Neither Gaga nor Taylor have confirmed whether the Tortured Poets Department artist had any involvement in the track. According to Mayhem ’s album credits, “How Bad Do U Want Me” was written by Andrew Watt, Henry Walter, Gaga, and her fiancé, Michael Polansky.

After five years away from the pop scene, Lady Gaga is back at long last with her long-awaited seventh studio album, Mayhem, out now via Interscope Records.