Investigation of the Higgs Potential Renormalization Group Flow

Abstract

In this paper, critical points are investigated as characteristics of the asymptotic behavior of induced transitions and the evolution of the surface of extrema of effective Higgs potentials to evaluate several characteristics, for example, asymptotic stability in the case of the given parameters. Critical phenomena in evolution of the surface of extrema of the Higgs potential in a system with two doublets of complex fields are evaluated. A study of renormalization group of coupling flows of the effective expansion potential of the Higgs sector of the Standard Model has been performed. The asymptotic behavior of couplings and characteristics of critical points are determined, and the plots for self-interaction couplings in phase spaces are constructed. The results manifest the existence of stable nontrivial fixed points, indicating asymptotically the \(O\)(2) symmetry in the IR case. The point (0,0) turns out to be stable, since the theory reduces to a fixed point of the free field of the scalar theory. By tuning, we can obtain a wide range of energies in which fixed points determine the behavior of the theory.