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In p.726 of Peskin QFT, it says:

The theta terms are total derivative, that terms involving $SU(2)$ and $U(1)$ have no observable effects.

However for the strong $SU(3)$, it costs a strong CP problem. Why is that?

Question: Why there are no theta terms observable effects for $SU(2)$ and $U(1)$? But only $SU(3)$?

Just to be clear, the discussion here is already making the quark rotations to reduce the CKM matrix coupling for the $W$ weak flavor current to only a complex phase $e^{i \phi}$ (which also violates CP).

So other than this $e^{i \phi}$, because we had already rotated the quarks, we may generate the theta angles for all $SU(3)$, $SU(2)$ and $U(1)$. Because we already rotated the quarks to reduced the CKM matrix -- in my opinion, we should not rotate the quarks again to reduce the theta terms $\theta$ of $SU(3)$, $SU(2)$ and $U(1)$ (!?) -- otherwise, rotating the quarks again will generate back CKM matrix with more complex phases!! (this is the dilemma if you want to

(1) remove the theta terms and also

(2) remove the complex phases of CKM, and

(3) keep the Yukawa-Higgs coupling to a good mass eigenstate basis.

So please explain carefully what we are going to do to deal with (1),(2),(3) altogether? (!?)

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  • $\begingroup$ To whom closed my question -- I asked something different --- I ask the compatibility of (1) remove the theta terms and also (2) remove the complex phases of CKM, and (3) keep the Yukawa-Higgs coupling to a good mass eigenstate basis. $\endgroup$
    – ann marie cœur
    Commented Dec 26, 2020 at 19:28
  • $\begingroup$ I think your question is clearly a more specific version of the question I linked as duplicate, and the answer there answers this one, too. If you think otherwise, please edit your question to be specific about the parts not covered by the duplicate, in particular try to explain why the answer to the duplicate would not be a full answer to this question, too. $\endgroup$
    – ACuriousMind ♦
    Commented Dec 26, 2020 at 19:41
  • $\begingroup$ Thanks,The linked answer only explains how to remove the theta term when we have left-handed fermions coupled to SU(2) which is about (1). But my question has issues about do (1),(2),(3) together - how can we still remove the theta term $\endgroup$
    – ann marie cœur
    Commented Dec 26, 2020 at 23:03

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