Constraints on the Richness-Mass Relation and the Optical-SZE Positional
  Offset Distribution for SZE-Selected Clusters
  We cross-match galaxy cluster candidates selected via their
Sunyaev-Zel'dovich effect (SZE) signatures in 129.1 deg$^2$ of the South Pole
Telescope 2500d SPT-SZ survey with optically identified clusters selected from
the Dark Energy Survey (DES) science verification data. We identify 25 clusters
between $0.1\lesssim z\lesssim 0.8$ in the union of the SPT-SZ and redMaPPer
(RM) samples. RM is an optical cluster finding algorithm that also returns a
richness estimate for each cluster. We model the richness $\lambda$-mass
relation with the following function $\langle\ln\lambda|M_{500}\rangle\propto
B_\lambda\ln M_{500}+C_\lambda\ln E(z)$ and use SPT-SZ cluster masses and RM
richnesses $\lambda$ to constrain the parameters. We find $B_\lambda=
1.14^{+0.21}_{-0.18}$ and $C_\lambda=0.73^{+0.77}_{-0.75}$. The associated
scatter in mass at fixed richness is $\sigma_{\ln M|\lambda} =
0.18^{+0.08}_{-0.05}$ at a characteristic richness $\lambda=70$. We demonstrate
that our model provides an adequate description of the matched sample, showing
that the fraction of SPT-SZ selected clusters with RM counterparts is
consistent with expectations and that the fraction of RM selected clusters with
SPT-SZ counterparts is in mild tension with expectation. We model the
optical-SZE cluster positional offset distribution with the sum of two
Gaussians, showing that it is consistent with a dominant, centrally peaked
population and a sub-dominant population characterized by larger offsets. We
also cross-match the RM catalog with SPT-SZ candidates below the official
catalog threshold significance $\xi=4.5$, using the RM catalog to provide
optical confirmation and redshifts for additional low-$\xi$ SPT-SZ
candidates.In this way, we identify 15 additional clusters with $\xi\in
[4,4.5]$ over the redshift regime explored by RM in the overlapping region
between DES science verification data and the SPT-SZ survey.
