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We constrain the mass--richness scaling relation of redMaPPer galaxy clustersidentified in the Dark Energy Survey Year 1 data using weak gravitationallensing. We split clusters into $4\times3$ bins of richness $\lambda$ andredshift $z$ for $\lambda\geq20$ and $0.2 \leq z \leq 0.65$ and measure themean masses of these bins using their stacked weak lensing signal. By modelingthe scaling relation as $\langle M_{\rm 200m}|\lambda,z\rangle = M_0(\lambda/40)^F ((1+z)/1.35)^G$, we constrain the normalization of the scalingrelation at the 5.0 per cent level as $M_0 = [3.081 \pm 0.075 ({\rm stat}) \pm0.133 ({\rm sys})] \cdot 10^{14}\ {\rm M}_\odot$ at $\lambda=40$ and $z=0.35$.The richness scaling index is constrained to be $F=1.356 \pm 0.051\ ({\rmstat})\pm 0.008\ ({\rm sys})$ and the redshift scaling index $G=-0.30\pm 0.30\({\rm stat})\pm 0.06\ ({\rm sys})$. These are the tightest measurements of thenormalization and richness scaling index made to date. We use a semi-analyticcovariance matrix to characterize the statistical errors in the recovered weaklensing profiles. Our analysis accounts for the following sources of systematicerror: shear and photometric redshift errors, cluster miscentering, clustermember dilution of the source sample, systematic uncertainties in the modelingof the halo--mass correlation function, halo triaxiality, and projectioneffects. We discuss prospects for reducing this systematic error budget, whichdominates the uncertainty on $M_0$. Our result is in excellent agreement with,but has significantly smaller uncertainties than, previous measurements in theliterature, and augurs well for the power of the DES cluster survey as a toolfor precision cosmology and upcoming galaxy surveys such as LSST, Euclid andWFIRST.

Dark Energy Survey Year 1 Results: Weak Lensing Mass Calibration of redMaPPer Galaxy Clusters