Quartic Scalar Coupling Research Articles

Do non-asymptotically-free known interactions invalidate the unification hypothesis?

The running coupling constants and possible unification of the known interaction group product are considered. For fractional and integral quark charges, non-asymptotically-free U(1) gauge and quartic scalar coupling constants are shown not to exceed order unity prior to appropriate embedding mass scales for unification with gravity and for lepton-hadron unification, respectively. Empirical bounds on the mass scale for lepton-hadron unification are shown to be somewhat lower than previously estimated. Essential quartic scalar-field couplings within proposed ${[\mathrm{S}\mathrm{U}(4)]}^{4}$ embedding symmetry are shown to be non-asymptotically-free.

Radiatively induced spontaneous symmetry breaking for asymptotically free gauge theories

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 $\mathrm{SU}(n)$ and $\mathrm{O}(n)$. 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.

Scalar bound states and dynamical symmetry breaking

The possibility of a model with a massive fermion, axial-vector and scalar mesons, and a massless vector meson originating as a dynamical consequence of a chiral U(1) \ifmmode\times\else\texttimes\fi{} U(1) gauge-invariant model with a massless fermion and vector and axial-vector mesons is explored. A recent approach due to Cornwall which makes use of an effective Lagrangian combined with the Callan-Symanzik equations, and its extension, are used with an assumption similar to that of the Baker-Johnson finite quantum electrodynamics. The physical quartic scalar coupling constant and the ratios of physical masses of axial-vector and scalar mesons with respect to that of fermions are expressed in terms of the vector and axial-vector gauge coupling constants.