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We study the evolution of QCD phase transition-generated magnetic fields in freely decaying MHD turbulence of the expanding Universe. We consider a magnetic field generation model that starts from basic non-perturbative QCD theory and predicts stochastic magnetic fields with an amplitude of the order of 0.02 µG and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: "weakly helical" turbulence regime, when magnetic helicity increases during decay, and "fully helical" turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective magnetic field being 0.007 nG. We demonstrate that the considered model of magneto-genesis can provide the seed magnetic field for galaxies and clusters.

We study gravitational waves generated by the cosmological magnetic fields induced via bubble collisions during the electroweak (EW) and QCD phase transitions. The magnetic field generation mechanisms considered here are based on the use of the fundamental EW minimal supersymmetric (MSSM) and QCD Lagrangians. The gravitational waves spectrum is computed using a magnetohydrodynamic (MHD) turbulence model. We find that gravitational wave spectrum amplitude generated by the EW phase transition peaks at frequency approximately 1-2 mHz, and is of the order of 10 −20 − 10 −21 ; thus this signal is possibly detectable by Laser Interferometer Space Antenna (LISA). The gravitational waves generated during the QCD phase transition, however, are outside the LISA sensitivity bands. PACS numbers: 98.70.Vc,98.80.Cq

We estimate the energy of the lowest charmonium and upsilon states with hybrid admixtures using the method of QCD Sum Rules. Our results show that the Ψ ′ (2S) and Υ(3S) states both have about a 50% admixture of hybrid and meson components. From this we find explanations of both the famous ρ − π puzzle for charmonium, and the unusual pattern of σ decays that have been found in Υ decays. Moreover, this picture can be used for predictions of heavy quark production with the octet model for RHIC.