Is Anomaly Transferred thorough Multi-loop Process?

We investigated the multi-loop anomaly transfer to QCD sector from another one and its ability to solve strong CP problem. If the anomalous symmetry is spontaneously broken, its Nambu-Goldstone (NG) boson can couple to the QCD $G\tilde{G}$ through this transfer effect and behave as an axion. In our result, such a particle acquire mass pertabatively in fact, and really massless mode doesn’t have couplings with $G\tilde{G}$. Consequently, this pseudo-NG boson is found not to solve the problem.