Meat and mental health: Meat eaters suffer less depression, anxiety
I'd say the first big thing to highlight is that correlation is not causation - you wouldn't want someone to take this study as proof that eating meat makes you less depressed. I would imagine that vegans (in particular vegans who chose their diet on ethical grounds) are overall more concerned about the state of the world around them - or are at least subjected to more of an echo-chamber effect from their peers - which would contribute to anxiety and depression?