Scattering of D0-branes and Strings

It has been known for about thirty years that a scattering amplitude involving D0-branes and closed strings suffers from infrared divergences beyond tree level. These divergences arise because the conventional world-sheet approach cannot account for the difference between the D0-brane's momentum before and after scattering. We show that, by using string field theory, the divergence can be removed and the amplitude rendered finite and unambiguous. We illustrate this using the simplest possible example in bosonic string theory: a three-point function with one incoming and one outgoing D0-brane and an incoming or outgoing closed string tachyon.