4-dimensional spontaneously broken U(1)L gauge theories without asymptotic quarks and Higgs boson

Abstract

We show, in the case of a U(1)L spontaneously broken gauge theory, how introducing a composite Wess-Zumino field, with a derivative coupling to the fermionic current, and a composite scalar sector leads to infinitely massive quarks and Higgs boson, making them unobservable as asymptotic states. This results from the constraints that need to be introduced in the Feynman path integral to take into account the non-independent scalar degrees of freedom, and from the breaking of the symmetry by the non-vanishing vacuum expectation value of the Higgs boson. Unitarity and gauge invariance are achieved; the former can be made explicit by "gauging" the Wess-Zumino field into the third component of the massive gauge boson; the latter is recovered at the level of Green functions through the cancellation of the non-invariance of the action with that of the fermionic measure. The compensation of the anomaly can also be seen as a consequence of the infinite mass of the fermions. The pseudoscalar partner of the Higgs is shown to behave like an abelian pion, specially as far are its leptonic decays are concerned; in particular, no extra scale of interaction is needed, unlike in "technicolour" theories. The correct decay of the pion into two photons is recovered despite the abscence of anomaly. Arguments are given in favour of renormalizability. The leptonic sector is the object of a subsequent work.