The supersymmetric spinning polynomial

TL;DR

This paper introduces supersymmetric spinning polynomials as a new basis for analyzing four-point scattering amplitudes, ensuring super Poincare invariance and unitarity constraints.

Contribution

It constructs the supersymmetric spinning polynomials and the supersymmetric EFThedron, linking algebraic Jacobi-polynomials to amplitude analysis under supersymmetry.

Findings

Polynomials serve as an orthogonal basis for amplitude expansion.

The supersymmetric EFThedron geometrically constrains Wilson coefficients.

Polynomials are identified with algebraic Jacobi-polynomials.

Abstract

In this paper, we construct the supersymmetric spinning polynomials. These are orthogonal polynomials that serve as an expansion basis for the residue or discontinuity of four-point scattering amplitudes, respecting four-dimensional super Poincare invariance. The polynomials are constructed by gluing on-shell supersymmetric three-point amplitudes of one massive two massless multiplets, and are identified with algebraic Jacobi-polynomials. Equipped with these we construct the supersymmetric EFThedron, which geometrically defines the allowed region of Wilson coefficients respecting UV unitarity and super Poincare invariance.