Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation

We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced by us [D. Bini and T. Damour, Phys. Rev. D 96, 104038 ( 2017)], we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the effective one-body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.