Compton amplitude and Contact term(s) in the Spinor Helicity formalism

TL;DR

This paper investigates contact terms in gauge theories within the spinor helicity formalism, demonstrating a method to determine contact terms in Compton amplitudes that are gauge-invariant and free of spurious poles.

Contribution

It introduces a principle based on gauge invariance to explicitly compute contact terms in Compton amplitudes using the spinor helicity formalism, applicable to massive spinning particles.

Findings

Contact terms can be determined using gauge invariance principles.

The resulting Compton amplitudes are free from spurious poles.

Method applies to tree-level processes involving massive particles and photons.

Abstract

In gauge theories, contact terms play an important role in ensuring gauge invariance. In the spinor helicity formalism, the choice of a gauge-fixing condition manifests itself in the form of the choice of reference vector to write the massless polarization vector(s). However, this choice must be irrelevant in any gauge-invariant observable. We use this principle to determine contact term for Electromagnetic Compton amplitude. We considered three-point function between two massive particles \& a photon to be one which is responsible for soft photon theorem/Coulomb and demonstrate that it is possible to use the above-mentioned principle to find the contact term for the tree-level Compton amplitude of two bosonic massive spinning particles and two photons. The final result does not suffer from any spurious poles.