs [9–11]. Of course, N-body simulations do not include baryons, so the NFW profile is not expected to hold exactly in the real universe. But the fact that the “zeroth-order” profile does not readily explain the coarse features of galaxies and clusters of galaxies should at least give us pause. The empirical success or failure of DM particles hinges ultimately on complex baryonic feedback processes. 
Quantifying the impact of baryonic physics is an area of active research, but simulations do not yet offer a clear picture. Even qualitative questions, such as whether baryons make the DM profile more cuspy or shallower in the core of galaxies, are still hotly debated [2]. In the absence of a precise answer, the best one can do when fitting data is incorporate baryonic expectations (e.g., adiabatic contraction [12, 13]) through empirical modifications of the NFW profile. Examples include the generalized NFW profile, cored NFW profile, Buckert profile [14], etc. See [15] for a recent comparison of how these fare at fitting galactic rotation curves. 
Meanwhile, despite the complexity of baryonic physics, actual structures in our universe show a remarkable level of regularity, embodied in empirical scaling relations. A famous example is the Tully-Fisher relation [16], which relates the luminosity of spiral galaxies to the asymptotic velocity v∞ of their rotation curves: L∼v4... Another example is the Faber-Jackson relation [17] for elliptical galaxies L∼σ4, where σ is the stellar velocity dispersion. These relations are quite puzzling from the particle DM perspective — why should the rotational velocity in the galactic tail where DM completely dominates be so tightly correlated with the baryonic mass in the inner region? The hope is that these scaling relations will eventually emerge somehow from realistic simulations of coupled baryons and dark matter

MOdified Newtonian Dynamics (MOND) is a radical alternative proposal [18–20]. It attempts to replace dark matter entirely with a modified gravitational force law that kicks in once the acceleration drops to a critical value a0 : a=aN  if a0≪aand a=√(a0aN) if aN≪a... where aN=GNM(r)/r2 is the standard Newtonian acceleration. By construction, the MOND force law accounts both for the flat rotation curves of spiral galaxies and the Tully-Fisher relation. Indeed, in the MOND regime the acceleration of a test particle orbiting a spiral galaxy satisfies v2/r = √(GNMa0/r2), hence v4= GNMa0 . This matches  the Tully-Fisher relation with M ∼ L... 
An intriguing fact is that the best-fit value for the characteristic acceleration is comparable to the Hubble parameter: a0galaxies≈ 1/6×H0≈1.2 × 10-8 cm/s2.
The MOND force law has been remarkably successful at explaining a wide range of galactic phenomena, from dwarf galaxies to ellipticals to spirals. See [21, 24] for comprehensive reviews. It explains the observed upper limit on the surface brightness of spirals, known as Freeman’s law [25], the characteristic surface brightness in ellipticals, known as the Fish law [26], as well as the FaberJackson law for ellipticals mentioned earlier. Even if DM particles do exist and gravity is standard, Milgrom’s scaling relation (3) should nonetheless be viewed on the same footing as the Tully-Fisher and Faber-Jackson relations. It is a powerful empirical relation that must be explained by standard theories of galaxy formation. 
Unfortunately, the empirical success of MOND is limited to galaxies. On cluster scales, the MOND force law fails miserably [27]. The baryonic component in clusters is dominated by gas, which to a good approximation is in hydrostatic equilibrium and in the MONDian regime. Hydrostatic equilibrium determines the temperature profile T(r) in terms of the observed density profile ρ(r) and the (MONDian) acceleration law a(r). The result does not match the observed isothermal profile of clusters... MOND proponents are forced to assume dark matter, usually in the form of massive neutrinos with mν∼2 eV [30–32] and/or cold (∼ 3K), dense gas clouds [33].  
On cosmological scales, the MOND law requires a relativistic completion. This was achieved just over ten years by Sanders and Bekenstein with a Tensor-Vector-Scalar (TeVeS) theory [34–36]. See [37] for an elegant reformulation of the theory, and [38, 39] for connections to Einstein-aether theories [40]. (Since TeVeS, other relativistic extensions have been proposed [41–44]. See [45] for a review.) First, some good news: perturbations in the vector field accelerate the growth of density perturbations, which allows for the formation of structures. More problematic is the CMB spectrum. An early analysis already revealed some tensions with the height of the third peak [46], and one would expect that the situation is now much worse with the exquisite data at higher multipoles from the Planck satellite [47] and ground-based experiments [48, 49] significant dark matter component, the baryonic oscillations in the matter power spectrum tend to be far too pronounced [46, 51]. Finally, numerical simulations of MONDian gravity with massive neutrinos fail to reproduce the observed cluster mass function [52, 53]. 
To summarize, the Cold Dark Matter (CDM) picture is very successful on linear scales, but the jury is still out as to whether it can explain the detailed structure of galaxies and their empirical scaling relations. MOND, on the other hand, is very successful on galactic scales, but it seems highly improbable that it can ever be made consistent with the detailed shape of the CMB and matter power spectra
Justin Khoury
(Submitted on 29 Aug 2014 (v1), last revised 11 Dec 2014 (this version, v3))


A snapshot of a hypothetical hybridization based on a superfluid analogy
Now let us make a risky step forward in these murky territories all filled with promises and traps. The following is of course highly speculative but I have found it interesting for its use of the superfluid analogy in a quite simple way (but sophisticated motivation) and most importantly for providing a rich list of potential observational implications. 
What we have learned is that MOND and CDM are each successful in almost mutually exclusive regimes... This has led various people to propose hybrid models that include both DM and MOND phenomena [75-79-82]. For instance, one of us recently proposed such a hybrid model, involving two scalar fields [83]: one scalar field acts as DM, the other mediates a MOND-like force law. This model enjoys a number of advantages compared to TeVeS and other relativistic MOND theories. For starters, it only requires two scalar fields, as opposed to the scalar and vector fields of TeVeS. Secondly, unlike TeVeS, its predictions on cosmological scales are consistent with observations, thanks to the DM scalar field. Finally, the model offers a better fit to the temperature profile of galaxy clusters. 
The improved consistency with data does come at the price of having two a priori distinct components — a DM-like component and a modified-gravity component. It would be much more compelling if these two components somehow had a common origin. Furthermore, the theory must be adjusted such as to avoid co-existence of DM-like and MOND-like behavior. This requires that the parameters of the theory be mildly scale or mass dependent, which adds another layer of complexity 
In this paper, along with its shorter companion [84], we propose a unified framework for the DM and MOND phenomena. The DM and MOND components have a common origin, representing different phases of a single underlying substance. This is achieved through the rich and well-studied physics of superfluidity.  
Our central idea is that DM forms a superfluid inside galaxies, with a coherence length of order the size of galaxies. As a back-of-the-envelope calculation, we can estimate the condition for the onset of superfluidity by ignoring interactions among DM particles. With this simplifying approximation, the requirement for superfluidity amounts to demanding that the de Broglie wavelength λdB ∼ 1/mv of DM particles should overlap. Using the typical velocity v and density of DM particles.in galaxies, this translates into an upper bound m <2 eV on the DM particle mass 
Another requirement for Bose-Einstein condensate is that DM thermalize within galaxies. We assume that DM particles interact through contact repulsive interactions. Demanding that the interaction rate be larger than the galactic dynamical time places a lower bound of σ/m>0.1cm2/g. This is just below the most recent constraint <0.5cm2/g from galaxy cluster mergers [85], though we will argue such constraints must be carefully reanalyzed in the superfluid context.  
Again ignoring interactions, the critical temperature for DM superfluidity is Tc∼mK, which intriguingly is comparable to known critical temperatures for cold atom gases, e.g., 7Li atoms have Tc0.2 mK. We will see that cold atoms provide more than just a useful analogy — in many ways, our DM component behaves exactly like cold atoms. In cold atom experiments, atoms are trapped using magnetic fields; in our case, it is gravity that attracts DM particles in galaxies 
The superfluid nature of DM dramatically changes its macroscopic behavior in galaxies. Instead of behaving as individual collisionless particles, the DM is more aptly described as collective excitations: phonons and massive quasi-particles. Phonons, in particular, play a key role by mediating a long-range force between ordinary matter particles. As a result, a test particle orbiting the galaxy is subject to two forces: the (Newtonian) gravitational force and the phonon-mediated force. Our postulate is that the phonon-mediated force is MONDian, such that the DM superfluid reproduces the empirical success of MOND in galaxies  
Specifically, it is well-known that the effective field theory (EFT) of phonon excitations at lowest order in derivatives is in general a P(X) theory [86]. Our postulate is that DM phonons are described by the non-relativistic MOND scalar action, 
P(X) ∼ ΛX √|X|;    X = θ' − mΦ − (θ)2/2m . (4) 
where Λ ∼ meV to reproduce the MOND critical acceleration, and Φ is the gravitational potential [The possible connection between MOND and superfluidity was mentioned briefly by Milgrom in [87]...]. To mediate a force between ordinary matter, θ must couple to the baryon density: 
Lint ∼ (Λ/ MPl) θρb . (5) 
From a particle physics standpoint, such a coupling is fairly innocuous — it represents a soft explicit breaking of the global U(1) symmetry. In the superfluid interpretation, however, where θ is the phase of a wavefunction, this coupling picks out a preferred phase, which seems unphysical. One possibility is that (5) follows from baryons coupling to the vortex sector of the superfluid... , 
[In the quasi-static limit (θ'=0) our action ∼X3/2 becomes invariant under time-dependent spatial Weyl transformations: hij→Ω2(x,t)hij [96, 97]. At lowest order in derivatives it is the unique action with this property. Intriguingly, the SO(4,1) global part of the 3d Weyl group coincides with the de Sitter isometry group, which hints at a deep connection between the MOND phenomenon and dark energy [97]]. The fractional 3/2 power would be strange if (4) described a fundamental scalar field. As a theory of phonons, however, it is not uncommon to see fractional powers in cold atom systems. For instance, the Unitary Fermi Gas (UFG) [91, 92], which has generated much excitement recently in the cold atom community, describes a gas of cold fermionic atoms tuned such that their scattering length diverges [9394]. The effective action for the UFG superfluid is uniquely fixed by 4d scale invariance at lowest-order in derivatives, LUFG(X) ∼ X5/2 , which is also non-analytic [95]...
As is familiar from liquid helium, a superfluid at finite temperature (but below the critical temperature) is best described phenomenologically as a mixture of two fluids [98–100]: i) the superfluid, which by definition has vanishing viscosity and carries no entropy; ii) the “normal” component, comprised of massive particles, which is viscous and carries entropy. The fraction of particles in the condensate decreases with increasing temperature. Thus our framework naturally distinguishes between galaxies (where MOND is successful) and galaxy clusters (where MOND is not). Galaxy clusters have a higher velocity dispersion and correspondingly higher DM temperature. For m∼ eV we find that galaxies are almost entirely condensed, whereas galaxy clusters are either in a mixed phase or entirely in the normal phase 
Assuming hydrostatic equilibrium with P∼ρ3, the resulting DM halo density profile is cored, not surprisingly, and therefore avoids the cusp problem of CDM. Remarkably, for our parameter values (m∼eV, Λ∼ meV) the size of the condensate halo is ∼100 kpc for a galaxy of Milky-Way mass. In the inner region of galaxies where rotation curves are probed, the DM condensate has a negligible effect on baryonic particles, and their motion is dominated by the phonon-mediated MOND force. In the outer region probed by gravitational lensing, the DM condensate gives the dominant contribution to the force on a test particle.  
In the vicinity of individual stars the phonon effective theory breaks down and the correct description is in terms of normal DM particles. This is good news on two counts. First, it is well-known that the MONDian acceleration, while giving a small correction to Newtonian gravity in the solar system, is typically too large to conform to planetary orbital constraints. This usually requires introducing additional complications to the theory [101]. In our case, the MONDian behavior is avoided entirely in the solar system, as DM behaves as ordinary particles. The second piece of good news pertains to experimental searches of axion-like particles. By allowing the usual axion-like couplings to Standard Model operators, our DM particles can be detected through the suite of standard axion experiments, e.g., [102].

The idea of a Bose-Einstein DM condensate (BEC) in galaxies has been studied before [103, 104, 113–125].5 There are important differences with the present work. In BEC DM galactic dynamics are caused by the condensate density profile, similar to what happens in CDM, with phonons being irrelevant. In our case, phonons play a key role in generating flat rotation curves and explaining the BTFR. Moreover, the equation of state is different: the BEC DM is governed by two-body interactions and hence has P∼ρ2, compared to ∼ρin our case. This difference only has a minor effect on the condensate density profiles, but it does imply a different phonon sound speed. In particular, for the Bullet Cluster the sound speed in BEC DM is only cs ∼<100 km/s, i.e., more than an order of magnitude smaller than the bullet infall velocity. As a result dissipation is important, which puts BEC DM in tension with observations [129]. 
(Submitted on 3 Jul 2015)

We conclude with some astrophysical implications of our DM superfluid: 
Vortices: When spun faster than a critical velocity, a superfluid develops vortices. The typical angular velocity of halos is well above critical [24], giving rise to an array of DM vortices permeating the disc [51]. It will be interesting to see whether these vortices can be detected through substructure lensing, e.g., with ALMA [52]. 
Galaxy mergers: A key difference with ΛCDM is the merger rate of galaxies. Applying Landau’s criterion, we find two possible outcomes. If the infall velocity vinf is less than the phonon sound speed cs (of order the viral velocity [24]), then halos will pass through each other with negligible dissipation, resulting in multiple encounters and a longer merger time. If vinf >cs, however, the encounter will excite DM particles out of the condensate, resulting in dynamical friction and rapid merger. 
Bullet Cluster: For merging galaxy clusters, the outcome also depends on the relative fraction of superfluid vs normal components in the clusters. For subsonic mergers, the superfluid cores should pass through each other with negligible friction (consistent with the Bullet Cluster), while the normal components should be slowed down by self interactions. Remarkably this picture is consistent with the lensing map of the Abell 520 “train wreck” [53– 56], which show lensing peaks coincident with galaxies (superfluid components), as well as peaks coincident with the X-ray luminosity peaks (normal components). 
Dark-bright solitons: Galaxies in the process of merging should exhibit interference patterns (so-called darkbright solitons) that have been observed in BECs counterflowing at super-critical velocities [57]. This can potentially offer an alternative mechanism to generate the spectacular shells seen around elliptical galaxies [58]. 
Globular clusters: Globular clusters are well-known to contain negligible amount of DM, and as such pose a problem for MOND [59]. In our case the presence of a significant DM component is necessary for MOND. If whatever mechanism responsible for DM removal in ΛCDM is also effective here, our model would predict DM-free (and hence MOND-free) globular clusters
(Submitted on 25 Jun 2015)

A last reminder on the experimental physics of the unitary Fermi gas 
After such wild quantum speculations let's landing on down to Earth tabletop experiments but still fascinating physics:
Ultracold Fermi gases are dilute systems with interparticle interactions that can be controlled through Feshbach resonances, which allow the access of strongly interacting regimes. Until recently, superfluids were classified as either Bardeen-Cooper-Schrieffer (BCS) states or the Bose-Einstein Condensate (BEC). In fact they are limit cases of a continuum of the interaction strength. The possibility of tuning the parameters to observe changes from one regime to the other is conceptually interesting, but real enthusiasm came from the experimental realization of the BCS-BEC crossover [1]. 
The three dimensional unitary Fermi gas is a strongly interacting system with short-range interactions of remarkable properties. When the scattering length a diverges, 1/akF →0 (kF is the Fermi momentum of the system), the low-energy s-wave scattering phase shift is δ0=π/2. The ground state energy per particle E0 is proportional to the one of the noninteracting Fermi gas EFG in a box: 
E0EFG= ξ(3/10) 2kF2/M,  (1)  
where the constant ξ is known as the Bertsch parameter and M is the mass of the fermion. In the limit akF →∞, quantum Monte Carlo (QMC) results give the exact value of ξ = 0.372(5) [2], in agreement with experiments [3, 4]. 
One signature of superfluidity is the formation of quantized vortices. Since their first observations in superfluid 4He a large body of experimental and theoretical work has been carried out concerning bosonic systems [5–8]. On the other hand, the discovery of vortex lattices in a strongly interacting rotating Fermi gas of 6Li [9] was a milestone in the study of superfluidity in cold Fermi gases. 
A vortex line consists of an extended irrotational flow field, with a core region where the vorticity is concentrated. The quantization of the flow manifests itself in the quantized units h/2M of circulation. There is no evidence for quantized vortices with more than one unit of circulation. Many questions remain to be answered concerning the structure of the vortex core for fermions...

(Submitted on 27 Oct 2015)
 

mardi 13 octobre 2015

How could the standard model (core theory) be natural?

Taking into account neutrino mixing ...
The problem of the Higgs boson naturalness as phrased according to the current consensus in theoretical physics community (as well as its ideological use in experimental high energy physics programs) has already been evocated in this blog. I propose today to report on last developments of a work conducted mainly by Bryan Lynn under the seemingly mathematical scrutiny of late Raymond Stora that sheds an original light on this issue.
We defined the νDSMG as the global SU(3)C×SU(2)L×U(1)Y model of a complex Higgs doublet, and Standard Model (SM) quarks and leptons, augmented by 3 right-handed neutrinos with Dirac masses. With SM isospin and hypercharge assignments for fermions, νDSMG has zero axial anomaly. We showed that the weak-scale low-energy effective Lagrangian of the spontaneously broken νDSMG is severely constrained by, and protected by, new rigid/global spontaneous symmetry breaking (SSB) axial-vector Ward-Takahashi identities (WTI) and a Goldstone theorem, In particular, the weakscale SSB νDSMG has an SU(2)L shift symmetry... which protects it from any Brout-Englert-Higgs fine-tuning problem, and causes the complete decoupling of certain heavy M2 Heavy m2 W eak BSM matter-particles. (Note that such decoupling is modulo special cases: e.g. heavy Majorana νR, and possibly .... dimension≤ 4 operators, non-analytic in momenta or a renormalization scale µ2, involve heavy particles, and are beyond the scope of this paper.) Renormalized observable <H>2 , m2h;pole are therefore not fine-tuned, but instead Goldstone Exceptionally Natural, with far more powerful suppression of fine-tuning than G. ’t Hooft’s naturalness criteria [... 13] would demand 
But such heavy-particle decoupling is historically (i.e. except for high-precision electro-weak S,T and U parameters [... 46]) the usual physics experience, at each energy scale, as experiments probed smaller and smaller distances. After all, Willis Lamb did not need to know the top quark or BEH mass [47] in order to interpret theoretically the experimentally observed O(meα5ln α) splitting in the spectrum of hydrogen. Such heavy-particle decoupling may be the reason why the Standard Model, viewed as an effective low-energy weak-scale theory, is the most experimentally and observationally successfull and accurate theory of Nature known to humans, i.e. when augmented by classical General Relativity and neutrino mixing: that “Core Theory” [48] has no known experimental or observational counterexamples...

Imagine we are able to extend this work to the Standard Model itself...! With its local/gauge group SU(3)Color×SU(2)L×U(1)Y , we would build 3 sets of rigid/global WTIs: unbroken SU(3)Color; unbroken electromagnetic U(1)QED; and spontaneously broken SU(2)L. It is then amusing to elevate such rigid/global WTIs to a “Principle of Nature”, so as to give them predictive power for actual experiments and observations. The SU(3)Color and U(1)QED WTIs are unbroken vector-current IDs, and will not yield information analogous with that of SSB extended-AHM here. But the axial-vector current inside the SSB SU(2)L WTIs will require and demand a nonzero SSB Dirac mass for each and every one of the the weak-interaction eigenstates mDiracνe, mDiracνµ , mDiracντ  0. The observable PNMS mixing matrix would then rotate those to mass-eigenstates mDiracν1 , mDiracν2 , mDiracν3   0. Would we then claim that spontaneouly broken SU(2)L WTIs predict neutrino oscillations? To make possible connection with Nature, although current experimental neutrino mixing data cannot rule out an exactly-zero mass for the lightest neutrino..., the mathematical self-consistency of SU(2)L WTIs would! 

(Submitted on 21 Sep 2015)

jeudi 8 octobre 2015

Neutrino mixing : a small step beyond the Standard Model and a giant leap for geometry of spacetime?

A snapshot of the benefits of the important empirical fact of neutrino oscillations for the building of spectral noncommutative models
I have chosen to celebrate the 2015 physics Nobel prize in a way you will probably not find anywhere else. I find it interesting indeed to underline the fact that the experimental evidence of neutrino mixing has not only provided us with the first hint of new physics beyond the standard model but also triggered a decisive progress in a potential better understanding in the geometric raison d'être for the standard model paving the way to its extension at higher energy. 
The present paper shows that the modification of the standard model required by the phenomenon of neutrino mixing in fact resulted in several improvements on the previous descriptions of the standard model via noncommutative geometry. In summary we have shown that the intricate Lagrangian of the standard model coupled with gravity can be obtained from a very simple modification of space-time geometry provided one uses the formalism of noncommutative geometry. The model contains several predictions and the corresponding section 5 of the paper can be read directly, skipping the previous sections.
(Submitted on 23 Oct 2006)


In our first approach [8] to the understanding of the Lagrangian of the Standard Model coupled to gravity, we used the above new paradigm of spectral geometry to model space-time as a product of an ordinary 4-manifold (we work after Wick rotation in the Euclidean signature) by a finite geometry F. This finite geometry was taken from the phenomenology i.e. put by hand to obtain the Standard Model Lagrangian using the spectral action. The algebra AF , the Hilbert space HF and the operator DF for the finite geometry F were all taken from the experimental data. The algebra comes from the gauge group, the Hilbert space has as a basis the list of elementary fermions and the operator is the Yukawa coupling matrix. This worked fine for the minimal Standard Model, but there was a problem [31] of doubling the number of Fermions, and also the Kamiokande experiments on solar neutrinos showed around 1998 that, because of neutrino oscillations, one needed a modification of the Standard Model incorporating in the leptonic sector of the model the same type of mixing matrix already present in the quark sector. One further needed to incorporate a subtle mechanism, called the see-saw mechanism, that could explain why the observed masses of the neutrinos would be so small. At first our reaction to this modification of the Standard Model was that it would certainly not fit with the noncommutative geometry framework and hence that the previous agreement with noncommutative geometry was a mere coincidence. After about 8 years it was shown in [19] and [13] that the only needed change (besides incorporating a right handed neutrino per generation) was to make a very simple change of sign in the grading for the anti-particle sector of the model (this was also done independently in [3]). This not only delivered naturally the neutrino mixing, but also gave the see-saw mechanism and settled the above Fermion doubling problem. The main new feature that emerges is that when looking at the above table of signs giving the KO-dimension, one finds that the finite noncommutative geometry F is now of dimension 6 modulo 8. Of course the space F being finite, its metric dimension is 0 and its inverse line-element is bounded. In fact this is not the first time that spaces of this nature— i.e. whose metric dimension is not the same as the KO-dimension— appear in noncommutative geometry and this phenomenon had already appeared for quantum groups and related homogeneous spaces [23].
... since we want the finite geometry F to be of KO dimension 6, we are left only with the second case and we obtain among the very few choices of lowest dimension the case AF = M2()⊕M4() where H is the skew field of quaternions... 
We can now describe the predictions obtained by comparing the spectral model with the standard model coupled to gravity. The status of “predictions” in the above spectral model is based on two hypothesis: 
(1) The model holds at unification scale 
(2) One neglects the new physics up to unification scale. 
The spectrum of the fermionic particles, which is the number of states in the Hilbert space per family is predicted to be 42 = 16 which is a consequence of the algebra of the discrete space being M2()⊕M4(). In addition the surviving algebra consistent with the axioms of noncommutative geometry, in particular the order one condition, is given by ⊕M3() which gives rise to the gauge group of the standard model. A consequence of this is that the 16 spinors get the correct quantum number with respect to the standard model gauge group which follows the decomposition:  
(4, 4) → (1R+1'R+2L, 1+3) = (1R, 1) + (1'R, 1) + (2L, 1) + (1R, 3) + (1'R, 3) + (2L, 3) 
These spinors correspond to νR, eR, lL, uR, dL, qL respectively, where lL is the left-handed neutrino-electron doublet and qL is the left-handed up-down quark doublet. In addition to the gauge bosons of SU(3)×SU(2)×U(1) which are the inner fluctuations of the metric along continuous directions, we also have a Higgs doublet which correspond to the inner fluctuations of the metric along the discrete directions. What is peculiar about this Higgs doublet, is that its mass term as determined from the spectral action comes with a negative sign and a quartic term with a plus sign, thus predicting the phenomena of spontaneous breakdown of the electroweak symmetry


If you ask for the theoretical physics' community (string theory oriented?) take about the relevance of such a sophisticated lift of degeneracy between two concepts of dimension you can start reading the following answer by Urs Schreiber on Physics Stack Exchange
If you think K-theory is useless for physics think again and have a look at the recent developments in the field of topological insulators and superconductors and their periodic table (the Physics Nobel Prize 2016 for David Thouless is my guess for next year). 

As far as the phenomenologists are concerned I guess the following skeptical blog post gives an idea of the consensus:
Is it possible that [Connes'] approach will provide new insights into the Standard Model and beyond? Not likely. As far as I understood, the fine structure of space-time has no implications that could be observed at the LHC or in other experiments in foreseeable future. Next, the Standard Model is not a unique system that allows for such a geometrical embedding.
Alain Connes' Standard Model, Jester Sunday 11 February 2007


I think time is proving Jester was not right. The fine structure of space-time has definitely a strong implication that has been observed at the LHC : there is one Standard Model like Higgs scalar visible at the TeV scale and probably no superparticle to make it purportedly natural!
The reader will find in the next paragraph more about this. 


Echo at the electroweak scale?


... the Higgs-Brout-Englert boson has been discovered with a mass around 125 GeV. This mass is problematic, or at least intriguing, because it lies just below the threshold of stability, meaning that electroweak vacuum is a metastable state rather than a stable one. One solution to stabilize the electroweak vacuum is to postulate there exists another scalar field, called σ, suitably coupled to the Higgs. Chamseddine and Connes have noticed in [14] that taking into account this new scalar field in the spectral action, by promoting the Yukawa coupling of the right neutrino (which is one of the constant component of the matrix DF ) to a field, 
kR → kR σ, (13) 
then one obtains the correct coupling to the Higgs as well as a way to pull back the mass of the Higgs from 170 to 126GeV. In [10, 15], ... its is shown how the substitution (13) can be obtained as a fluctuation of the Dirac operator, but in a slightly modified version inspired by the notion of twisted spectral triple introduced previously by Connes and Moscovici. The field σ thus appears as a Higgs-like field associated to a spontaneous symmetry breaking to the standard model of a “grand symmetry” model where the spin degrees of freedom (C(M) acting on the space of spinors) are mixed with the internal degrees of freedom (AF acting on the space of particles)
Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity Pierre Martinetti 2015



As already mentioned in former posts, this sigma field and its corresponding new singlet scalar boson should not be directly testable in a foreseeable future. It happens indeed that despite being linked to a natural type I see-saw mechanism that explains the low masses of left-handed neutrinos with the existence of right-handed Majorana neutrinos this scenario might be hard to test experimentally. Nevertheless neutrino physics seems to be full of surprise so let's wait and see... 
On the cosmological frontier I think it is reasonable to say that the sigma field can be interpreted as the B-L Higgs and as such it might be a good candidate for an inflaton. So who knows if one cannot hope for any indirect experimental tests?

Last but not least, I want to stress that the finite algebra A=M2()⊕M4() singled-out by noncommutative geometry - in hindsight thanks to the neutrino oscillations observations - has recently been proved to coincide exactly with the solution to encode 4-dimensional spin geometries with quantized volume in an operator algebraic way. Given that this last development due to Connes, Chamseddine and Mukhanov provides both a tentative picture for quanta of geometry and a geometrical setting for the new conformal degree of freedom of gravity uncovered by the last two authors, given that the first theoretical development can pave the way to a solution of the cosmological constant problem and the second one gives some hints for the dark matter and dark energy puzzles I hope to have convinced you that the neutrinos have already helped a lot noncommutative geometers to get a better insight into the Standard Model and beyond! And I think this is just a start... 


//last edition 1011/10/15