Oblique corrections when m W ≠ m Z cos θW at tree level

The parametrization of the oblique corrections through S, T , and U – later extended by V , W and X – is a convenient way of comparing the predictions for various electroweak observables at the one-loop level between the Standard Model and its extensions. That parametrization assumes that the extensions under consideration have SU (2) × U (1) gauge symmetry and the tree-level relation m W = m Z cos θW between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter T is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with m W ≠ m Z cos θW in terms of oblique parameters. The parameter T does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level m W ≠ m Z cos θW , by performing a simple substitution for T . We also discuss the difficulties in using oblique parameters when comparing a model with m W ≠ m Z cos θW to the Standard Model. Finally, we compute the relevant five oblique parameters S, U , V , W and X in the SM extended by both, hypercharge Y = 0 and Y = 1, triplet scalars. (author)