Watched an arrow hit high some years back in similar circumstances- Same thing, greasy arrow with no blood-had also seen the arrow tip an unseen twig on the way to the deer. Hit further back than I wanted and quite high. That greasy stuff is from the thin layer of fat along the back and likely closer to the rear end of the deer where its a bit heavier- IMHO.
Tracked VERY slowly for some time and then saw 3 deer in the distance and one of them rolled onto its back and twisted all over the place. Kinda like a bear might rub its back on a tree while standing.
After they moved off I went over there to find NO BLOOD but lots of hair where the deer had rolled over and rubbed.
With that hit its likely not dead but carries a non life threatening wound- keep looking though.
A friend hit a fine buck early morning last season and the arrow appeared to him to be mid body and a bit far back. Little to no blood and the Deer ran off looking fine- He tracked for hours and looked all day. Was as disgusted as you are.
Several days later from the same stand he took that same buck as it chased a doe.
It had HUGE open wound on a rear quarter that ya would think woulda laid him up and gave him no toughts what so ever of chasing does.
This guy has taken dozens with the bow and had no idea he had struck so far back. Swore it was mid body.
Remember their nervous system is nowhere near as advanced as ours. Some wounds that would lay us up for months, they are marginally aware of.
Understandably ya feel lousy but don't give up on never seeing that deer again.
Too bad , but loosing one is a part of the game we play and it happens to most everyone sooner or later.
We are the predators.
BTW have see it take much more than 40 yds to start bleeding- sometimes nothing and then suddenly a torrent- especially with a high one lung shot.