Congradulations on your deer. I bet you were pumped.

As far as your arrow breaking. Thats probably more rare for a carbon than an aluminum, but when the deer ran is hard telling what force was asserted on that arrow by trees, brush etc. I once shot a dandy buck, to far back, in the paunch with an aluminum arrow. Later after trailing it through two woods, several fields and it had jumped two fences, we found him with the arrow. The distance was like 3/4 mile and the arrow was perfectly straight. So anything is possible.
Whether broken or lost, one concern then is where is the broadhead when you field dress it.
Happy Hunting
Dan