Non-relativistic fermion–fermion scattering in higher derivative gravity

Abstract

In this note, we examine the scattering of two identical fermions in theories where fermionic fields minimally coupled to higher derivative gravity. In particular, we consider the extension of general relativity with R 2 corrections or non-local terms. We expand the action of fermions around the flat space background and obtain two fermion-one graviton vertex. Then, by considering the scattering amplitude of two fermions, we calculate the non-relativistic limit and that obtain the potential for two fermion-fermion interaction which would be the usual Newtonian potential corrected with a Yukawa-like term. At the end, we briefly discuss the astronomical effects of such Yukawa-like potential by computing the gravitational pressure of a spherical star and use it for a white dwarf to obtain quantum corrections of Chandrasekhar radius.

Gravity and Spin Forces in Gravitational Quantum Field Theory

“…Then our result of the scattering amplitude, except for the overall coefficient and F (p 1 − p 3 ) term that are related to the background field, is consistent with the leading order result shown in Ref. [14]. If we were working in another gauge fixing condition, the difference would be terms proportional to q µ q ν /q 2 , contracted with the vertex will gives the term ū3 (p ̸ 3 − p ̸ 1 )u 1 or (p 3 − p 1 ) • (p 3 + p 1 ), both of which are vanishing because of the on-shell condition of the external fermions.…”

“…Then our result of the scattering amplitude, except for the overall coefficient and F (p 1 −p 3 ) term that are related to the background field, is consistent with the leading order result shown in [14].…”