Electroweak instantons,axions, and the cosmological constant

If there is explicit violation of baryon plus lepton number at some energy scale, then the electroweak theory depends upon a θ-angle. Due to a singular integration over small scale size instantons, this θ  -dependence is sensitive to very high momentum scales. Assuming that there is no new physics between the electroweak and Planck scales, for an electroweak axion the energy difference between the vacuum at θ≠0$\theta \ne 0$, and that at θ=0$\theta =0$, is of the correct order of magnitude to be the dark energy observed in the present epoch.