Optical-SZE Scaling Relations for DES Optically Selected Clusters within
  the SPT-SZ Survey
  We study the Sunyaev-Zel'dovich effect (SZE) signature in South Pole
Telescope (SPT) data for an ensemble of 719 optically identified galaxy
clusters selected from 124.6 deg$^2$ of the Dark Energy Survey (DES) science
verification data, detecting a stacked SZE signal down to richness
$\lambda\sim20$. The SZE signature is measured using matched-filtered maps of
the 2500 deg$^2$ SPT-SZ survey at the positions of the DES clusters, and the
degeneracy between SZE observable and matched-filter size is broken by adopting
as priors SZE and optical mass-observable relations that are either calibrated
using SPT selected clusters or through the Arnaud et al. (2010, A10) X-ray
analysis. We measure the SPT signal to noise $\zeta$-$\lambda$, relation and
two integrated Compton-$y$ $Y_\textrm{500}$-$\lambda$ relations for the
DES-selected clusters and compare these to model expectations accounting for
the SZE-optical center offset distribution. For clusters with $\lambda > 80$,
the two SPT calibrated scaling relations are consistent with the measurements,
while for the A10-calibrated relation the measured SZE signal is smaller by a
factor of $0.61 \pm 0.12$ compared to the prediction. For clusters at $20 <
\lambda < 80$, the measured SZE signal is smaller by a factor of
$\sim$0.20-0.80 (between 2.3 and 10~$\sigma$ significance) compared to the
prediction, with the SPT calibrated scaling relations and larger $\lambda$
clusters showing generally better agreement. We quantify the required
corrections to achieve consistency, showing that there is a richness dependent
bias that can be explained by some combination of contamination of the
observables and biases in the estimated masses. We discuss possible physical
effects, as contamination from line-of-sight projections or from point sources,
larger offsets in the SZE-optical centering or larger scatter in the
$\lambda$-mass relation at lower richnesses.
