We review the general analysis of the contributions of electroweak vacuum polarization diagrams to precision experiments. We first, review the representation of these contributions by three parameters S, T, and U, and discuss the assumptions involved in this reduction. We then discuss the contributions to these parameters from various models of new physics. We show that S can be computed by a dispersion relation, and we use this technique to estimate S in technicolor models of the Higgs sector. We discuss the reliability and the gauge invariance of this estimate.Finally, we present the limits on S and T imposed by current experimental results.

We show that an integral S over the spectral function of spin-1 states of the Higgs sector is constrained by precision weak-interaction measurements. Current data exclude large technicolor models; asymmetry measurements at the CERN e + e ~ collider LEP and the SLAC Linear Collider will soon provide more stringent limits on Higgs-boson strong interactions. PACS numbers: 12.15.Cc, 12.15.Ji, 12.50.Lr The most pressing question in the study of weak interactions is the nature of the Higgs sector. In the standard SU(2)xU(l) theory of weak interactions, some new particle or set of forces is needed to break the gauge symmetry. However, experiment cannot yet distinguish models of these particles ranging from a minimal doublet of scalar fields to elaborate theories with a rich spectrum of resonances.Among our limited set of constraints on the nature of the Higgs sector, the most important comes from precision measurements of weak-interaction parameters. 1 The famous relation 2 mw = mzco$ 2 0w implies that the Higgs sector has an approximate global SU(2) "custodial" symmetry. 3 A small deviation from this prediction measures the SU(2)-symmetry violation of the Higgs sector.In this Letter, we will extend this conclusion to demonstrate that precision weak-interaction experiments also constrain an isospin-symmetric observable of the Higgs sector. In essence, we will show that, by comparing weak-interaction parameters, one can constrain not only the isospin asymmetry of this sector but also its total size. A longer and more complete version of this argument will be presented in Ref. 4. Our analysis will be based on the general formalism for weak-interaction radiative corrections presented in Refs. 5-7. This work begins from the observation that radiative corrections to weak-interaction processes involving light quarks and leptons due to new physics beyond the standard model appears dominantly through vacuum-polarization amplitudes ("oblique corrections"). For example, modifications of the Higgs sector give vacuum-polarization corrections of order a, while vertex and box diagrams are suppressed by an additional factor of (m/mw) 2 > where m is the external fermion mass. The oblique corrections organize themselves into compact formulas which permit a general analysis of their effects.To write these formulas, we use the subscript 1,3 to denote the weak isospin currents Jf^ and the subscript Q to denote the electric-charge current Jfe. We write the Z° current as (e/ SC)U?>-S 2 JQ),where s^s'mOw, c=cos0jr. Then the W-boson self-energy is i(e 2 /s 2 ) xriii(