Compton amplitude and contact term(s) in the spinor helicity formalism

A bstract 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 terms for electromagnetic Compton amplitude. We considered three-point amplitude between two massive particles & a photon to be one which is responsible for soft photon theorem/Coulomb interaction. We demonstrate that it is possible to use the above-mentioned principle to find the contact term for the tree-level Compton amplitude which makes it gauge invariant, unitary and free of spurious poles. We also verify the results with the amplitude factorization approach.