Evolution equations for the effective four-quark interactions in QCD

Abstract

A nonperturbative renormalization group equation describes how the momentum dependent four-quark vertex depends on an infrared cutoff. We find a quasilocal one-particle irreducible piece generated by (anomaly-free) multi-gluon exchange. It becomes important at a cutoff scale where scalar and pseudoscalar meson-bound states are expected to play a role. This interaction remains subleading as compared to the effective one-gluon exchange contribution. The local instanton induced four-quark interaction becomes dominant at a scale around 800 MeV. In absence of a gluon mass the strong dependence of the one-gluon exchange on the transferred momentum indicates that the pointlike interactions of the Nambu-Jona-Lasinio model cannot give a very accurate description of QCD. A pointlike effective four-quark interaction becomes more realistic in case of spontaneous color symmetry breaking.

24 pages, LaTeX file, + 6 PS figures

References in corpus (1)

• Exact evolution equation for the effective potential

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