Mitigating Nonlinear Systematics in Weak Lensing Surveys II: Stability and Diagnostics with Intrinsic Alignment

The Bernardeau-Nishimichi-Taruya (BNT) transform provides a powerful framework for analysing tomographic cosmic shear data by improving the localization of shear correlations in physical scale. It operates by performing a linear combination of the shear data vector in $\ell$-space, yielding a transformed vector that is better localized in both redshift and $k$-space. BNT is particularly useful for estimating cosmological parameters while minimizing the impact of poorly understood nonlinear physics, without discarding large amounts of information as is typically done with simple scale cuts. In our previous work, we showed that BNT outperforms traditional weak-lensing analyses; however, that study did not include intrinsic alignments (IA). In the present work, we assess the robustness of our BNT-based $k$-cut framework in the presence of realistic IA models. We consider two cases: (i) when the assumed IA model used in sampling is close to, but not identical to, the true one, and (ii) when the assumed IA model is significantly biased compared to the true one. In the first case, the $k$-cut framework yields precise and unbiased $S_8$ constraints even with limited knowledge of large-scale modes. Using Euclid-like mock data and a stringent $k$-cut of $k \le 0.1\;{\rm Mpc^{-1}}$ for all tomographic bins, we found that BNT can constrain $S_8$ with a precision better than 2\% while non-BNT has lost all constraining power. In the second case, the BNT transform serves as a powerful diagnostic tool, revealing internal inconsistencies in $k$-space and redshift-space both exceeding 5$\sigma$ when the functional form of the sampling and fiducial IA models differ fundamentally.