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Jessica and her new man, Billy Corgan, may have been taking it slow, but looking at these pix of a happy Jessica looking up at her new guy with adoring eyes in the music studio, we'd say it might be getting more serious!

Jessica followed her rock star beau into the studio where he's recording his eighth album with his band Smashing Pumpkins.

Jessica retweeted the pix (that were originally posted by Corgan's producer) on her Twitter, saying "I am blessed," and commenting on another that it's "fun to be lost in laughter."

So will her third musician be her charm?