We derive general bounds on the Type-III Seesaw parameters from a global fit to flavor and electroweak precision data. We explore and compare three Type-III Seesaw realizations: a general scenario, where an arbitrary number of heavy triplets is integrated out without any further assumption, and the more constrained cases in which only 3 or 2 (minimal scenario) additional heavy states are included. The latter assumption implies rather non-trivial correlations in the Yukawa flavor structure of the model so as to reproduce the neutrino masses and mixings as measured in neutrino oscillations experiments and thus qualitative differences can be found with the more general scenario. In particular, we find that, while the bounds on most elements of the dimension 6 operator coefficients are of order 10 −4 for the general and 3-triplet cases, the 2-triplet scenario is more strongly constrained with bounds between 10 −5 and 10 −7 for the different flavours. We also discuss how these correlations affect the present CMS constraints on the Type-III Seesaw in the minimal 2-triplet scenario.

Noncommutative geometry provides both a unified description of the Standard Model of particle physics together with Einstein-Hilbert action (in Euclidean signature) and some tools to go beyond the Standard Model. In this paper, we extend to the full noncommutative geometry of the Standard Model the twist (in the sense of Connes-Moscovici) initially worked out for the electroweak sector and the free Dirac operator only. Namely, we apply the twist also to the strong interaction sector and the finite part of the Dirac operator. To do so, we are forced to take into account a violation of the twisted first-order condition. As a result, we still obtain the extra scalar field required to stabilize the electroweak vacuum and fit the Higgs mass, but it now has two chiral components. We also get the additive field of 1-forms already pointed out in the electroweak model, but with a richer structure. Finally, we obtain a pair of Higgs doublets, which are expected to combine into a single Higgs doublet in the action formula, as will be investigated in the second part of this work.

We classify the twists of almost commutative spectral triples that keep the Hilbert space and the Dirac operator untouched. The involved twisting operator is shown to be the product of the grading of a manifold by a finite dimensional operator, which is not necessarily a grading of the internal space. Necessary and sufficient constraints on this operator are listed.

This is a review of recent results regarding the application of Connes' noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected 1-form field. By computing the fermionic action, we show how this field induces a transition from the Euclidean to the Lorentzian signature. Hints on a twisted version of the spectral action are also briefly mentioned. IntroductionNoncommutative geometry "a la Connes" [10] allows to obtain the Lagrangian of the Standard Model of elementary particles -including the Higgs sector -minimally coupled with Einstein-Hilbert action (in Euclidean signature) from geometrical principles. In addition, it offers some guidelines to go beyond the Standard Model by playing with the mathematical rules of the game (for a recent review, see [9]).Early attempts "beyond the SM" were considering new fermions (see e.g.[28] and other papers of the same author). One may also relax one of the axioms of noncommutative geometry, the first-order condition discussed below [8]; or modify another axiom regarding the real structure (also discussed below) [3,4]. Other proposals are based on some Clifford bundle structure [16], or non-associativity [2]. Here we focus on a model consisting in twisting the original noncommutative geometry [19,23,22].From the examples listed above, all but the first are minimal extensions of the Standard Model: they allow to produce the kind of extra scalar field σ suggested by particle physicists to stabilise the electroweak-vacuum (which also permits to make the calculation of the Higgs mass in noncommutative geometry compatible with its experimental value), without adding new fermions.By using twisted noncommutative geometry, one gets in addition an supplementary piece, namely a 1-form field, which surprisingly turns out to be related to the transition from Euclidean to Lorentzian signature.We give an overview of these results below, beginning in §2 with a recalling on the Standard Model in noncommutative geometry. Then we summarise in §3 how to apply a twist to the geometry, and why this is related to a transition from the Euclidean to the Lorentzian. In §4 we show how this transition is actually realised at the level of the fermionic action. We also stress some projects regarding the spectral (i.e. bosonic) action.1

We review the applications of twisted spectral triples to the Standard Model. The initial motivation was to generate a scalar field, required to stabilise the electroweak vacuum and fit the Higgs mass, while respecting the first order condition. Ultimately, it turns out that the trues interest of the twist lies in a new, and unexpected, field of 1-forms, which is related to the transition fron euclidean to lorentzian signature.