Using the science verification data of the Dark Energy Survey (DES) for a new sample of 106 X-Ray selected clusters and groups, we study the stellar mass growth of Bright Central Galaxies (BCGs) since redshift 1.2. Compared with the expectation in a
semi-analytical model applied to the Millennium Simulation, the observed BCGs become under-massive/under-luminous with decreasing redshift. We incorporate the uncertainties associated with cluster mass, redshift, and BCG stellar mass measurements into analysis of a redshift-dependent BCG-cluster mass relation, $m_{*}propto(frac{M_{200}}{1.5times 10^{14}M_{odot}})^{0.24pm 0.08}(1+z)^{-0.19pm0.34}$, and compare the observed relation to the model prediction. We estimate the average growth rate since $z = 1.0$ for BCGs hosted by clusters of $M_{200, z}=10^{13.8}M_{odot}$, at $z=1.0$: $m_{*, BCG}$ appears to have grown by $0.13pm0.11$ dex, in tension at $sim 2.5 sigma$ significance level with the $0.40$ dex growth rate expected from the semi-analytic model. We show that the buildup of extended intra-cluster light after $z=1.0$ may alleviate this tension in BCG growth rates.
