Disguising the Oblique Parameters

TL;DR

The work identifies operator identities, derived from the SM effective field theory equations of motion, that connect oblique corrections ($S$, $T$, $U$) to operators altering fermion–gauge couplings and to operators modifying triple gauge boson couplings. In the linear realization there are two independent relations; in the nonlinear (chiral) realization there are three. These relations imply that oblique effects can be mimicked by adjusting fermion couplings and gauge self-interactions, making some new-physics scenarios harder to constrain with precision electroweak data alone. The authors illustrate the idea with a triplet-scalar toy model and discuss potential extensions in extra-dimensional contexts, highlighting the necessity of measuring triple gauge couplings to robustly constrain such effects. Overall, the paper highlights a path for model-building that leverages specific operator combinations and underscores the importance of TGC measurements for ruling out hidden oblique-like new physics.

Abstract

We point out a set of operator identities that relate the operators corresponding to the oblique corrections to operators that modify fermion couplings to the gauge bosons as well as operators that modify triple gauge boson couplings. Such identities are simple consequences of the equations of motion. Therefore the contributions from new physics to the oblique parameters can be disguised as modifications of triple gauge boson couplings provided the fermion couplings to the gauge bosons are suitably modified by higher dimensional operators. Since the experimental constraints on triple gauge boson couplings are much weaker than the constraints on the oblique parameters this observation allows extra room for model building. We derive operator relations in effective theories of the Standard Model with the electroweak symmetry either linearly or nonlinearly realized and discuss applications of our results.