Strong CP violation in large scale magnetic fields

We explore the possibility of improving on the present experimental bounds on Strong CP violation, by studying processes in which the smallness of 0 is compensated by the presence of some other very large scale. In particular, we study the response of the e vacuum to large-scale magnetic fields, whose correlation lengths can be as large as the size of galaxy clusters. We find that, if strong interactions break CP, an external magnetic field would induce an electric vacuum polarization along the same direction. As a consequence, u,(d) over bar and d,(u) over bar quarks would accumulate in the opposite regions of the space, giving raise to an electric dipole moment. We estimate the magnitude of this effect both at T = 0 and for 0 < T < 150 MeV We find that the effect is extremely small today (i.e. for T = 0), but is enhanced at finite temperature. Given the smallness of e, we conclude that this phenomenon could be relevant only in regions of the Universe in which either temperature is very large or the field is very intense.