All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order.

D Chicherin,Y Zhang,T Gehrmann,S Zoia,J M Henn,P Wasser

doi:10.1103/physrevlett.123.041603

Abstract

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2→3 scattering process, thereby opening up a new level of precision collider phenomenology.

Highlights

Introduction.—The ever-improving experimental precision at the LHC challenges theoretical physicists to keep up with the accuracy of the corresponding theoretical predictions
Thanks to recent progress in quantum field theory methods, today we are at the brink of a next-to-next-to leading order (NNLO) revolution
The new ideas include cutting-edge integral reduction techniques based on finite fields and algebraic geometry [17,18,19], a systematic mathematical understanding of special functions appearing in Feynman integrals [20,21], and their computation via differential equations [22] in the canonical form [23]

Summary

Introduction

Introduction.—The ever-improving experimental precision at the LHC challenges theoretical physicists to keep up with the accuracy of the corresponding theoretical predictions. A useful conjecture [23,24] allows one to predict which Feynman integrals satisfy the canonical differential equation by analyzing their four-dimensional leading singularities. The method involves computing leading singularities in Baikov representation [26].

Objectives

Results

Conclusion