Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function

TL;DR

This paper calculates complex three-loop quantum chromodynamics corrections to the thrust soft function, advancing precision in event shape analysis and enabling higher-order resummation and subtraction schemes in particle physics.

Contribution

It provides the first complete computation of specific three-loop soft contributions, crucial for precise theoretical predictions in collider physics.

Findings

Achieved the ${ m O}(\a_s^3)$ double-real-virtual and double-virtual-real soft corrections.

Facilitates N${}^3$LL' and N${}^4$LL resummation of thrust.

Supports N${}^3$LO N-jettiness subtraction scheme.

Abstract

We compute the ${\cal O}(\alpha_s^3)$ 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 ${\cal O}(\alpha_s^3)$ thrust soft function. The results presented here serve as the key input to realize the next-to-next-to-next-to-leading logarithmic prime (N${}^3$LL') % and even the next-to-next-to-next-to-next-to-leading logarithmic (N${}^4$LL) resummation of the thrust event shape. The obtained results also constitute the important ingredients of the $N$-jettiness-subtraction scheme at next-to-next-to-next-to-leading order (N${}^3$LO).