Constraints on New Physics in the Electroweak Bosonic Sector from Current Data and Future Experiments

Extensions of the Standard Model which involve a new scale, $\Lambda$, may, for energies sufficiently small compared to this new scale, be expressed in terms of operators with energy dimension greater than four. The coefficients of just four SU(2)$\times$U(1)-gauge-invariant energy-dimension-six operators are sufficient to parameterize the contributions of new physics in the electroweak bosonic sector to electroweak precision measurements. In this letter we update constraints on the coefficients of these four operators due to recent precision measurements of electroweak observables. We further demonstrate how such constraints may be improved by experiments at TRISTAN, LEP2 and at a future linear $e^+e^-$ collider. The relationship of these operators to the oblique parameters $S$, $T$ and $U$ is examined. Two of the operators contribute to a non-standard running of the electroweak charge form-factors $\overline{\alpha}(q^2)$, $\overline{s}^2(q^2)$, $\overline{g}_Z^2(q^2)$ and $\overline{g}_W^2(q^2)$; in the special case where the coefficients of these two vanish the operator analysis reduces to an analysis in terms of $S$, $T$ and $U$ with $U = 0$.