Heavy Higgs bosons in the Weinberg-Salam model

We search for a systematic way to characterize the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy-Higgs-boson sector. We find that it is convenient to view this theory as the regulated version of a nonlinear $\sigma$ model coupled to an $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ Yang-Mills theory. Within this framework, $M_H$ acts as the regulator. Using the symmetry properties of the nonlinear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to $M_H$. We find that, at one loop, the greatest sensitivity is logarithmic. An illustration of these ideas is provided by a calculation of the one-loop, $M_H$-dependent corrections to the natural relation $\frac{M_W}{M_Z}$ $cos\theta =1\mathrm{}$. Finally, we discuss other possible applications of this technique.