  We study the wave-particle interactions between lower band chorus whistlers
and an anisotropic tenuous population of relativistic electrons. We present the
first direct comparison of first-principle Particle-in-Cell (PIC) simulations
with a quasi-linear diffusion code, in this context. In the PIC approach, the
waves are self-consistently generated by a temperature anisotropy instability
that quickly saturates and relaxes the system towards marginal stability. We
show that the quasi-linear diffusion and PIC results have significant
quantitative mismatch in regions of energy/pitch angle where the resonance
condition is not satisfied. Moreover, for pitch angles close to the loss cone
the diffusion code overestimates the scattering, particularly at low energies.
This suggest that higher order nonlinear theories should be taken in
consideration in order to capture non-resonant interactions, resonance
broadening, and to account for scattering at angles close to $90^\circ$.
