  Complex organic molecules (COMs) have been observed to be abundant in the gas
phase toward protostars. Deep line surveys have been carried out only for a
limited number of well-known high-mass star forming regions using the Atacama
Large Millimeter/submillimeter Array (ALMA), which has unprecedented resolution
and sensitivity. Statistical studies on oxygen-bearing COMs (O-COMs) in
high-mass protostars using ALMA are still lacking. With the recent CoCCoA
survey, we are able to determine the column density ratios of six O-COMs with
respect to methanol (CH$_3$OH) in a sample of 14 high-mass protostellar sources
to investigate their origin through ice and/or gas-phase chemistry. The
selected species are: acetaldehyde (CH$_3$CHO), ethanol (C$_2$H$_5$OH),
dimethyl ether (DME, CH$_3$OCH$_3$), methyl formate (MF, CH$_3$OCHO),
glycolaldehyde (GA, CH$_2$OHCHO), and ethylene glycol (EG, (CH$_2$OH)$_2$). DME
and MF have the highest and most constant ratios within one order of magnitude,
while the other four species have lower ratios and exhibit larger scatter by
1-2 orders of magnitude. We compare the O-COM ratios of high-mass CoCCoA
sources with those of 5 low-mass protostars available from the literature,
along with the results from experiments and simulations. We find that the O-COM
ratios with respect to methanol are on the same level in both the high- and
low-mass samples, which suggests that these species are mainly formed in
similar environments during star formation, probably in ice mantles on dust
grains during early pre-stellar stages. Current simulations and experiments can
reproduce most observational trends with a few exceptions, and hypotheses exist
to explain the differences between observations and simulations/experiments,
such as the involvement of gas-phase chemistry and different emitting areas of
molecules.
