Flat space Fermionic Wave-function coefficients

TL;DR

This paper studies the structure of flat-space wavefunction coefficients for fermionic operators, deriving cutting rules and an iterative reconstruction method from the S-matrix, showing the four-particle test aligns with S-matrix consistency.

Contribution

It introduces a novel analysis of fermionic wavefunction coefficients, deriving cutting rules and an iterative method to reconstruct WFCs from the S-matrix, ensuring correct pole structure.

Findings

Derived cutting rules for internal-fermion lines.

Established an iterative procedure to reconstruct WFCs from the S-matrix.

Showed the four-particle test aligns with S-matrix consistency.

Abstract

In this work we analyze the analytic structure of tree-level flat-space wavefunction coefficients (WFCs), with particular attention to fermionic operators, and derive cutting rules for internal-fermion lines. Building on these results, we set up an iterative procedure that, starting from the flat-space S-matrix, reconstructs the 3- and 4-point WFCs with the correct partial- and total-energy poles and satisfying the requisite cutting rules. Consequently, the "four-particle test" for flat-space WFCs imposes no additional constraints beyond the consistency of the flat-space S-matrix.