Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
Arpan Bhattacharyya, Saptaswa Ghosh, Sounak Pal
Abstract
A bstract We investigate the correction to the potential that gives rise to the bound orbits and radiation from non-spinning inspiralling binary black holes in a dark matter environment consisting of axion-like particles and dark photons using the techniques of Worldline Effective Field Theory . We compute the conservative dynamics up to 1PN order for gravitational, electromagnetic, and Proca fields and up to 2PN order for the scalar field. The effect of axion-electromagnetic coupling ( g aγγ ) arises to the conservative dynamics at 2.5PN order and the kinetic mixing constant ( γ ) at 1PN order. Furthermore, we calculate the radiation due to the various fields present in our theory. We find that the contribution of g aγγ to the gravitational radiation appears at N (7) LO and to the scalar radiation appears at N (5) LO . We also find that these radiative corrections due to the coupling g aγγ vanishes for any orbit confined to a plane because of the existence of a binormal like term in effective radiative action but give rise to non-zero contributions for any orbit that lies in three dimensions . Last but not the least, γ contributes to the gravitational radiation at N (2) LO and N (4) LO .