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One of the main limitations in precision cluster cosmology arises fromsystematic errors and uncertainties in estimating cluster masses. Using theMock-X pipeline, we produce synthetic X-ray images and derive cluster andgalaxy group X-ray properties for a sample of over 30,000 simulated galaxygroups and clusters with $M_{\rm 500crit}$ between $10^{12}$ and $2\times10^{15}$ M$_{\odot}$ in IllustrisTNG. We explore the similarities anddifferences between IllustrisTNG predictions of the Sunyaev-Zel'dovich andX-ray scaling relations with mass. We find a median hydrostatic mass bias $b =0.125 \pm 0.003$ for $M_{\rm 500crit}$ $>10^{13}$ M$_{\odot}$. The biasincreases to $b = 0.17 \pm 0.004$ when masses are derived from synthetic X-rayobservations. We model how different underlying assumptions about thedependence of $Y_{\rm X}$ on halo mass can generate biases in the observed$Y_{\rm SZ} - M_{Y_{\rm X}}$ scaling relation. In particular, the simplifyingassumption that $Y_{\rm X} - M_{\rm tot}$ is self-similar at all mass scaleslargely hides the break in $Y_{\rm SZ} - M_{\rm tot}$ and overestimates $Y_{\rmSZ}$ at galaxy and groups scales. We show that calibrating the $Y_{\rm X}-$massproxy using a new model for a smoothly broken power law reproduces the trueunderlying $Y_{\rm SZ} - M_{\rm tot}$ scaling relation with high accuracy.Moreover, $M_{Y_{\rm X}}$ estimates calibrated with this method lead to $Y_{\rmSZ} - M_{Y_{\rm X}}$ predictions that are not biased by the presence of lowermass clusters or galaxy groups in the sample. Finally, we show that oursmoothly broken power law model provides a robust way to derive the $Y_{\rmX}-$mass proxy, significantly reducing the level of mass bias for clusters,groups, and galaxies.

Unifying Sunyaev-Zel'dovich and X-ray predictions from clusters to galaxy groups: the impact of X-ray mass estimates on the $Y-M$ scaling relation