Axial-Vector Current Anomaly, Decay Constants, and η-η'-η_c Problem in an N-Flavour Quark Model

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The η-η' complex is treated in an N-flavour model of QCD. We consider the case that the underlying chiral U(N) ×U(N) symmetry is broken by quark masses and also by an anomalous term A_5(x ; N) in the singlet axial-vector current divergence. We treat the term A_5 phenomenologically and determine its matrix element between vacuum and the 0-th pseudoscalar boson state from known spectroscopy of physical 0^--mesons. Setting up a natural model in which heavy quarks are approximately decoupled from the lighter ones, the above matrix element of A_5 is seen to be proportional to the flavour number N. This N-dependence is confirmed empirically in realistic models for N=3 and 4. Thus, the term A_5 is naturally identified with the Adler-Bell -Jackiw type anomaly coming from the quark-gluon coupling. Various decay constants of 0^--mesons are also determined to be compared with experiment ; all decay constants are roughly equal respecting flavour SU(4)-symmetry and the η_c(2.83) stays in an almost pure cc^^--state.
理論物理学刊行会の論文
1978-10-25