It's an awful thing to witness and deal with but you're clearly an animal lover @ArcticHeron as evidenced by your reaction and your desire to go find the owners, have empathy and do the right thing. Plenty of scumbags would have dumped the cat's body somewhere and carried on as if nothing happened.
You have a sight hound, as do I, and you know that they nearly all have extremely high prey drives. Mild mannered and placid 99% of the time but bred over centuries to chase small furry things. I liken it to a red mist that instantly descends as they can go from almost snoozing to full on attack mode. It's in their DNA and while it is of course possible to train it out of them it is really, really hard, especially if you didn't have them as a puppy. You were in your own home and there's no expectation of having to keep them on a lead or muzzled there. They'll hit top speed (probably about 40mph for a greyhound) in six strides from a standing start - you can't stop them when they go. It's just a really horrible situation but don't beat yourself up too much about it.
You have a sight hound, as do I, and you know that they nearly all have extremely high prey drives. Mild mannered and placid 99% of the time but bred over centuries to chase small furry things. I liken it to a red mist that instantly descends as they can go from almost snoozing to full on attack mode. It's in their DNA and while it is of course possible to train it out of them it is really, really hard, especially if you didn't have them as a puppy. You were in your own home and there's no expectation of having to keep them on a lead or muzzled there. They'll hit top speed (probably about 40mph for a greyhound) in six strides from a standing start - you can't stop them when they go. It's just a really horrible situation but don't beat yourself up too much about it.