Momentum shift and on-shell recursion relation for electroweak theory

TL;DR

This paper introduces the ALT shift for on-shell recursion in massive spin-1 theories, applies it to electroweak interactions, and demonstrates automatic cancellation of high-energy growth terms, aiding the study of real-world amplitudes.

Contribution

It develops the ALT shift method for massive particles, applies it to electroweak theory, and shows automatic cancellation of high-energy divergences in recursive amplitude construction.

Findings

Four-point gauge boson contact terms arise automatically and cancel high-energy growth.

The ALT shift is valid for spin ≤ 1 theories and helps handle contact term ambiguities.

UV completion constraints are explored to ensure unitarity.

Abstract

We study the All-Line Transverse (ALT) shift which we developed for on-shell recursion of amplitudes for particles of any mass. We discuss the validity of the shift for general theories of spin $\leq$ 1, and illustrate the connection between Ward identity and constructibility for massive spin-1 amplitude under the ALT shift. We apply the shift to the electroweak theory, and various four-point scattering amplitudes among electroweak gauge bosons and fermions are constructed. We show explicitly that the four-point gauge boson contact terms in massive electroweak theory automatically arise after recursive construction, independent of UV completion, and they automatically cancel the terms growing as (energy)$^4$ at high energy. We explore UV completion of the electroweak theory that cancels the remaining (energy)$^2$ terms and impose unitarity requirements to constrain additional couplings. The ALT shift framework allows consistent treatment in dealing with contact term ambiguities for renormalizable massive and massless theories, which we show can be useful in studying real-world amplitudes with massive spinors.