New scalar fields in noncommutative geometry

In this publication we present an extension of the standard model within the framework of Connes’ noncommutative geometry. The model presented here is based on a minimal spectral triple which contains the standard model particles, new vectorlike fermions, and a new $U(1)$ gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions, and the standard Higgs particle. The bosonic part of the action is given by the spectral action which also determines relations among the gauge couplings, the quartic scalar couplings, and the Yukawa couplings at a cutoff energy of $\sim {10}^{17}\mathrm{GeV}$. We investigate the renormalization group flow of these relations. The low energy behavior allows to constrain the Higgs mass, the mass of the new scalar, and the mixing between these two scalar fields.

Figure 1

Krajewski diagram of the extended standard model. The dotted line indicates the Dirac mass term leading to the new scalar field $\phi$.

Figure 2

Dependence of ${\lambda }_2(m_{\phi })$ (circles) and ${\lambda }_3(m_{\phi })$ (crosses) on $g_4(m_Z)$ for ${\mu }_2(m_{\phi })\ll m_W$.

Figure 3

Dependence of the Higgs mass $m_H$ (circles) and the mass of the new scalar $m_{\phi }$ (crosses) on $g_4(m_Z)$ for ${\mu }_2(m_{\phi })\ll m_W$.

Figure 4

$g_4(m_Z)=0.01$: The left figure shows the dependence of $m_{H_1}$ and $m_{H_2}$ on $v_2$. The constant line is the 114 GeV experimental LEP threshold for the standard model Higgs mass. The right figure shows the dependence of the mixing angle $\theta$ on $v_2$.

Figure 5

$g_4(m_Z)=0.3$: The left figure shows the dependence of $m_{H_1}$ and $m_{H_2}$ on $v_2$. The constant line is the 114 GeV experimental LEP threshold for the standard model Higgs mass. The right figure shows the dependence of the mixing angle $\theta$ on $v_2$.

Figure 6

$g_4(m_Z)=0.7$: The left figure shows the dependence of $m_{H_1}$ and $m_{H_2}$ on $v_2$. The constant line is the 114 GeV experimental LEP threshold for the standard model Higgs mass. The right figure shows the dependence of the mixing angle $\theta$ on $v_2$.