Dynamical Higgs Mechanism without Elementary Scalars: A Lesson from Instantons

The generation of gauge–dependent fermion vacuum condensates in Yang– Mills theory would dynamically break the gauge symmetry and thus provide an alternative to the Higgs mechanism in unified theories. We explore a simple example: instanton-induced quark pair (diquark) condensation in QCD with 2 flavors and Nc colors. We do find diquark condensates in the vacuum, but only for Nc = 2, where they are equivalent to the standard quark-antiquark condensate. At Nc ≥ 3 diquark condensates exist as meta–stable saddle points of the instanton-induced effective QCD action and may strongly affect the properties of matter under extreme conditions. The scalar diquark excitation, which is a Goldstone boson at Nc = 2, becomes unbound for Nc ≥ 3. Typeset using REVTEX 1 Instanton-induced quark interactions provide a well-known mechanism for spontaneous chiral symmetry breaking by quark-antiquark pair condensation in the QCD vacuum [1]. In this letter we persue the question whether these interactions, which are attractive in certain quark-quark channels, might also induce diquark condensates. Since such condensates are not gauge invariant (except for Nc = 2), they would signal dynamical gauge symmetry breaking. Diquark condensates, which are a direct analogue of Cooper pair condensates in superconductive materials, could furthermore serve as a prototype for dynamical gauge symmetry breaking in other theories and thus as an alternative to the standard Higgs mechanism. Even if they are absent in the ground state of a theory, however, they might still form in a state corresponding to a saddle point of the effective action. Such meta-stable states could, for example, play an important role in cosmology and in the evolution of the universe. Our study is based on the effective quark interaction [1,2] L = g {(