Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order

Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post-Newtonian expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around a Schwarzschild black hole. We extract coefficients up to 20 post-Newtonian order from numerical results that are calculated with an accuracy greater than 1 part in 10^500. These results can be used to calibrate parameters in effective-one-body models of compact binaries, specifically the spin-orbit part of the effective Hamiltonian and the dynamically significant tidal part of the main radial potential of the effective metric. Our calculations are performed in a radiation gauge, which is known to be singular away from the particle. To overcome this irregularity, we define suitable Detweiler--Whiting singular and regular fields in this gauge, and we compute the invariants using mode-sum regularization in combination with averaging from two sides of the particle. The detailed justification of this regularization procedure will be presented in a forthcoming companion paper.