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  • $\begingroup$ I think you are confusing the U(1) puzzle and the strong CP problem. There is no problem with the anomalous U(1)_A. Because of the anomaly no Goldstone boson is expected, and indeed none is observed. $\endgroup$
    – Thomas
    Commented Oct 21, 2015 at 3:08
  • $\begingroup$ There is (somewhat related, but different) puzzle called the strong CP problem. The existence of the amomaly makes it clear that the $\theta$ parameter is physical, and that observables do depend on it. But $\theta$ violates CP, so it must be very small. The $U(1)_{PQ}$ is a symmetry of a proposed extension of QCD, in which $\theta=0$ dynamically. However, you should keep in mind that i) there is nothing wrong with setting $\theta=0$ by hand, ii) there is no evidence for axions. $\endgroup$
    – Thomas
    Commented Oct 21, 2015 at 3:11
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    $\begingroup$ Isn't $U(1)_{PQ}$ itself anomalous? The dynamical solution (axion) is related to the spontaneous symmetry breaking of $U(1)_{PQ}$. How can an anomalous $U(1)_{PQ}$ lead to the appearance of a Goldstone boson? Judging by the fact that indeed $U(1)_A$ because it is anomalous it doesn't lead to Goldstones in the spectrum. $\endgroup$
    – EEEB
    Commented Oct 21, 2015 at 11:04
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    $\begingroup$ I see what you are asking. $\endgroup$
    – Thomas
    Commented Oct 21, 2015 at 13:58