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

Avijit Sen Majumder* and Sourav Bhattacharya†

  • Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Kolkata 700 032, India

  • *Contact author: senmajumderavijit@gmail.com
  • †Contact author: sbhatta.physics@jadavpuruniversity.in
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Phys. Rev. D 113, 125004 – Published 2 June, 2026

DOI: https://doi.org/10.1103/nsft-3lh9

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 nonrelativistic 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 exchange. Leading Newton potential, as well as the subleading spin or polarization dependent terms at O(G) have been computed. We also consider the next to the leading order [O(G2)] 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.

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Phys. Rev. D 113, 125004– Published 2 June, 2026
  • Received 29 December 2025
  • Accepted 11 May 2026
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