Renormalization Group Analysis of the Higgs Boson Mass in a Noncommutative Geometry

Within one loop approximation, the renormalization group analysis of theHiggs boson mass is performed with an initial condition induced by$m_{_H}=\sqrt{2}m_{_W}$ which is presented in the new scheme of ournoncommutative differential geometry for the reconstruction of the standardmodel. This initial condition holds at energy derived from $g^2=(5/3)g'^2$ withthe 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 couplingconstant is not realized in this scheme. The physical mass of the Higgs bosonconsiderably depends on the top quark mass $m_{top}$ since the top quark Yukawacoupling constants gives a large negative contribution to $\beta$ function ofthe Higgs quartic coupling constant in wide range. The Higgs boson mass variesfrom 153.42GeV to 191.94GeV corresponding to $168{\rm GeV}\leq m_{top}\leq192{\rm GeV}$. We find $m_{_H}=164.01$GeV for $ m_{top}=175$GeV and$m_{_H}=171.92$GeV for $ m_{top}=180$GeV.Comment: 13 pages, two figures, epsfig.st