# Pair production processes and flavor in gauge-invariant perturbation theory

## TL;DR

This paper explores gauge-invariant perturbation theory in the standard model, analyzing how it describes bound states and flavor, with implications for collider processes and potential experimental tests.

## Contribution

It develops a framework for gauge-invariant perturbation theory, connecting bound states and flavor, and assesses its impact on fermion pair production at colliders.

## Key findings

- Ordinary perturbation theory is the leading approximation.
- Sub-leading corrections could be significant for heavy fermions.
- Potential experimental tests for top quark production scenarios.

## Abstract

Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout-Englert-Higgs effect. Such gauge-invariant states are composite operators which have necessarily only global quantum numbers. As a consequence, flavor is exchanged for custodial quantum numbers in the standard model, recreating the fermion spectrum in the process. Here, we study the implications of such a description, possibly also for the generation structure of the standard model. In particular, this implies that scattering processes are essentially bound-state-bound-state interactions, and require a suitable description. We analyze the implications for the pair-production process $e^+e^-\to{\bar f}f$ at a linear collider to leading order. We show how ordinary perturbation theory is recovered as the leading contribution. Developing a suitable PDF-type language, we also assess the impact of sub-leading contributions. We find that only for very heavy fermions in the final state, especially top quarks, sizable corrections could emerge. This gives an interesting, possibly experimentally testable, scenario for the formal field theory underlying the electroweak sector of the standard model.