Abstract
In this paper we study dynamical chiral symmetry breaking of a generic quantum field theoretical model with global chiral flavor symmetry. By purely algebraic means we analyze the vacuum structure for different symmetry breaking schemes and show explicitly how the ensuing non-trivial flavor vacuum condensate characterizes the phenomenon of field mixing. In addition, with the help of Ward-Takahashi identities we demonstrate the emergence of a correct number of Nambu-Goldstone modes in the physical spectrum.
Highlights
Particle mixing represents one of the most exciting topics in modern theoretical and experimental physics [1]
There, it was observed that field mixing is not the same as wave-function mixing and, corrections to neutrino oscillation formula were found in the quantum field theoretical (QFT) setting [10,11]
In Appendix B we show that dynamically generation of mixing cannot occur in the breaking scheme SUð2ÞL × SUð2ÞR × Uð1ÞV → Uð1ÞV × Uð1ÞmV, as it could be expected from point (iii) in Sec
Summary
Particle mixing represents one of the most exciting topics in modern theoretical and experimental physics [1]. In contrast to most of the works on dynamical generation of masses and mixing [18,19], this paper is primarily devoted to a study of general algebraic aspects of field mixing and vacuum structure rather than to phenomenological issues. This approach allows us to identify the flavor vacuum condensate structure, originally obtained in the study of the generator of mixing transformations [9].
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