The Richness-to-Mass Relation of CAMIRA Galaxy Clusters from
  Weak-lensing Magnification in the Subaru Hyper Suprime-Cam Survey
  We present a statistical weak-lensing magnification analysis on an optically
selected sample of 3029 \texttt{CAMIRA} galaxy clusters with richness $N>15$ at
redshift $0.2\leq z <1.1$ in the Subaru Hyper Suprime-Cam (HSC) survey. We use
two distinct populations of color-selected, flux-limited background galaxies,
namely the low-$z$ and high-$z$ samples at mean redshifts of $\approx1.1$ and
$\approx1.4$, respectively, from which to measure the weak-lensing
magnification signal by accounting for cluster contamination as well as masking
effects. Our magnification bias measurements are found to be uncontaminated
according to validation tests against the "null-test" samples for which the net
magnification bias is expected to vanish. The magnification bias for the full
\texttt{CAMIRA} sample is detected at a significance level of $9.51\sigma$,
which is dominated by the high-$z$ background. We forward-model the observed
magnification data to constrain the normalization of the richness-to-mass
($N$--$M$) relation for the \texttt{CAMIRA} sample with informative priors on
other parameters. The resulting scaling relation is $N\propto
{M_{500}}^{0.92\pm0.13} (1 + z)^{-0.48\pm0.69}$, with a characteristic richness
of $N=\left(17.72\pm2.60\right)$ and intrinsic log-normal scatter of
$0.15\pm0.07$ at $M_{500} = 10^{14}h^{-1}M_{\odot}$. With the derived $N$--$M$
relation, we provide magnification-calibrated mass estimates of individual
\texttt{CAMIRA} clusters, with the typical uncertainty of $\approx39\%$ and
$\approx32\%$ at richness$\approx20$ and $\approx40$, respectively. We further
compare our magnification-inferred $N$--$M$ relation with those from the
shear-based results in the literature, finding good agreement.
