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Using dedicated hydrodynamical simulations, we present systematic analyses simulating the expected weak-lensing profiles from clusters in a variety of dynamic states and for a wide range of redshifts. In order to derive cluster masses, we use a model consistent with the implementation within the <jats:italic>Euclid<\/jats:italic> Consortium of the dedicated processing function and find that when we jointly model the mass and concentration parameter of the Navarro\u2013Frenk\u2013White halo profile, the weak-lensing masses tend to be biased low by 5\u201310% on average with respect to the true mass, up to <jats:italic>z<\/jats:italic>\u2004=\u20040.5. For a fixed value for the concentration <jats:italic>c<\/jats:italic><jats:sub>200<\/jats:sub>\u2004=\u20043, the mass bias is decreases to lower than 5%, up to <jats:italic>z<\/jats:italic>\u2004=\u20040.7, along with the relative uncertainty. Simulating the weak-lensing signal by projecting along the directions of the axes of the moment of inertia tensor ellipsoid, we find that orientation matters: when clusters are oriented along the major axis, the lensing signal is boosted, and the recovered weak-lensing mass is correspondingly overestimated. Typically, the weak-lensing mass bias of individual clusters is modulated by the weak-lensing signal-to-noise ratio, which is related to the redshift evolution of the number of galaxies used for weak-lensing measurements: the negative mass bias tends to be stronger toward higher redshifts. However, when we use a fixed value of the concentration parameter, the redshift evolution trend is reduced. These results provide a solid basis for the weak-lensing mass calibration required by the cosmological application of future cluster surveys from <jats:italic>Euclid<\/jats:italic> and <jats:italic>Rubin<\/jats:italic>.<\/jats:p>","DOI":"10.1051\/0004-6361\/202346058","type":"journal-article","created":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T19:57:13Z","timestamp":1702670233000},"page":"A67","source":"Crossref","is-referenced-by-count":28,"title":["<i>Euclid<\/i> preparation"],"prefix":"10.1051","volume":"681","author":[{"name":"Euclid Collaboration","sequence":"first","affiliation":[]},{"given":"C.","family":"Giocoli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1225-7084","authenticated-orcid":false,"given":"M.","family":"Meneghetti","sequence":"additional","affiliation":[]},{"given":"E.","family":"Rasia","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6151-6439","authenticated-orcid":false,"given":"S.","family":"Borgani","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6150-4112","authenticated-orcid":false,"given":"G.","family":"Despali","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4607-2830","authenticated-orcid":false,"given":"G. 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