Instanton--Antiinstanton pair induced Asymptotics of Perturbation Theory in QCD

The instanton–antiinstanton pair induced asymptotics of perturbation theory expansion for QCD correlators is considered. It is argued that though the true asymptotics is dominated by renormalon, the instanton-induced contribution may dominate in the intermediate asymptotics $n=5÷15$. Obtained asymptotic formulae are valid for $N_f\le N_c$. For $N_f=N_c$ the finite nonperturbative expression for instanton–antiinstanton contribution was also found. At $q^2<0$ the imaginary part of correlators in the case $N_f=N_c$ is suppressed like $1\mathrm{/}\log (q\mathrm{/}\mathrm{\Lambda })$, but the present accuracy of instanton calculations allows to fix it unambiguously. The series of corrections to the instanton induced asymptotics of the order of $\sim (\log (n)\mathrm{/}n{)}^k$ is found.