On the instabiity of the SM for magnetic fields larger than M super(2) sub(W)/e

It is known that the Standard Model (SM) shows an instability threshold at the critical magnetic field value B = M super(2) sub(W)/e. This effect is determined by the non-Abelian origin of the W particles. The nature of the instability is revisited here. It is underlined that the pure magnetic field within the SM is unstable already at the classical level and shows exponentially growing with time solutions. It is noted that the homogeneity of the system implies that there are also crystalline field configurations with similar rapidly increasing with time behavior. The crystalline distributions of W fields show vortical electric currents similar to the ones exhibited by the Abrikosov's vortices in second kind superconductors. With the use of the spatial dependence of these solutions, static variational configurations of the fields are defined here for minimizing the energy of the system. The constructed static field distributions show appreciably lower energies than the classical magnetic field, and have the energy minimum at a finite lattice size. Therefore, the results give further support to former proposals in the literature about the existence of periodic vortex-like vacuum in the SM at magnetic fields larger than M super(2) sub(W)/e. ( copyright 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)