Another forum had suggested that twitter doesn't base its serp effects off of links directly but rather the quality and amount of followers, then it pulls the relative content from the profile or retweets and that is what effects your serp. Then again other people came right back and said it was complete FUBAR so I don't know what to go with or whether or not to invest my time in really building a twitter following.
As far as traffic, twitter only provides temp traffic and not much of it becomes or organic (that I've experienced), so its not dependable. But if it turns out that twitter does effect your serps then your getting traffic and serp rankings with the effort you put in so answers are needed, haha.
just watch the QA session of 2011 by matt cutts on you tube. you can find it googlewebmasterhelp videos. It does affect your website ranking as well. Not only twitter but facebook and google plus also.
Does twitter effect your serp rank?
If it does, is it long term, short term, or does it depend on retweets and views?
SERP rank depends on the traffic got and the quality content. As how much your site content be found more time that much you get your serp rank increase. And if you have provided the best quality content in your twitter post and more followers then it will definitely help to get the better serp using twitter.
I think it is Yes, Major search engines like Google use social media metrix and signals a lot to determine the relevance and significance of a website hence it is important to stay active in social networking sites like twitter