Comments on Higher Derivative Terms for the Tachyon Action
  We consider the open string tachyon action in a world-sheet sigma model approach. We present explicit calculations up to order 8 in derivatives for the bosonic string, and mimic these to order 6 for the superstring, including terms with multiple derivatives acting on the tachyon field. We reproduce lower derivative terms obtained elsewhere, and speculate on the role of the world-sheet contact terms regularizing the action for the superstring tachyon. 
Mark Laidlaw and Madoka Nishimura