Effective vertexes in magnetized quark-gluon plasma

In quark-gluon plasma (QGP), at high temperatures $T$ the spontaneous generation of color magnetic fields, $b^3(T), b^8(T) \not = 0$ (3, 8 are color indexes), and usual magnetic field $b(T) \not = 0$ happens. Also, the Polyakov loop and related to it the $A_0(T)$ condensate, which is solution to Yang-Mills imaginary time equations, create. Recently, with the new type two-loop effective potential, which generalizes the known integral representation for the Bernoulli polynomials and takes into consideration the magnetic background, these effects were derived. The corresponding effective potential $W(T, b^3, b^8, b, A_0 )$ was calculated either in SU(2) gluodynamics or full quantum chromodynamics (QCD). The values of magnetic field strengths at different temperatures were calculated and the mechanism for stabilizing the background due to $A_0(T)$ was also discovered. In present paper, we concentrate on the one-loop quark contributions. In particular, we derive the effective vertexes, which couple magnetic fields and $A_0$. The vertexes result in new specific effects signalling the creation of QGP in heavy ion collision experiments. Key words: spontaneous magnetization, high temperature, asymptotic freedom, effective potential, $A_0$ condensate, effective vertexes.