Patterns of Deviation from the Standard Model

TL;DR

The article develops a gauge-invariant effective Lagrangian framework to study physics beyond the Standard Model, showing that tree-level generation of dimension-six operators generally dominates over loop-level generation, while some dimension-eight operators can be comparably important for certain observables such as trilinear gauge couplings. It systematically classifies operators under decoupling and nondecoupling assumptions, examining both linear and nonlinear Higgs sectors, and provides explicit mappings from operator coefficients to measurable shifts in gauge couplings. The work highlights that dimension-eight contributions can violate relations valid for dimension-six operators, potentially altering interpretations of precision data, and uses NDA to estimate typical operator sizes in strongly coupled scenarios. Collectively, the results guide where to look for deviations from the Standard Model at current and future colliders and clarify the roles of tree-level versus loop-induced effects in electroweak precision tests.

Abstract

Effective Lagrangians can be used to parametrize the effects of physics beyond the standard model. Assuming the complete theory is a gauge theory, we determine which effective operators may be generated at tree level, and which are only generated at loop level. The latter are be suppressed by factors of $1/ 16π^2$ and will therefore be quite difficult to detect. In particular, all operators changing the Standard-Model structure of the triple-gauge-vector couplings fall into this category. We also point out that in certain cases, dimension-eight operators may be more important than dimension-six operators. We discuss both the linear and non-linear representation of the Higgs sector.