Question: Why there is NO Charge-Parity (CP) violation from a potential Theta term in the electroweak SU(2)weak,flavor sector by θelectroweak∫F∧F?
(ps. an explicit calculation is required.)
Background:
We know for a non-Abelian gauge theory, the F∧F term is nontrivial and breaks CP symmetry (thus break T symmetry by CPT theorem), which is this term:
∫F∧F
with a field strength
F=dA+A∧A.
∙ SU(3)strong,color QCD:
To describe strong interactions of gluons (which couple quarks), we use QCD with gauge fields of non-Abelian SU(3)color symmetry. This extra term in the QCD Lagrangian:
θQCD∫G∧G=θQCD∫d4xGaμν∧˜Gμν,a
which any nonzero
θQCD breaks
CP symmetry. (p.s. and there we have the
strong CP problem).
∙ Compare the strong interactions θQCD,strong to U(1)em θQED: For U(1) electromagnetism, even if we have θQED∫F∧F, we can rotate this term and absorb this into the fermion (which couple to U(1)em) masses(?). For SU(3) QCD, unlike U(1) electromagnetism, if the quarks are not massless, this term of θQCD cannot be rotated away(?) as a trivial θQCD=0.
∙ SU(2)weak,flavor electro-weak:
To describe electroweak interactions, we again have gauge fields of non-Abelian SU(2)weak,flavorsymmetry. Potentially this extra term in the electroweak Lagrangian can break CP symmetry (thus break T symmetry by CPT theorem):
θelectroweak∫F∧F=θelectroweak∫d4xFaμν∧˜Fμν,a
here the three components gauge fields
A under SU(2) are: (
W1,
W2,
W3) or (
W+,
W−,
Z0) of W and Z bosons.
Question [again as the beginning]: We have only heard of CKM matrix in the weak SU(2) sector to break CP symmetry. Why there is NO CP violation from a potential Theta term of an electroweak SU(2)weak,flavor sector θelectroweak∫F∧F? Hint: In other words, how should we rotate the θelectroweak to be trivial θelectroweak=0? ps. I foresee a reason already, but I wish an explicit calculation is carried out. Thanks a lot!
This post imported from StackExchange Physics at 2014-06-04 11:35 (UCT), posted by SE-user Idear