A note on instantons, $\hat{I}¸$-dependence and strong CP

Abstract

I review the standard instanton framework for determining the $\hat{I}¸$-dependence of instanton-dominated correlation functions in QCD. I then contrast these well-established semiclassical results with the recent assertion of [1,2], that $\hat{I}¸$-phases are absent and that strong interactions preserve CP for all values of $\hat{I}¸$. In all scenarios considered, the $\hat{I}¸$-dependence is shown to be intrinsically non-trivial, being governed either by instantons in the weak-coupling regime or by alternative, non-perturbative considerations when the theory is strongly coupled.

v2: Extended discussion with additional references; 11 pages and 1 figure