Predictions for the higgs mass from the stability and triviality conditions

In the context of the Standard Model (SM), we use the one-loop and two-loop Renormalization Group Equations (RGE) in order to analyze the evolution of the Higgs quartic coupling AH in the interval [m_t, E_GU] where m_t is the mass of the top quark and E_GU = 10 ¹⁴GeV. The analytical solution for the one-loop differential equation (Riccati type) is obtained and analyzed and in the two-loop case we obtain a numerical solution which takes into account all the parameters (couplings) at the same order of approximation. In both cases, we restrict the possible initial values for λ_H by means of imposing the triviality and stability conditions which determine the range of energies where the SM is valid. We obtain the following bounds: 0.387 < λ_H < 0.623 for the one-loop case and 0.360 < λ_H < 0.628 for the two-loop case. These results determine the interval of the possible Higgs mass values: 151.9 < M_H < 192.3 GeV, 143.8 < M_H < 190.3 GeV for the one-loop and two-loop cases, respectively.