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We perform a measurement of the mass--richness relation of the redMaPPergalaxy cluster catalogue using weak lensing data from the Sloan Digital SkySurvey. We have carefully characterized a broad range of systematicuncertainties, including shear calibration errors, photo-$z$ biases, dilutionby member galaxies, source obscuration, magnification bias, incorrectassumptions about cluster mass profiles, cluster centering, halo triaxiality,and projection effects. We also compare measurements of the lensing signal fromtwo independently-produced shear and photometric redshift catalogues tocharacterize systematic errors in the lensing signal itself. Using a sample of5,570 clusters from $0.1\le z\le 0.33$, the normalization of our power-law massvs.\ $\lambda$ relation is $\log_{10}[M_{200m}/h^{-1}\ M_{\odot}]$ = $14.344\pm 0.021$ (statistical) $\pm 0.023$ (systematic) at a richness $\lambda=40$, a7 per cent calibration uncertainty, with a power-law index of$1.33^{+0.09}_{-0.10}$ ($1\sigma$). The detailed systematics characterizationin this work renders it the definitive weak lensing mass calibration for SDSSredMaPPer clusters at this time.

Weak Lensing Measurement of the Mass--Richness Relation of SDSS redMaPPer Clusters