An estimation of the Higgs boson mass in the two loop approximation in a noncommutative differential geometry

In the two loop approximation, a renormalization group analysis of the Higgs boson mass is performed based on the condition $g^2=(5/3)g'^2=4\lambda$ for SU(2)_L, U(1)_Y gauge and the Higgs quartic coupling constants, respectively. This condition is introduced in the new scheme of our noncommutative differential geometry (NCG) for the reconstruction of the standard model. However, contrary to SU(5) GUT without supersymmetry, the grand unification of coupling constants is not realized in this scheme. The physical mass of the Higgs boson depends strongly on the top quark mass $m_{top}$ through the Yukawa coupling of the top quark in the $\beta$ functions.The two loop effect lowers the numerical value calculated within the one loop approximation by several GeV. The Higgs boson mass varies from 150.25GeV to 167.15GeV corresponding to 169.34GeV< m_{top}<181.02GeV. We find the Higgs boson mass m_H=158.18GeV for m_{top}=175.04GeV and $m_H=166.12GeV for m_{top}=180.34GeV.