Analyzing and Implementing the Local Analytic Sector Subtraction Scheme for Handling Infrared Singularities at NNLO in QCD

Abstract

This thesis analyzes and implements the Local Analytic Sector Subtraction (LASS) scheme for handling infrared singularities in next-to-next-to-leading order (NNLO) calculations in perturbative Quantum Chromodynamics (QCD). The LASS method provides a fully local and analytic procedure for subtracting infrared divergences in real-radiation contributions by partitioning the phase space into sectors containing a minimal set of singularities. The key aspects of the scheme, including the construction of sector functions, parametrization of singular limits, derivation of subtraction counterterms, and analytic integration techniques, are examined in detail. A novel approach combining a satisfiability modulo theories (SMT) solver and symbolic manipulation program is developed to automatically generate the color bases required for color decomposition of QCD amplitudes. The complete LASS framework is numerically implemented, with a focus on the process of electron-positron annihilation into three jets as a proof-of-concept. The limiting behavior of the subtraction terms, the finite remainders of the double-virtual contribution, and the effect of the technical cut parameter are meticulously investigated. Differential cross sections for several event shape observables are computed, showcasing the stability and efficiency of the method. This work lays the foundation for the development of a fully automated tool for NNLO calculations in QCD using the LASS scheme.