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Dynamical solution of the strong CP problem within QCD ?

The strong CP problem is inseparably connected with the topology of gauge fields and the mechanism of color confinement, which requires nonperturbative tools to solve it. In this talk I present results of a recent lattice investigation of QCD with the $θ$ term in collaboration with Yoshifumi Nakamura. The tool we are using to address the nonperturbative properties of the theory is the gradient flow, which is a particular realization of momentum space RG transformations. The novel result is that within QCD the vacuum angle $θ$ is renormalized, together with the strong coupling constant, and flows to $θ= 0$ in the infrared limit. This means that CP is conserved by the strong interactions.