Scattering of massive spin-2 field via graviton exchanges with different spin fields and the long range gravitational potential

TL;DR

This paper calculates the gravitational scattering amplitudes of a massive spin-2 field with various particles, deriving the corresponding long-range potentials within general relativity, and explores higher-order corrections.

Contribution

It provides the first detailed computation of graviton-mediated scattering amplitudes involving a massive spin-2 field with different spins, including higher-order gravitational potential corrections.

Findings

Derived Newtonian and spin-dependent potentials at order G

Computed next-to-leading order scattering amplitudes at order G^2

Demonstrated the spin-independent spherically symmetric potential for higher spin fields

Abstract

In this work, we compute the graviton mediated scattering amplitude of a massive spin-2 Fierz-Pauli field with various other massive spin fields, and in the non-relativistic limit, find out the corresponding two-body gravitational potentials. The massive spin-2 field does not represent gravity here. The theory of gravity is taken to be the usual massless general relativity, and the massive spin-2 field is taken as a test quantum field coupled to gravity via the standard minimal prescription. We first compute the tree level 2-2 scattering of a massive spin-2 field with massive scalar, spin-1, and spin-1/2 fields with one graviton exchanges. Leading Newton potential, as well as the subleading spin or polarisation dependent terms at ${\cal O}(G)$ have been computed. We also consider the next to the leading order (${\cal O}(G^2)$) scattering of the massive spin-2 field with a massive scalar, and demonstrate the spin independent, spherically symmetric leading part of the two body gravitational potential. The present paper can be considered as an attempt to compute the gravitational potential in the context of a higher spin field theory.