One-Loop Calculation of the Oblique S Parameter in Higgsless Electroweak Models

TL;DR

This paper calculates the oblique S parameter at one-loop in Higgsless electroweak models, analyzing how resonance masses affect compatibility with electroweak precision data.

Contribution

It provides a comprehensive one-loop calculation of the S parameter in Higgsless models using a general effective Lagrangian and short-distance constraints.

Findings

Resonance masses must be above 1.8 TeV to satisfy experimental limits.

Vector resonance mass M_V > 1.8 TeV at 3σ level in asymptotically-free theories.

Axial resonance mass M_A > 2.5 TeV at 3σ level.

Abstract

We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking and analyze the phenomenological implications of the available electroweak precision data. We use the most general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)_L x SU(2)_R -> SU(2)_{L+R} with Goldstones, gauge bosons and one multiplet of vector and axial-vector massive resonance states. Using the dispersive representation of Peskin and Takeuchi and imposing the short-distance constraints dictated by the operator product expansion, we obtain S at the NLO in terms of a few resonance parameters. In asymptotically-free gauge theories, the final result only depends on the vector-resonance mass and requires M_V > 1.8 TeV (3.8 TeV) to satisfy the experimental limits at the 3 \sigma (1\sigma) level; the axial state is always heavier, we obtain M_A > 2.5 TeV (6.6 TeV) at 3\sigma (1\sigma). In strongly-coupled models, such as walking or conformal technicolour, where the second Weinberg sum rule does not apply, the vector and axial couplings are not determined by the short-distance constraints; but one can still derive a lower bound on S, provided the hierarchy M_V < M_A remains valid. Even in this less constrained situation, we find that in order to satisfy the experimental limits at 3\sigma one needs M_{V,A} > 1.8 TeV.