The strong CP problem solved by itself due to long-distance vacuum effects

The vacuum of quantum chromodynamics has an incredibly rich structure at the nonperturbative level, which is intimately connected with the topology of gauge fields, and put to a test by the strong CP problem. We investigate the long-distance properties of the theory in the presence of the topological $\theta$ term. This is done on the lattice, using the gradient flow to isolate the long-distance modes in the functional integral measure and tracing it over successive length scales. The key point is that the vacuum splits into disconnected topological sectors with markedly different physical characteristics, which gives rise to a nontrivial behavior depending on $\theta$. We find that the color fields produced by quarks and gluons are screened, and confinement is lost, for bare vacuum angles $|\theta| > 0$, thus providing a natural solution of the strong CP problem. The renormalized vacuum angle $\theta$ is found to flow to zero in the infrared limit, leading to a self-consistent solution within QCD.