Abstract
We formulate an effective field theory describing large mass scalars and fermions minimally coupled to gravity. The operators of this effective field theory are organized in powers of the transfer momentum divided by the mass of the matter field, an expansion which lends itself to the efficient extraction of classical contributions from loop amplitudes in both the post-Newtonian and post-Minkowskian regimes. We use this effective field theory to calculate the classical and leading quantum gravitational scattering amplitude of two heavy spin-1/2 particles at the second post-Minkowskian order.
Highlights
This necessarily entails the calculation of higher orders in the post-Newtonian (PN) and post-Minkowskian (PM) expansions
Techniques were recently presented in refs. [25, 26] to convert fully relativistic amplitudes for scalar-scalar scattering to the classical potential, and for obtaining the scattering angle directly from the scattering amplitude [27, 28]
While significant progress has been made in understanding the relationship between gravitational scattering amplitudes and classical gravitational quantities, it remains uneconomical to extract the few classically contributing terms from the multitude of other terms that constitute the full amplitude
Summary
In quantum field theory we are accustomed to working with units where both the reduced Planck constant and the speed of light c are set to unity, obscuring the classical limit. As mentioned above, we must distinguish between the momentum of a massless particle pμ and its wavenumber pμ. They are related through pμ = pμ. The momenta and masses of the massive particles must be kept constant, whereas for massless particles it is the wavenumber that must be kept constant. While this result is achieved formally through the consideration of wavefunctions in ref. We are interested in the scattering of two massive particles, where the momentum q is transferred via massless particles (photons or gravitons). The classical limit of the kinematics is associated with the limit |q| → 0
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