We study the properties of $\mathrm{SU}{(N}_f)$ light quarks in the multi-instanton vacuum of QCD. We formulate the dynamical symmetry breaking for light quarks of various numbers of flavor $N_f$ with the inclusion of the instanton size distribution. We find that the quark mass function increases rapidly toward small Euclidean momenta when the finite size distribution is introduced with a power law fall-off of large instanton size, ${\rho }^{-n}\hspace{0.5em}\mathrm{}(n>\mathrm{}3\mathrm{}).$ We observe a confining feature of light quarks for small fall-off parameter n and for large packing fraction $\overline{\rho }/\overline{R}$ in the behavior of the quark mass function extrapolated to the timelike region.

• Received 25 October 1999

DOI:https://doi.org/10.1103/PhysRevD.62.054005