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

Abstract

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 $g^2=(5/3)g^{\prime 2}$ 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 $\mathrm{SU}(5)$ 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 $168\mathrm{GeV}\le m_{top}\le 192\mathrm{GeV}$. We find $m_{{}_H}=164.01$GeV for $m_{top}=175$GeV and $m_{{}_H}=171.92$GeV for $m_{top}=180$GeV.

Comments: 13 pages, two figures, epsfig.sty