Un, deux voire trois diamants de plus dans la poche du Mendiant* / One, two or three more diamonds in the pocket of the Beggar

Le grand frère du boson de Higgs est-il le scalaire complexe de charge +2 sous le groupe de jauge local U(1)_B-L? / Is the big br(other of the Higgs b)oson a complex scalar with +2 charge under the local gauge group U(1)_B-L?

Le blogueur rentre de vacances pour découvrir que l'hypothétique boson scalaire réel qui permettait (il y a presque deux ans jour pour jour) de corriger la prédiction de masse du boson de Higgs électrofaible dans le modèle standard spectral presque commutatif, est peut-être bien complexe, du moins si on le conçoit comme le boson de Higgs "baryoleptonique" (B-L) responsable de la brisure de symétrie associée à U(1)_B-L:

In our previous paper [16], we found a reformulation of non-commutative geometry (NCG) that simplified and unified the mathematical axioms while, at the same time, resolving a problem with the NCG construction of the standard model Lagrangian, by precisely eliminating 7 terms which had previously been problematic. In this paper, we show that this same reformulation leads to a new perspective on the gauge symmetries associated to a given NCG, uncovering some that were previously missed. In particular, when we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find a new U(1)_B-L gauge symmetry (and, correspondingly, a new B−L gauge boson [C_µ ]). This, in turn, implies the existence of a new complex Higgs field σ that is a singlet under SU(3)_C×SU(2)_L×U(1)_Y  but transforms with charge +2 under U(1)_B-L, allowing it to form a majorana-like yukawa coupling σν_Rν_R with two right-handed neutrinos (so that, if it obtains a large VEV, it induces see-saw masses for the neutrinos). It is striking that, on the one hand, this precise extension of the standard model has been previously considered in the literature [22, 23] on the basis of its cosmological advantages; and, on the other hand, that the new field σ can resolve a previous discrepancy between the observed Higgs mass and the NCG prediction [18, 19, 21]. Note that in the previous works [18, 19, 21] which introduced the σ field for this purpose, it was a real field, and a gauge singlet. By contrast, from the perspective presented here, the fact that σ is complex, and transforms under U(1)_B-L, is the key to its existence: had it been real, it would not have been induced by the covariance argument of the previous section

Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry

Shane Farnsworth, Latham Boyle (Submitted on 22 Aug 2014)

*  Mendiant =  Modèle Standard vu sous l'angle spectral presque commutatif 
Beggar = Standard Model in the spectral and almost commutative framework

Une nouvelle raison d'être pour les neutrinos de chiralité droite? / A new raison d'être for right-handed neutrinos? 

Or donc le modèle spectral non commutatif et sa possible extension sous  un angle non associatif révèlent aux yeux des physiciens la présence de deux joyaux cachés dans  les arcannes du Modèle Standard à savoir deux bosons de jauge "baryoleptoniques" (l'un au sens ordinaire) C_µ et (l'autre au sens non commutatif) σ. A ces deux nouvelles particules il faut naturellemment en ajouter une troisième, le neutrino de chiralité droite dont l'existence, si elle était déjà subodorée de longue date, gagne néanmoins un supplément de sens en la mariant aux deux bosons précités, c'est du moins le message de l'extrait suivant:

The ordinary standard model makes sense, with or without the right-handed neutrino. In particular, since the right-handed neutrino is a singlet under the standard model gauge group, it does not contribute to anomaly cancellation: in the standard model, the anomalies cancel whether or not the right-handed neutrino exists. The right-handed neutrino has recently been tacked on to the standard model in order to account for the observed neutrino oscillations – but not for any independent theoretical reason. It is important to emphasize that the situation is very different in a Minimal Dimensionless Standard Model (MDSM) [that would consist of a standard model plus 3 right-handed neutrinos with the additional constraint of classical conformal invariance to eliminate all dimensionful couplings, augmented by a new U(1)_B-L gauge symmetry carried by a new gauge boson C_µ and a complex scalar field, singlet under SU(3)_C×SU(2)_L×U(1)_Y  that couples to the new symmetry with charge +2]... 

In this case, the right-handed neutrino is charged under U(1)_B-L, and thus plays an essential role in the anomaly cancellation [requirement for renormalizability]...  Relative to the standard model, this [MDSM] contains two new fields: the complex scalar field [σ] and the (B−L) gauge field C_µ. In this subsection, we would like to stress the elegantly economical way in which [σ] simultaneously accomplishes several important phenomenological tasks in this model. On the one hand, its properties – i.e. its SU(3)_C×SU(2)_L×U(1)_Y×U(1)_B-L charges ... – were determined by requirement that it should be able to provide a Majorana-like Yukawa coupling to right-handed neutrinos, in order to give a see-saw mechanism for neutrino mass. 

On the other hand, these same properties are precisely what is needed in order for [σ] to perform another crucial task: spontaneously break (B−L) symmetry, and give mass to the C_µ boson via the Higgs mechanism, without leaving any additional unwanted Goldstone bosons. 

At the same time, we have seen that [σ] expands the scalar sector in a way that leads to successful electroweak symmetry breaking via the Coleman-Weinberg mechanism, an inflaton candidate, a dark matter candidate, and a possible explanation for the cosmological matter/anti-matter asymmetry. 

Finally, this model contains 4 different quantities that all must be rather large, for very different phenomenological/cosmological reasons: (i) the mass of the Z′µ boson, (ii) the masses of the heavy neutrinos; (iii) the mass of the [σ] boson, and (iv) the inflaton VEV. And yet, in [MDSM], all 4 large dimensionful quantities have a common origin in the large VEV of the field [σ].

The Minimal Dimensionless Standard Model (MDSM) and its Cosmology

Latham Boyle, Shane Farnsworth, Joseph Fitzgerald, Maitagorri Schade 

(Submitted on 1 Nov 2011 (v1), last revised 12 Mar 2013 (this version, v2)).

Remark : in the original article the complex scalar field σ is written ϕ and the MDSM discussed here is MDSM₃