A general treatment of oblique parameters

Abstract

A reexamination is made of one-loop oblique electroweak corrections. General definitions are given of the oblique parameters without reference to any $q^2$-expansion scheme. The old oblique parameters S,T and U are defined as differences of gauge boson vacuum polarization $Π$-functions and suffice to describe certain observable ratios on the Z-peak and the $ρ$ parameter at $q^2=0$. Regarding the new oblique parameters V,W and X, the first two are defined in terms of differences of $Π$-functions as well as the wavefunction renormalization of the corresponding weak boson, and the third in terms of the difference of differences of two $Π$-functions for $γ-Z$ mixing. Explicit expressions for measurable quantities involving all six oblique parameters are given and experimental bounds are obtained on the latter, some for the first time. A review of these constraints suggests that the linear approximation of Peskin and Takeuchi is robust.