regex for validating email?

There isn't a correct one. Check that there's something, then an @, then something with no spaces, and then send them a message with a link. That's the only test that tells you whether it's a real address that belongs to them.

^[^@\s]+@[^@\s]+$ and move on. Every stricter one I've seen in production rejects somebody's real address, usually with a plus sign or a newer TLD in it.

The full RFC one is a page long. People print it out to frighten juniors.