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A bstract The future Electron-Ion Collider (EIC) at Brookhaven National Laboratory, along with its primary capacity to elucidate the nuclear structure, will offer new opportunities to probe physics beyond the Standard Model coupled to the electroweak sector. Among the best motivated examples of such new physics are new heavy neutral leptons (HNLs), which are likely to play a key role in neutrino mass generation and lepton number violation. We study the capability of the EIC to search for HNLs, which can be produced in electron- proton collisions through charged current interactions as a consequence of their mixing with light neutrinos. We find that, with the EIC design energy and integrated luminosity, one is able to probe HNLs in the mass range of 1 – 100 GeV with mixing angles down to the order of 10 − 4 − 10 − 3 through the prompt decay signatures, and in the mass range of 1 10 GeV with | U e | 2 ~ 10 − 6 – 10 − 4 via the displaced decay signatures. We also consider the invisible mode where an HNL is undetected or decaying to dark sector particles. One could potentially probe heavy HNLs for mixing angles in the window 10 − 3 – 10 − 2 , provided SM background systematics can be brought under control. These searches are complementary to other probes of HNLs, such as neutrino-less double- β decay, meson decay, fixed-target, and high-energy collider experiments. 

Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.