QCD and Electroweak Vacuum θ-Term Axion Angle Inheritanceby Tommy on 9/01/2017
This is exactly what I was looking for!
(In)dependence of Theta in the Higgs Regime without Axions, Mikhail Shifman and Arkady Vainshtein (2 January 2017)
We revisit the issue of the vacuum angle theta dependence in weakly coupled (Higgsed) Yang-Mills theories. Two most popular mechanisms for eliminating physical theta dependence are massless quarks and axions. Anselm and Johansen noted that the vacuum angle θ, associated with the electroweak SU(2) in the Glashow-Weinberg-Salam model, is unobservable although all fermion fields obtain masses through Higgsing and there is no axion. We generalize this idea to a broad class of Higgsed Yang-Mills theories.
In the second part we consider consequences of Grand Unification. We start from a unifying group, e.g. SU(5), at a high ultraviolet scale and evolve the theory down within the Wilson procedure. If on the way to infrared the unifying group is broken down into a few factors, all factor groups inherit one and the same theta angle – that of the unifying group. We show that embedding the SM in SU(5) drastically changes the Anselm-Johansen conclusion: the electroweak vacuum angle θEW, equal to θQCD becomes in principle observable in ∆B = ∆L
See also: https://arxiv.org/abs/hep-ph/9305271
Can Electro-Weak θ-Term be Observable?, A. A. Anselm and A. A.Johansen (14 May 1993)
We rederive and discuss the result of the previous paper that in the standard model θ-term related to W-boson field can not be induced by weak instantons. This follows from the existence of the fermion zero mode in the instanton field even when Yukawa couplings are switched on and there are no massless particles. We consider the new index theorem connecting the topological charge of the weak gauge field with the number of fermion zero modes of a certain differential operator which depends not only on gauge but also on Higgs fields. The possible generalizations of the standard model are discussed which lead to nonvanishing weak θ-term. In SU(2)L × SU(2)R model the θ dependence of the vacuum energy is computed.
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