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Modelling uncertainties at small scales, i.e. high $k$ in the power spectrum$P(k)$, due to baryonic feedback, nonlinear structure growth and the fact thatgalaxies are biased tracers poses a significant obstacle to fully leverage theconstraining power of the {\it Euclid} wide-field survey. $k$-cut cosmic shearhas recently been proposed as a method to optimally remove sensitivity to thesescales while preserving usable information. In this paper we generalise the$k$-cut cosmic shear formalism to $3 \times 2$ point statistics and estimatethe loss of information for different $k$-cuts in a $3 \times 2$ point analysisof the {\it Euclid} data. Extending the Fisher matrix analysisof~\citet{blanchard2019euclid}, we assess the degradation in constraining powerfor different $k$-cuts. We work in the idealised case and assume the galaxybias is linear, the covariance is Gaussian, while neglecting uncertainties dueto photo-z errors and baryonic feedback. We find that taking a $k$-cut at $2.6\ h \ {\rm Mpc} ^{-1}$ yields a dark energy Figure of Merit (FOM) of 1018. Thisis comparable to taking a weak lensing cut at $\ell = 5000$ and a galaxyclustering and galaxy-galaxy lensing cut at $\ell = 3000$ in a traditional $3\times 2$ point analysis. We also find that the fraction of the observedgalaxies used in the photometric clustering part of the analysis is one of themain drivers of the FOM. Removing $50 \% \ (90 \%)$ of the clustering galaxiesdecreases the FOM by $19 \% \ (62 \%)$. Given that the FOM depends so heavilyon the fraction of galaxies used in the clustering analysis, extensive effortsshould be made to handle the real-world systematics present when extending theanalysis beyond the luminous red galaxy (LRG) sample.

Euclid: Forecasts for $k$-cut $3 \times 2$ Point Statistics