Implication of Compensator Field and Local Scale Invariance in the Standard Model

Abstract

We introduce Weyl's scale symmetry into the standard model (SM) as a local symmetry. This necessarily introduces gravitational interactions in addition to the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X U(1). The only other new ingredients are a new scalar field \sigma and the gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that the system admits the St\" uckelberg-type compensator. The \sigma couples to the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\" uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg formalism corresponds to \sigma = M_P, and the Hilbert action is induced automatically. In this sense, our model presents yet another mechanism for breaking scale invariance at the classical level. We show that our model naturally accommodates the chaotic inflation scenario with no extra field.