Jessica Simpson and Billy Corgan may or may not be collaborating in a romantic sense, but the pair are most certainly making sweet music together this week at an undisclosed studio.

The unlucky-in-love singer invited fans to glimpse at what it's like to hang out with one of alternative rock's most prolific artists. "I am blessed," she told her Twitter followers. "Going over a song w@billy and the boxer."

According to PEOPLE, Simpson and the Smashing Pumpkin have been dating for four months, but neither have confirmed such reports. Today, she says it's "fun to be lost in laughter."

Simpson linked to two photos of her and Corgan, and one shows the singer looking intently at the guitarist as he performs. "He braids my prayers," she commented.