  We present a multi-wavelength photometric and spectroscopic study of 42
Brightest Cluster Galaxies (BCGs) in two samples of galaxy clusters chosen for
a gravitational lensing study. The study's initial sample combines 25 BCGs from
the Cluster Lensing and Supernova Survey with Hubble (CLASH) sample and 37 BCGs
from the Sloan Giant Arcs Survey (SGAS) with a total redshift range of 0.2 < z
< 0.7. Using archival GALEX, Hubble Space Telescope, Wide-field Infrared Survey
Explorer, Herschel, and Very Large Array data we determine the BCGs' stellar
mass, radio power, and star formation rates. The radio power is higher than
expected if due to star formation, consistent with the BCGs being active
galactic nucleus (AGN)-powered radio sources. This suggests that the AGN and
star formation are both fueled by cold gas in the host galaxy. The specific
star formation rate (sSFR) is low and constant with redshift. The mean sSFR is
9.42 * 10^-12 yr^-1, which corresponds to a mass doubling time of 105 billion
years. These findings are consistent with models for hierarchical formation of
BCGs, which suggest that star formation is no longer a significant channel for
galaxy growth for z < 1. Instead, stellar growth (of the order of a factor of
at least two) during this period is expected to occur mainly via minor dry
mergers
