Your picture threw my blood pressure through the roof! I recently had the same experience with a murdered pet chicken and the culprit was in deed a cat. It wasn't decapitated though, but still similar.
I SAW the cat with the carcass and have previously and since chased the same cat stalking my babies in their fairly well protected run.
The initial (& fatal) attack from the cat appeared to have been grabbed from the front of the neck and dragged. She had a broken leg and that thigh and breast meat had been devoured (obviously post mortem) on my property because the cat couldn't leave with it because of my fenced yard. I am still furious and have since bought a cage trap from harbor freight for 20 bucks. If I catch it, it's going to the pound pronto especially since the 'owners' called it a stray (yeah right... it is one of the lone surviving kittens from their unfixed momma cat... enough said on that issue).
I'd like to get a copy of the predator list too. My run is better now but not Fort Knox yet... I've found 2 of my beloved hens out again (they like to perch HIGH and I've since seen them fly up flapping wings and knocked the tarp covering loose at a corner and then flew out... thank God they were fine but it is SO scary especially after losing one so tragically. Now I have a roll of chicken wire for the top of the dog kennel in addition to the hardware cloth at the bottom to keep digging critters out. I had no idea they could Fly THAT high... it's amazing! But I don't want to clip wings, instead I'll make my run into an aviary covered run.
I'm so sorry for what has happened to you... and I know it is devastating and isn't easy to soon forget, but use that energy to figure out how to best protect your flock. That's all we can do, except for catching the predator once and for all. The only other predators I've sighted in my area are hawks, owls and a black rat snake... but in my case I SAW the cat laying there like a LION with it's kill after the feast. I think if you have raccoons, you will see them around... and I thought a hawk or owl will fly OFF with it's prey... but I'm not an expert. This is my first season having chickens. I read something about a martin???? that decapitates the head, but I don't know what a martin is... anybody????