  We use the worldline formalism to study tree-level scattering processes
involving gravitons. A massless spin 2 particle is described by an $N=4$
supersymmetric worldline action which is also $O(4)$ symmetric. More generally,
$N=2S$ supersymmetric worldline actions exhibiting $O(N)$ symmetry describe
free spin $S$ particles. Recently a BRST approach was used to construct the
on-shell background graviton emission vertex from a graviton worldline.
Nonetheless, an action describing the coupling of higher spin ($S\geq 2$)
particles with generic background gravity is unknown. In this paper, we found
that in order to reproduce Einstein's general relativity 3-point graviton
vertex, interpreted as the emission of an off-shell graviton from the
worldline, the coupling to background gravity must break the $O(4)$ symmetry to
$O(2) \times O(2)$. In addition to this symmetry-breaking feature, we also
found that the coefficient $\beta$ of the worldline action counterterm $\beta
R$ differs from previous results in the literature. By comparing the linearized
graviton and photon emission vertex operators from different worldlines, we
noticed that they obey a squaring relation. For MHV (Maximal Helicity
Violating) amplitudes, these squaring relations among the linearized vertex
operators directly result in double-copy-like relations between the scattering
amplitudes.
