Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region

TL;DR

This paper advances precision QCD predictions for the thrust distribution in electron-positron annihilation by performing NNLL resummation, deriving the two-loop soft function, and matching to fixed-order NNLO results.

Contribution

It provides the first independent derivation of the two-loop soft function and analytical expression for the NNLL resummation coefficient g_3 for the thrust distribution.

Findings

Achieved NNLL resummation accuracy for the thrust distribution.

Derived analytical expression for the two-loop soft function.

Developed matching procedures to combine resummed and fixed-order results.

Abstract

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL approximation to the fixed-order NNLO distribution.