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The capacity of Stage IV lensing surveys to measure the neutrino mass sum anddifferentiate between the normal and inverted mass hierarchies depends on theimpact of nuisance parameters describing small-scale baryonic astrophysics andintrinsic alignments. For a Euclid-like survey, we perform the first combinedweak lensing and galaxy clustering Fisher analysis with baryons, intrinsicalignments, and massive neutrinos for both hierarchies. We use a matter powerspectrum generated from a halo model that captures the impact of baryonicfeedback and adiabatic contraction. For weak lensing, we find that baryonscause severe degradation to forecasts of the neutrino mass sum, $\Sigma$,approximately doubling $\sigma_{\Sigma}$. We show that including galaxyclustering constraints from Euclid and BOSS, and cosmic microwave background(CMB) Planck priors, can reduce this degradation to $\sigma_{\Sigma}$ to 9% and16% for the normal and inverted hierarchies respectively. The combinedforecasts, $\sigma_{\Sigma_{\rm{NH}}}=0.034\, \rm{eV}$ and$\sigma_{\Sigma_{\rm{IH}}}=0.034\, \rm{eV}$, preclude a meaningful distinctionof the hierarchies but could be improved upon with future CMB priors on $n_s$and information from neutrinoless double beta decay to achieve a 2$\sigma$distinction. The effect of intrinsic alignments on forecasts is shown to beminimal, with $\sigma_{\Sigma}$ even experiencing mild improvements due toinformation from the intrinsic alignment signal. We find that while adiabaticcontraction and intrinsic alignments will require careful calibration toprevent significant biasing of $\Sigma$, there is less risk presented byfeedback from energetic events like AGN and supernovae.

Towards determining the neutrino mass hierarchy: weak lensing and galaxy clustering forecasts with baryons and intrinsic alignments