  We test the regime of validity of the effective field theory (EFT) of
intrinsic alignments (IA) at the one-loop level by comparing with 3D halo shape
statistics in N-body simulations. This model is based on the effective field
theory of large-scale structure (EFT of LSS) and thus a theoretically
well-motivated extension of the familiar non-linear alignment (NLA) model and
the tidal-alignment-tidal-torquing (TATT) model. It contains a total of $8$
free bias parameters. Specifically, we measure the dark matter halo shape-shape
multipoles $P_{EE}^{(0)}(k), P_{EE}^{(2)}(k), P_{BB}^{(0)}(k), P_{BB}^{(2)}(k)$
as well as the matter-shape multipoles $P_{\delta E}^{(0)}(k), P_{\delta
E}^{(2)}(k)$ from the simulations and perform a joint fit to determine the
largest wavenumber $k_{\text{max}}$ up to which the theory predictions from the
EFT of IA are consistent with the measurements. We find that the EFT of IA is
able to describe intrinsic alignments of dark matter halos up to
$k_\text{max}=0.30\,h/\text{Mpc}$ at $z=0$. This demonstrates a clear
improvement over other existing alignment models like NLA and TATT, which are
only accurate up to $k_\text{max}=0.05\,h/\text{Mpc}$ . We examine the
posterior distributions of the higher-order bias parameters, and show that
their inclusion is necessary to describe intrinsic alignments in the
quasi-linear regime. Further, the EFT of IA is able to accurately describe the
auto-spectrum of intrinsic alignment B-modes, in contrast to the other
alignment models considered.
