Does Chappell music own the Beatles songs?
No. Sony Music controls their catalog, and owns much of it. (Michael Jackson owned their catalog, but sold much of it to Sony.) Rights to John Lennon’s share reverted to his estate gradually, but Yoko Ono reassigned it to Sony, and pocketed the cash for it. Paul McCartney owns some of their pre-Northern Songs music, like “Love Me Do”. Chappell may have published songs the Beatles recorded early on. Their recordings are still owned and controlled by EMI, and/or Apple Corps Ltd.