Mass generation by Weyl symmetry breaking

A massless electroweak theory for leptons is formulated in a Weyl space, W-4, yielding a Weyl invariant dynamics of a scalar field phi, chiral Dirac fermion fields psi(L) and psi(R), and the gauge fields K-mu, A(mu), Z(mu), W-mu, and W-mu(dagger), allowing for conformal rescalings of the metric g(mu nu) and all fields with nonvanishing Weyl weight together with the corresponding transformations of the Weyl vector fields, K-mu, representing the D(1) or dilatation gauge fields. The local group structure of this Weyl electroweak (WEW) theory is given by G = SO(3, 1) circle times D(1) circle times (G) over tilde-or its universal coverging group (G) over bar for the fermions-with (G) over tilde denoting the electroweak gauge group SU(2)(W) x U(1)(Y). In order to investigate the appearance of nonzero masses in the theory the Weyl symmetry is explicitly broken by a term in the Lagrangean constructed with the curvature scalar R of the W-4 and a mass term for the scalar field. Thereby also the Z(mu) and W-mu gauge fields as well as the charged fermion field (electron) acquire a mass as in the standard electroweak theory. The symmetry breaking is governed by the relation D(mu)Phi(2) = 0, where Phi is the modulus of the scalar field and D-mu denotes the Weyl-covariant derivative. This true symmetry reduction, establishing a scale of length in the theory by breaking the D(1) gauge symmetry, is compared to the so-called spontaneous symmetry breaking in the standard electroweak theory, which is, actually, the choice of a particular (non-linear) gauge obtained by adopting an origin, <(phi)over cap>, in the coset space representing phi, with <(phi)over cap> being invariant under the electromagnetic, gauge group U(1)(c.m.). Particular attention is devoted to the appearance of Einstein's equations for the metric after the Weyl symmetry breaking, yielding a pseudo-Riemannian space, V-4, from a W-4 and a scalar field with a constant modulus <(phi)over cap>(0). The quantity <(phi)over cap>(2)(0) affects Einstein's gravitational constant in a manner comparable to the Brans-Dicke theory. The consequences of the broken WEW theory are worked out and the determination of the parameters of the theory is discussed.