Loops in twistor space

We elucidate the one-loop twistor-space structure corresponding to momentum-space maximally helicity-violating diagrams. We also discuss the infrared divergences, and argue that only a limited set of maximally helicity-violating diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the "holomorphic anomaly" pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.