Radiative Corrections to Gauge Boson Masses

Abstract

There is by now abundant experimental support for the standard SU(2) ⊗ U(l) theory of electroweak interactions. The discovery of the Z-boson since this conference only strengthens this evidence. One of the reasons for the popularity of the standard model is the fact that it is a renormalisable theory, so that it is possible to calculate higher order effects in a consistent manner. It means on the other hand that there are parameters which have to be given as inputs. In practice already a few parameters are sufficient to be able to give predictions. If one works in lowest order, the fine-structure constant α, the Fermi-constant G_F and the Weinberg-angle sin ²θ_w are sufficient inputs to predict (again to lowest order) the intermediate bosons through:

$${M_W}^{(0)}=\frac{1}{{\sin {\theta _W}}}{(\frac{{\Pi\alpha}}{{{G_F}\sqrt 2 }})^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/{\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}}},$$

((1))

$${M_W}^{(0)}=\frac{1}{{\sin{\theta_W}\cos {\theta _W}}}{(\frac{{\Pi\alpha}}{{{G_F}\sqrt 2 }})^{{\raise0.7ex\hbox{$1$}\!\mathord{\left/{\vphantom{1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}}}$$

((1))

One would like to test these relations as precisely as possible. The main difficulties here are the fact that sin ²θ_w is at present not known very accurately and of course that the Z and W are not very well known ¹⁾.