Double-real-virtual and double-virtual-real corrections to the three-loop thrust soft function

Abstract

Abstract We compute the $$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 ) double-real-virtual (RRV) and double-virtual-real (VVR) soft contributions to the thrust/zero-jettiness event shape. The result clears up one of the most stubborn obstacles toward the complete $$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 ) thrust soft function. The results presented here serve the key input to realize the next-to-next-to-next-to-leading logarithmic prime (N3LL’) resummation of the thrust event shape. The obtained results also constitutes the important ingredients of the N -jettiness-subtraction scheme at next-to-next-to-next-to-leading order (N3LO).