  We present new calculations of the energy flux of a spinning test-body on
circular orbits around a Schwarzschild black hole at linear order in the
particle spin. We compute the multipolar fluxes up to $\ell=m=6$ using two
independent numerical solvers of theTeukolsky equation, one in the time domain
and the other in the frequency domain. After linearization in the spin of the
particle, we obtain an excellent agreement ($\sim 10^{-5}$) between the two
numerical results.The calculation of the multipolar fluxes is also performed
analytically (up to $\ell=7$) using the post-Newtonian (PN) expansion of the
Teukolsky equation solution; each mode is obtained at 5.5PN order beyond the
corresponding leading-order contribution. From the analytical fluxes we obtain
the PN-expanded analytical waveform amplitudes. These quantities are then
resummed using new procedures either based on the factorization of the orbital
contribution (and resumming it independently from the spin-dependent factor) or
on the factorization of the tail contribution solely for odd-parity multipoles.
We compare these prescriptions and the resummation procedure proposed in Pan et
al. [Phys. Rev. D 83 (2011) 064003] to the numerical data. We find that the new
procedures significantly improve over the existing one that, notably, is
inconsistent with the numerical data for $\ell+m=\text{odd}$ multipoles already
at low orbital frequencies. Our study suggests that the approach to waveform
resummation used in current effective-one-body-based waveform models should be
modified to improve its robustness and accuracy all over the binary parameter
space.
