There are reasons to suspect that the spontaneous breakdown of the gauge symmetries of the observed weak and electromagnetic interactions may be produced by the vacuum expectation values of massless weakly coupled elementary scalar fields. A method is described for finding the broken-symmetry solutions of such theories even when they contain arbitrary numbers of scalar fields with unconstrained couplings. In any such theory, there should exist a number of heavy Higgs bosons, with masses comparable to the intermediate vector bosons, plus one light Higgs boson, or "scalon" with mass of order a GF '". The mass and couplings of the scalon are calculable in terms of other masses, even without knowing all the details of the theory. For an SU(2) U(1) model with arbitrary numbers of scalar isodoublets, the scalon mass is greater than 5.26 GeV; a likely value is 7-10 GeV. The production and decay of the scalon are briefly considered. Some comments are offered on the relation between the mass scales associated with the weak and strong interactions.
It is shown that one cannot artifically establish a gauge hierarchy of any desired magnitude by arbitrarily adjusting the scalar-field parameters in the Lagrangian and using the tree approximation to the potential; radiative corrections will set an upper bound on such a hierarchy. If the gauge coupling constant is approximately equal to the electromagnetic coupling constant, the upper bound on the ratio of vector-meson masses is of the order of a-"', independent of the sclar-field masses and their self-couplings. In particular, the usual assumption that large scalar-field mass ratios in the Lagrangian can induce large vector-meson mass ratios is false. A thus far unsuccessful search for natural gauge hierarchies is briefly discussed. It is shown that if such a hierarchy occurred, it would have an upper bound of the order of a-"'.
We investigate the possibility that the symmetry of asymptotically free theories whose effective scalar quartic coupling constants (in the sense of the renormalization group) take on negative values is dynamically spontaneously broken. We find this phenomenon to be common for theories whose scalars transform as the irreducible second-rank tensor representations of SU(n) and O(n). The symmetry-breaking pattern is determined by the tree approximation in some cases, by the one-loop approximation in other cases, but for none of these models does it allow for an asymptotically free theory whose S-matrix elements are defined. Our dynamical mechanism does provide a natural explanation of superstrong spontaneous symmetry breaking.
We study the effects of a fermion with Yukawa-type coupling upon the tunneling of the double-well anharmonic oscillator. These effects prove to be nondramatic, despite the zero-frequency bound-state eigenmode one would encounter if one applied the conventional boundary conditions to the path integral.
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