Renormalization group analysis of the Higgs boson mass in a noncommutative differential geometry

Within one loop approximation, the renormalization group analysis of the Higgs boson mass is performed with an initial condition induced by $m_{_H}=\sqrt{2}m_{_W}$ which is presented in the new scheme of our noncommutative differential geometry for the reconstruction of the standard model. This initial condition holds at energy derived from $g^2=(5/3)g'^2$ with the running SU(2)$_{_L}$ and U(1)$_{_Y}$ gauge coupling constants. $\sin^2\theta_{_W}=3/8$ is obtained under same conditions. However, contrary to ${\rm SU(5)}$ GUT without supersymmetry, the grand unification of coupling constant is not realized in this scheme. The physical mass of the Higgs boson considerably depends on the top quark mass $m_{top}$ since the top quark Yukawa coupling constants gives a large negative contribution to $\beta$ function of the Higgs quartic coupling constant in wide range. The Higgs boson mass varies from 153.42GeV to 191.94GeV corresponding to $168{\rm GeV}\leq m_{top}\leq 192{\rm GeV}$. We find $m_{_H}=164.01$GeV for $m_{top}=175$GeV and $m_{_H}=171.92$GeV for $m_{top}=180$GeV.