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

Abstract

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 $n= 5\div 15$. 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 $1/\log (q/\Lambda)$, 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 $\sim (\log(n)/n)^k$ is found.