Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the so-called U(1) standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem for a nonlinear wave-Klein-Gordon system that couples (Dirac, scalar, gauge) massive equations together. In particular, we investigate here the Dirac operator and its energy functional defined with respect to the hyperboloidal foliation of Minkowski spacetime. We also provide a decay result for the Dirac equation which is uniform in the mass coefficient, and thus allow for the mass coefficient to be arbitrarily small. Our energy bounds are uniform (modulo a logarithm growth) with respect to the hyperboloidal time variable.