Massless-Massive Amplitude Correspondence II: Constructive Massive Amplitudes in Standard Model

TL;DR

This paper develops a systematic on-shell method for constructing higher-point massive amplitudes in the Standard Model, extending massless-massive amplitude correspondence using contact amplitudes and recursion relations.

Contribution

It introduces a framework combining contact amplitudes and recursion relations to systematically build massive electroweak amplitudes, extending the massless-massive correspondence to general n-point functions.

Findings

Constructed all standard model massive contact amplitudes.

Demonstrated the use of bootstrap and recursion techniques for higher-point amplitudes.

Extended the massless-massive amplitude correspondence to n-point amplitudes.

Abstract

In the minimal helicity-chirality formalism, we systematically construct higher-point massive amplitudes from the fundamental building blocks: the contact three-point and four-point massive amplitudes. The inclusion of four-point contact amplitudes is essential to maintain gauge invariance in the spontaneously broken Standard Model. We construct all the standard model massive contact amplitudes and identify the physical light-cone gauge nature of massive amplitudes. Then only using the contact minimal helicity-chirality amplitudes at the leading order, we show both bootstrap techniques and on-shell recursion relations can be utilized to compute higher-point massive amplitudes. This provides a systematic framework for constructing various higher-point electroweak amplitudes, analogous to established on-shell methods for massless theories. Finally by deforming the gauge-invariant $n$-point amplitudes, we extend the massless-massive correspondence from three-and-four point contact amplitudes to general $n$-point factorized amplitudes.