### If ifs and ands were safe and secured/Avec quelques si et une poignée de et ...

**... there'd be already a known left handed neutrino mass spectrum**

**! / on connaitrait déjà le spectre de masse des neutrinos de chiralité gauche!**

We present cosmological upper limits on the sum of active neutrino masses using large-scale power spectrum data from the WiggleZ Dark Energy Survey and from the Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) sample of Luminous Red Galaxies (LRG). Combining measurements on the Cosmic Microwave Background temperature and polarisation anisotropies by the Planck satellite together with WiggleZ power spectrum results in a neutrino mass bound of 0.37 eV at 95% confident level(C. L.), while replacing WiggleZ by the SDSS-DR7 LRG power spectrum, the 95% C.L. bound on the sum of neutrino masses is 0.38 eV.Adding Baryon Acoustic Oscillation (BAO) distance scale measurements, the neutrino mass upper limits greatly improve, since BAO data break degeneracies in parameter space.Within a ΛCDM model, we find an upper limit of 0.13 eV (0.14 eV) at 95% C.L., when using SDSSDR7 LRG (WiggleZ) together with BAO and Planck. The addition of BAO data makes the neutrino mass upper limit robust, showing only a weak dependence on the power spectrum used. We also quantify the dependence of neutrino mass limit reported here on the CMB lensing information.The tighter upper limit (0.13 eV) obtained with SDSS-DR7 LRG is very close to that recently obtained using Lyman-alpha clustering data, yet uses a completely different probe and redshift range, further supporting the robustness of the constraint. This constraint puts under some pressure the inverted mass hierarchy and favours the normal hierarchy

(Submitted on 18 Nov 2015 (v1), last revised 28 Apr 2016 (this version, v3))

A recent seminar at Fermilab reviewed the status of the sum of the masses of neutrinos from various cosmological measurements [1]. If those limits are taken seriously then we already have measurements of the masses of the three neutrinos with some precision. This note reduces the simple algebra of the neutrino masses to graphical form to illustrate this.The cosmological limits on the sum of neutrino masses is a long and growing list of measurements [2].I have chosen to use the latest result of the Planck collaboration [3], M = Σ m, to work in units of meV since all the interesting numbers are cleanly represented to appropriate precision as integers, and to use the PDG’s averages for the neutrino masssquared differences:_{i}< 230 meV

*∆m*

_{12}^{2}= m_{2}^{2}− m_{1}^{2}= 75.3 ± 1.8 meV^{2}*∆m*

_{32}^{2}= m_{3}^{2}− m_{2}^{2}= 2420 ± 60 meV^{2}Normal hierarchy*−∆m*

_{32}^{2}= m_{2}^{2}− m_{3}^{2}= 2490 ± 60 meV^{2}Inverted hierarchy*M = Σ m*

_{i}= m_{1}+ m_{2}+ m_{3}The dependence of the masses of the three neutrinos as a function of M, the sum of the masses, are shown as the colored curves of figure {below}. These curves illustrate the well known results that the minimum mass of the heaviest neutrino is 50 meV for either hierarchy and the minimum sum of the neutrino masses are 59 meV and 98 meV for the Normal and Inverted hierarchies respectively. The bounds on M are shown as dashed lines on figure 1: the lower bound from the non-negativity of the lightest neutrino mass, and the upper bound from the Planck experimental limit.

The Planck limit is a 95%CL upper bound; there is a 5% probability that the physical value is higher. Ignoring that 5%the probability distribution for M is taken to be a box with zero probability beyond the limits and a constant between them representing our lack of any prior knowledge of the value of M within the limits. Those who have used wire chambers know by rote that the mean and standard deviation of a box distribution of width w are < w >= w/2 and σ = w/√ 12 respectively. Applying these to the normal and inverted hierarchy bounds yield measurements of M = 145 ± 49 meV and M = 165 ± 38 meV respectively.These values are shown as the point with horizontal error bars on figure {above}.Propagating those uncertainties to the individual neutrino masses yields the three colored points with error bars in the figure which are tabulated in table {below}.

The short summary is that the heaviest neutrino is 63 ± 11 meV and the lightest 40 ± 18 meV independent of hierarchy with differences small compared to the uncertainties. The error bars are slightly asymmetric due to the curvature of the mass curves, again with small differences compared to the uncertainties.As {the} figure {above} shows the three neutrino masses measured in this way are completely correlated: if M goes down all three massesm_{i}go down together...

A most important consideration is the subjunctive with which this paper began:If the cosmological limits on the sum of the neutrino masses are taken seriously.If these limits get down to < 100 meV , and are correct, then the Inverted hierarchy is ruled out and the neutrino masses would be measured with lower values and precisions of a few percent for the heaviest state. These would be very important results whose reliability can, and will, be vigorously questioned. The connection between the observables in experiments like Planck and the sum of the neutrino masses includes Physics modeling which is subject to systematic uncertainties.Critical evaluation of those systematics are serious questions which must be left to, and defended by, the experts in those models and experiments. Improvements to the < 100 meV level in direct measurements of a neutrino mass; the endpoint in Tritium beta decay, for example, will require advancements in experimental techniques which are, thus far, unachieved. People are trying [5].

(Submitted on 10 May 2016)

We study the phenomenological consequences of recent results from atmospheric and accelerator neutrino experiments, favoring normal neutrino mass orderingm_{1}<m_{2}<m_{3}, a near maximal lepton Dirac CP phase δ_{l}∼270° along with θ_{23}≥45°, for possible realization of natural structure in the lepton mass matrices characterized by (M_{ij})∼ O(√m_{i}m_{j}) for i, j=1,2,3. It is observed that deviations from parallel texture structures for M_{l}andM_{ν}are essential for realizing such structures. In particular,such hierarchical neutrino mass matrices are not supportive for a vanishing neutrino massm_{ν1}→0 characterized by DetM≠_{ν}0 and predict m_{ν1}≈ (0.1−8.0)meV,m_{ν2}≈(8.0−13.0)meV,m_{ν3}≈(47.0−52.0)meV, Σ≈(56.0−71.0)meV and <mee>≈(0.01−10.0)meV, respectively, indicating that the task of observing a 0νββ decay may be rather challenging for near future experiments.

Implications of δCPl∼270° and θ23≳45° for texture specific lepton mass matrices and 0νββ decayRohit Verma (Submitted on 4 Jul 2016)

**... and a potential trio of ultra heavy right handed counterparts?/ et celui des neutrinos droits?**

We perform numerical fits of Grand Unified Models based on SO(10), using various combinations of 10-, 120- and 126-dimensional Higgs representations. Both the supersymmetric and non-supersymmetric versions are fitted, as well as both possible neutrino mass orderings. In contrast to most previous works, we perform the fits at the weak scale, i.e. we use RG evolution from the GUT scale, at which the GUT-relations between the various Yukawa coupling matrices hold, down to the weak scale. In addition, the right-handed neutrinos of the seesaw mechanism are integrated out one by one in the RG running. Other new features are the inclusion of recent results on the reactor neutrino mixing angle and the Higgs mass (in the non-SUSY case). As expected from vacuum stability considerations, the low Higgs mass and the large top-quark Yukawa coupling cause some pressure on the fits. A lower top-quark mass, as sometimes argued to be the result of a more consistent extraction from experimental results, can relieve this pressure and improve the fits.We give predictions for neutrino masses, including the effective one for neutrinoless double beta decay, as well as the atmospheric neutrino mixing angle and the leptonic CP phase for neutrino oscillations.

(Submitted on 19 Jun 2013 (v1), last revised 14 Sep 2013 (this version, v3))

I have emphasized one line of the table corresponding to a specific non supersymmetric SO(10) model model discussed in the next paragraph.

**...compatible with a partial unification scale type I seesaw mechanism and a flavoured leptogenesis?/ tous deux compatibles avec un mécanisme de bascule à une énergie d'unification partielle et une leptogénèse avec de forts effets de saveurs.**

We consider SO(10) Grand Unified Theories (GUTs) with vacuum expectation values (vevs) for fermion masses in the 10+126 representation. We show that the baryon asymmetry generated via leptogenesis is completely determined in terms of measured low energy observables and of one single high energy parameter related to the ratio of the 10 and 126 SU(2) doublet vevs. We identify new decay channels for the heavy Majorana neutrinos into SU(2) singlet leptons ec which can sizably affect the size of the resulting baryon asymmetry.We describe how to equip SO(10) fits to low energy data with the additional constraint of successful leptogenesis, and we apply this procedure to the fits carried out in {the article above}. We show that a baryon asymmetry in perfect agreement with observations is obtained.

(Submitted on 15 Dec 2014 (v1), last revised 29 Jan 2015 (this version, v2))

The most popular explanation for the neutrino mass suppression is undoubtedly provided by the see-saw mechanism [2] which requires the existence of very heavy right-handed (RH) Majorana neutrinos.Fermions with quantum numbers of RH neutrinos, that are singlets under the standard model (SM) gauge group, are found in the spinorial 16 representation of SO(10) [3, 4], which therefore provides a quite natural Grand Unified Theory (GUT) framework to embed the see-saw...

The see-saw RH neutrinos also play a key role in leptogenesis [5, 6], which is a very appealing scenario to explain the origin of the Baryon Asymmetry of the Universe (BAU). In leptogenesis, the cosmological baryon asymmetry is seeded by an initial asymmetry in lepton number generated in the out-of-equilibrium decay of the RH neutrinos, that is then transferred in part to baryons by means of the B + L violating ‘sphaleron’ interactions, that are non-perturbative SM processes. In SO(10), the order of magnitude of the RH neutrino masses is fixed around the scale of the spontaneous breaking of theU(1)_{B-L}symmetry, and it is consistent with the values of the RH neutrino masses required for successful leptogenesis M_{R}∼10...^{11±2}GeV. Indeed, the double role of RH neutrinos in the see-saw and in leptogenesis underlines the importance of deriving information on their mass spectrum

Recently, an analysis of the relations between the left-handed (LH) neutrino observables (mass-squared differences and mixings) and the RH neutrino spectrum, constrained to be of a compact form (i.e. with masses all of the same order of magnitude) was carried out within the framework of an SO(10)-inspired model[7], and a scenario for baryogenesis via leptogenesis was also constructed. The study in Ref. [7] was carried out under the simplifying assumption of a vanishing value of the lepton mixing angleθ_{13}, and in the leptogenesis analysis all lepton flavour effects [8a,8b,9,10] as well as the effects from the heavier RH neutrinos [11,12] had been neglected. However, recent experimental results hint to a nonvanishing value ofθ_{13}[13,14,15] and imply that the assumption θ_{13}=0 should be dropped.The inclusion of flavour effects isalsomandatory when leptogenesis occurs below T∼10^{12}GeV, since the one flavour ‘approximation’ is known to give unreliable results. Moreover, in the case of a compact RH spectrum, that is when all the RH neutrino masses fall within a factor of a few, to obtain a trustworthy result it is also necessary to include the asymmetry production and washouts from the two heavier RH neutrinos...

In the present paper we consider a scenario similar to the one in Ref. [7] improving on several points. We fixθ_{13}to the nonvanishing best fit value given in Ref. [15]. This in turn implies that the Dirac phase δ of the Pontecorvo, Maki, Nagakawa and Sakata (PMNS) mixing matrix [16, 17] enters all the equations, and in particular contributes to the leptogenesis CP asymmetries. Most importantly, we clarify how the conditions ensuring a compact RH neutrino spectrum have consistent solutions only for δ ≠ 0, and how the corresponding solutions yield a surprisingly predictive scenario in which all the yet unknown low energy parameters, namely the LH neutrino mass scale m1 and the three PMNS CP violating phases δ, α and β, remain determined in terms of already measured quantities, modulo a few signs ambiguities. In the high energy sector, the RH neutrino spectrum is also predicted.The crucial test of the scenario is then the computation of the baryon asymmetry yield of leptogenesis. We include lepton flavour effects[8a,8b,9,10]in our analysis and argue that they are crucial to evaluate correctly the baryon asymmetry. Most importantly, the high level of predictability of our framework allows to predict both the size and the sign of the BAU. By requiring agreement with observations, we are then able to solve almost completely the residual signs ambiguities.

(Submitted on 5 Mar 2012 (v1), last revised 18 Jul 2012 (this version, v2))

The confirmation of the Brout-Englert-Higgs mechanism with the discovery of the Higgs boson at the LHC, an important ingredient of the seesaw mechanism, certainly corroborates the overall picture of leptogenesis. In addition, the non-discovery of new physics at LHC so far, quite strongly constrains models of baryogenesis at the TeV (or lower) energy scale. Moreover if the recent claim of a Bmode polarization signal in the CMB will be (even partially) confirmed (see [4a,4b] for critical analyses of BICEP2 results), it would support high inflationary scale V^{1/4}∼10^{16}GeV [5]. In this way high values of the reheat temperatureT_{RH}, though not necessarily implied, would be not only possible but even quite natural. This phenomenological picture is then well compatible with the original idea of a high energy scale thermal leptogenesis scenario, much above the TeV scale [2].

Values of T_{RH}greater than those required by successful leptogenesis,T_{RH}>10^{9}GeV [6a,6b,7], would be not only possible but even, as already mentioned, quite natural if the BICEP2 signal, even just a small fraction of it, will be confirmed as primordial.

(Submitted on 20 Nov 2014 (v1), last revised 9 Feb 2015 (this version, v3))

**History teaches us a bit of caution/ L'histoire nous apprend à être prudent**

The indications for neutrino mass from cosmology has kept changing for the last 20 years. In the scientific literature it is possible to find several authoritative claims for a non-zero value for Σ but these values cannot be all correct (at least), since they are different among each other. This calls us for a cautious attitude in their interpretation...

Evolution of some significant values for {the sum of the three active neutrino masses} Σ as indicated by cosmology, based on well-known
works [11, 12, 13, 14]. Since the error for the first value is not reported in the reference,
we assumed an error of 50% for the purpose of illustration. The yellow region includes values of
Σ compatible with the N H spectrum, but not with the IH one. The gray band includes values
of Σ incompatible with the standard cosmology and with oscillation experiments. Figure from
Ref. [2] |

Cosmology is making impressive progresses in producing stringent bounds on {the sumof the three active neutrino masses}Σ. The recent results from Ref. [14] indicates small values for the lightest neutrino mass (the authors find Σ < 84 meV at 1σ C. L.) and provides a 1σ preference for the normal hierarchy.A cautious attitude in dealing with the results from cosmological surveys is, anyway, highly advisable. Furthermore, these results enhance the importance of exploring the issue of mass hierarchy in laboratory experiments. From the point of view ofneutrinoless double beta decay (0νββ), the new results show that ton or multi-ton scale detectors will be needed in order to probe the range of mββ now allowed by cosmology. Nevertheless, if next generation experiments see a signal, it will likely be a 0νββ signal of new physics different from the light Majorana neutrino exchange. See Ref. [15] for details.

Journal of Physics: Conference Series 718 (2016) 062012

**Personal comments/ Commentaires personnels**

This post is my way to celebrate the 4th official birthday Higgs boson discovery at LHC. It is also an attempt to show that the actual situation in high energy physics might be less foggy than reported elsewhere. I would summarize it in the following way :

If we stick to the track from Higgs mass and neutrino oscillations without being distracted by the naturalness appeal of susy and dark matter particles, the clearest next energy scale for physics beyond the standard model is ultra high: somewhere between the exa to zetta eV scale. It cannot be reached with a man made collider but the sky is generous in all kind of astro-scale accelerators and mergers! It is up to us physicists to build the proper array of detectors and design the most efficient spectroscopesto mine the dark gold of spacetime.

I will also add that the experimental evidence for a standard model-like Higgs boson combined with the incremental progress in the neutrino sector - have triggered tremendous advances in at least one specific theoretical endeavour : the spectral noncommutative geometrisation of physics. My knowledge and understanding are both limited but I do not know of any other formal framework that offers today such a clear and fascinating connection between:

- the 125 GeV scalar boson detected by particle physics;
- the neutrino flavor oscillations measured from nuclear and astro-physics;
- the dark matter observed from astrometry;

(as reviewed in the post from July 1st entitled

*Made glorious summer*) and makes it possible to start a new construction - perfectly compatible with the paucity of experimental hints of physics beyond the standard model at the multi TeV scale - where:- the 125 GeV Higgs boson would be the expected key stone of the standard model;
- the left and right handed neutrinos would fit in a seesaw mechanism as the flying buttresses of a grand unification model;
- the mimetic dark matter would make the basic building blocks of a quantized spacetime.

/Ce billet est ma façon de fêter le quatrième anniversaire officiel de la découverte du boson de Higgs au LHC. C'est aussi une tentative de montrer que la situation actuelle en physique des hautes énergies n'est peut-être pas aussi brumeuse qu'on le dit ailleurs. Je résumerais les choses ainsi:

Si on s'en tient à suivre la piste indiquée par la masse du boson de Higgs et les oscillations de neutrinos sans se laisser distraire par les arguments esthétiques de naturalité spécifiques à la supersymétrie et aux nouvelles particules qui en découlent dont celle de matière noire, alors la prochaine échelle d'énergie caractéristique pour une nouvelle physique au delà du modèle standard est de l'ordre de l'exa ou du zetta électronvolt. Elle n'est pas accessible avec un collisionneur fabriqué par l'homme mais le ciel est plein d'accélérateurs et de "fusionneurs" aux échelles astronomiques! A nous physiciens de construire les bons réseaux de détecteurs et à concevoir les spectroscopes les plus efficaces pourextraire l'or sombre de l'espace-temps.

J'ajouterai aussi que la preuve expérimentale de la compatibilité du boson de Higgs avec le modèle standard combinée aux avancées successives dans la physique des neutrinos ont suscité des progrès spectaculaires dans un secteur théorique au moins : celui de la géométrisation de la physique dans le cadre noncommutatif spectral. Ma compréhension et mes connaissances sont limitées mais je ne connais pas d'autre cadre formel qui offre aujourd'hui une connexion aussi claire (à tout le moins fascinante) entre :

- le boson scalaire de 125 GeV détecté en physique des particules ;
- les oscillations de saveur des neutrinos mesurées par la physique nucléaire et l'astrophysique ;
- la matière noire cartographiée par l'astrométrie ;

(voir le billet du 1er juillet intitulé

*Made glorious summer*) et qui permette de démarrer une nouvelle construction - parfaitement compatible avec l'absence de signe empirique d'une physique au delà du modèle standard à l'échelle de la dizaine de TeV - où :- le boson de Higgs à 125 GeV serait - telle qu'attendue - la pierre angulaire du modèle standard ;
- les neutrinos gauches et droits s'intégreraient dans un mécanisme de bascule tels les arcs boutants d'un modèle de grande unification à la Pati Salam;
- la matière noire mimétique constituerait la pierre d'assise d'un espacetemps quantifié.

//last edit on July 6th

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