I don't understand why the CP violating term in QCD vanishes when we introduce the axion. The term is $$\left(\frac{a}{f_a}+\theta\right)G\tilde{G}$$ It is claimed that $\left\langle a\right\rangle=-\theta f_a$ which cancels the term, but why is the VEV this value?
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$\begingroup$ Related: physics.stackexchange.com/questions/326233/… $\endgroup$– SRSDec 14, 2019 at 21:04
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$\begingroup$ Indeed, answered here: physics.stackexchange.com/questions/326233/… $\endgroup$– ThomasDec 17, 2019 at 17:16
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2$\begingroup$ Does this answer your question? Why is is the vacuum expectation value (VEV) of the axion field such that it cancels the theta angle of QCD? $\endgroup$– ohneValFeb 25, 2021 at 9:39
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