spinney: A Form Library for Helicity Spinors

TL;DR

Spinney delivers a Form-based library for handling helicity spinors in four and n = 4 - 2ε dimensions, enabling efficient symbolic manipulation for one-loop amplitudes across tensor-reduction and unitarity-based approaches. It implements dimension splitting, the 't Hooft algebra, Chisholm identities, and Majorana spinor handling, paired with multiple representations and conversion routines to adapt to different computational stages. The package supports conventional tensor reduction and integrand-level methods, including careful sign management for Majorana fermions, and demonstrates applications to Feynman-diagram reductions, Majorana processes, and unitarity-based coefficient extraction. Overall, Spinney provides a practical, memory-efficient tool for high-energy calculations requiring large algebraic expressions and adjustable regularisation schemes.

Abstract

In this work, the library spinney is presented, which provides an implementation of helicity spinors and related algorithms for the symbolical manipulation program Form. The package is well suited for symbolic amplitude calculations both in traditional, Feynman diagram based approaches and unitarity-based techniques.

Figures (3)

• Figure 1: Three-point diagram ($e^+e^-\rightarrow t\bar{t}$) discussed in the example.
• Figure 2: The process ($ff \rightarrow VV$) mediated by the exchange of a Majorana fermion ($\chi$) as discussed in the example. The left hand figure shows the original diagram; the middle figure shows the first choice of fermion orientation; and the figure on the right shows the second choice of orientation.
• Figure 3: Possible helicity configurations of the two box diagrams contributing to the $f\bar{f}\rightarrow f\bar{f}$ amplitude.