Abstract
We suggest soft breaking of Peccei-Quinn symmetry as a simple solution to the strongCP problem without the presence of the axion. In the context of theSU(2) L ×U(1) model, it is shown how settingθ tree=0 keeps θ calculable and, furthermore, extremely small: θ≲10−16. Unlike in the case of the axion the model is free from the cosmological domain wall problem. Possible extension of this idea to grand unification is discussed.
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Sikivie, [9] has suggested a soft breaking ofU(1) PQ by anSU(2) L ×U(1) singlet as a way to eliminate the domain wall problem in the theories with the superlight axion. Our point, realized in a model below, is that there will be no axion whatsoever and furthermore, that the induced\(\bar \theta \) will be naturally small, contrary to the situation in his case
The supersymmetric extension of this work is presented in R.N. Mohapatra, S. Ouvry, G. Senjanović: Phys. Lett B (to appear)
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The idea to make a discrete symmetry a part of a gauge symmetry to avoid the domain wall problem was suggested by G. Lazarides, Q. Shafi: Phys. Lett.115B, 21 (1982). This is automatic in our model
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Mohapatra, R.N., Senjanović, G. A simple solution to the strongCP-problem. Z. Phys. C - Particles and Fields 20, 365–367 (1983). https://doi.org/10.1007/BF01407830
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DOI: https://doi.org/10.1007/BF01407830