Weak-lensing mass calibration of \emph{Planck} Sunyaev--Zel'dovich clusters with HSC-SSP Year~3

We present a weak gravitational lensing mass calibration of 19 $\mathit{\text{Planck}}$ Sunyaev–Zel’dovich (SZ) selected galaxy clusters using shape measurements from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Year 3 shape catalog. We measure the stacked weak-lensing signal $\mathrm{\Delta }\mathrm{\Sigma }(R)$ using per-cluster lensing weights that match the measurement pipeline’s stacking scheme, and construct an analytical covariance matrix that includes shape noise and projected large-scale structure contributions. Our primary constraint on the SZ mass bias comes from a forward-modeling approach that integrates over the halo mass function while accounting for the $\mathit{\text{Planck}}$ SZ selection function, Eddington bias from log-normal scatter in the SZ mass proxy, and cluster miscentering. Fitting four free parameters, the log mass bias $\ln (1-b)$, the miscentered fraction $f_{\mathrm{m}\mathrm{i}\mathrm{s}}$, the offset scale ${\sigma }_{\mathrm{o}\mathrm{f}\mathrm{f}}$, and the SZ scatter ${\sigma }_{\ln M}$, over the radial range $0.5$–$5.0h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$, we obtain $1-b=0.73_{-0.11}^{+0.10}$ with ${\chi }^2\mathrm{/}\mathrm{d}\mathrm{o}\mathrm{f}=5.2\mathrm{/}5$ at an effective redshift $z_{\mathrm{e}\mathrm{f}\mathrm{f}}\simeq 0.24$. This measurement is consistent with recent weak-lensing calibrations of SZ-selected clusters and supports the picture that significant mass bias corrections are required to reconcile cluster abundance measurements with primary cosmic microwave background constraints on cosmological parameters.