Amplification of hypercharge electromagnetic fields by a cosmological pseudoscalar

The origin of the cosmological baryon asymmetry remains one of the most fundamental open questions in high energy physics, in spite of the effort and attention it has attracted in the last three decades. In 1967 Sakharov noticed [1] that three conditions are essential for the creation of a net baryon number in a previously symmetric universe: 1) baryon non-conservation; 2) C and CP violation; 3) out of equilibrium dynamics . Since then many different hypothetical cosmological scenarios in which the three conditions could be fulfilled have been proposed as possible scenarios for baryogenesis. Among the different scenarios the electroweak (EW) scenario plays a leading role. It is particularly appealing because it involves physics that can be experimentally tested in the working colliders and those that will turn on during the coming years. Non-perturbative sphaleron processes, at thermal equilibrium at temperatures above the EW phase transition, erase any previously generated baryon excess along the B − L = 0 direction. In addition, if some asymmetry is generated during the transition it is erased immediately after the phase transition completes by the same sphaleron processes, if the transition is not strong enough to effectively suppress them [2]. The strength of the EW phase transition has been extensively studied in the Standard Model (SM) and its popular extensions [3,4], including leading quantum and thermal corrections to the finite temperature effective potential. In the SM the phase transition seems to be second order or even completely absent for those large values of the higgs mass that have not been ruled out by LEP II experiment. In addition it became clear that the mechanisms that were considered had difficulties to generate enough asymmetry to explain the observed baryon to entropy ratio [5]. One of the most dramatic conclusions that emerged from these studies was that either new physics beyond the SM able to change the character of the phase transition and generate enough asymmetry was relevant at the EW scale, or that new physics at much higher energies was responsible for a generation of an asymmetry B − L 6= 0 that has survived until today. It has been recently noticed [6] that hypermagnetic (HM) fields could be significant players in the EW scenario for baryogenesis. Long range uniform magnetic fields could strengthen the EW phase transition to the point that it is strong enough even for the experimentally allowed values of the SM higgs mass. The reason is that only the projection of the hyperfields along the massless photon can propagate inside the bubbles of the broken phase, while their projection along the massive Z-boson cannot propagate. This well-known effect in conductor-superconductor phase transition [7] adds a pressure term to the symmetric phase which can lower the transition temperature. A detailed study of this effect in the SM phase transition has been attempted in several recent papers [8]. The results are not quite conclusive at the moment, however, this effect could save a baryon asymmetry with B−L = 0 generated during the phase transition from erasure by sphaleron transitions in the broken phase and, therefore, may fix one of the two main SM dissabilities discussed above. A subtle effect of hyperelectromagnetic (HEM) fields in the EW scenario may also solve the other basic problem for EW baryogenesis, the amount of asymmetry that can be generated. Giovannini and Shaposhnikov have shown [6] that the topological Chern-Simons (CS) number stored in the HEM fields just before the phase transition is converted into a fermionic asymmetry along the direction B − L = 0. We have shown [9], that an extra axion-like pseudoscalar field coupled to the hypercharge topological number density can amplify HM fields in the unbroken phase of the EW plasma, while coherently rolling or oscillating around