Comments on the Standard Model of Electroweak Interactions

Abstract

Unité associée au CNRS D0 280. Abstract:The Standard Model of electroweak interactions is shown to include a gauge theory for the observed scalar and pseudoscalar mesons. This is done by exploiting the consequences of embedding the SU (2) L × U (1) group into the chiral group of strong interactions and by considering explicitly the Higgs boson and its three companions inside the standard scalar 4-plet as composite.No extra scale of interaction is needed. Quantizing by the Feynman path integral reveals how, in the 'Nambu Jona-Lasinio approximation', the quarks and the Higgs boson become unobservable, and the theory anomaly-free. Nevertheless, the 'anomalous' couplings of the pseudoscalar mesons to gauge fields spring again from the constraints associated with their compositeness itself. This work is the complement of ref.[1], where the leptonic sector was shown to be compatible with a purely vectorial theory and, consequently, to be also anomaly-free. The bond between quarks and leptons loosens. 11.15.Ex, 11.30.Rd, 11.40.Ha, 12.15.Ff, 12.38.Cy, 12.38.Lg, 12.60.Nz, 12.60.Rc, 13.40.Hq, 14.80.Bn, 14.80 PACS:

Chiral scalar fields, custodial symmetry in electroweak SU(2)L × U(1) and the quantization of the electric charge

“…Indeed, the reader can easily recover the same expressions for the action of the chiral group by sandwiching the matrices M between a N -vector Ψ of "quarks" in the fundamental representation of U (N ), an its conjugate Ψ, and by introducing a γ 5 in the definition of all P pseudoscalar states. The "left" and "right" generators are then respectively given a (1 − γ 5 )/2 or a (1 + γ 5 )/2 projectors when acting on the fermions, and the laws of transformations of the latter induce those of the mesons (see [5,6]); All group actions on J = 0 fields written in this work can be uniquely and straightforwardly deduced from the action on fermions when the former are written as scalar or pseudoscalar diquark operators.…”

“…After symmetry breaking, there exists a priori two SU (2) V mass scales for each quadruplet: the first is that of the vector triplet, the second that of the singlet, like for example the Higgs boson. So, in this framework, and without adding more information (like compositeness as has been done in [5,6]), there exists no link between the mass of the Higgs boson and that of the other gauge fields or J = 0 mesons. Let us now examine whether this symmetry can be considered as a local symmetry.…”

“…Some phenomenological aspects have already been tackled in [5,6], where the J = 0 mesons have been explicitly considered as composite. We recall that the latter approach is totally compatible with the present one, where fermions do not explicitly appear.…”

“…It is shown in refs. [6,7,5] that taking into account the compositeness of the mesons in building a quantum theory correctly reproduces those, too. The three works just quoted start from the fermionic point of view and perform a determination of the observed electroweak eigenstates in terms of the above representations; they go also further in the study of their physical interactions and decays.…”

“…), which has already been studied in[5] [6]; f is the leptonic decay constant supposed to be the same for all concerned mesons. The link with observed mesons was…”