  We calculate the quantum corrections to the gauge-invariant gravitational
potentials of spinning particles in flat space, induced by loops of both
massive and massless matter fields of various types. While the corrections to
the Newtonian potential induced by massless conformal matter for spinless
particles are well-known, and the same corrections due to massless minimally
coupled scalars [Class. Quant. Grav. 27 (2010) 245008], massless non-conformal
scalars [Phys. Rev. D 87 (2013) 104027] and massive scalars, fermions and
vector bosons [Phys. Rev. D 91 (2015) 064047] have been recently derived,
spinning particles receive additional corrections which are the subject of the
present work. We give both fully analytic results valid for all distances from
the particle, and present numerical results as well as asymptotic expansions.
At large distances from the particle, the corrections due to massive fields are
exponentially suppressed in comparison to the corrections from massless fields,
as one would expect. However, a surprising result of our analysis is that close
to the particle itself, on distances comparable to the Compton wavelength of
the massive fields running in the loops, these corrections can be enhanced with
respect to the massless case.
