The Weak Mixing Angle from an SU(3) Symmetry at a TeV

Abstract

The measured values of two electroweak gauge couplings appear to obey an approximate 5% SU(3) relation. Unless this is an accident caused by fortuitous Planck-scale physics, it suggests the presence of an SU(3) symmetry near the electroweak scale. We propose this to be a local SU(3) which spontaneously ``mixes'' with SU(2) x U(1) near a TeV. Although all the particles of the standard model are SU(3)-singlets, this symmetry relates the electroweak gauge couplings and can successfully predict the weak mixing angle with a precision of a few percent. Since this mechanism operates at a TeV, it does not require an energy desert and consequently can be embedded in theories of TeV-gravity.

Figures (4)

• Figure 1: Contours of constant $\delta$ in the ${\tilde{g}}'$--${\tilde{g}}$ plane (see text). On the ${\tilde{g}} = \sqrt{3}{\tilde{g}}'$ line there is no correction ($\delta=0$). Going outward from this line are regions with $\delta <2\%$ (red), $<4\%$ (yellow), $<6\%$ (green), and $>6\%$ (blue).
• Figure 2: Contours of constant $\delta$ in the $g_R$--$g_L$ plane for Pati-Salam. The thick black line corresponds to the parity-symmetric case. Going outward from the central region are regions with $\delta <2\%$ (green), $<4\%$ (blue), $<6\%$ (orange), and $>6\%$ (magenta).
• Figure 3: As in Figure \ref{['PS']}, but for quadrification. Again the parity-symmetric case is shown. The colors outward from the central region are $\delta <2\%$ (green), $<4\%$ (red), $<6\%$ (blue), and $>6\%$ (aqua).
• Figure 4: A diagrammatic description of the pseudo-Goldstone boson Higgs model. The two lines represent Goldstone bosons in the $(4,{\bar{4}})$ and $({\bar{4}},4)$ of two sets of $SU(4)_L\times SU(4)_R$ chiral symmetries. The circles represent the gauging of the diagonal linear combination of the $SU(4)_L$ symmetries and an $SU(2)\times U(1)$ subgroup of the $SU(4)_R$ symmetries.