The paper focuses on the evaluation of 3-loop two-point function integrals using a simplified sector decomposition (SD) method. The key points are:
The authors derive analytical expressions for the coefficients of the ultraviolet (UV) divergent terms in the Laurent series expansion of the integrals. These coefficients are obtained using the SD method.
For the finite parts of the integrals, the authors employ numerical integration techniques, including adaptive integration, the double-exponential formula, and Quasi-Monte Carlo methods. They use extrapolation methods to handle the singular behavior of the integrands.
Four specific 3-loop two-point function diagrams, referred to as Loop (I), (II), (III), and (IV), are studied in detail. The authors provide the analytical expressions for the UV divergent coefficients and present the numerical results for all the coefficients up to the constant term.
The numerical results are shown to agree well with previous analytical and numerical studies, demonstrating the effectiveness of the combined analytic and numerical approach.
The authors discuss the handling of pseudo-thresholds that appear in the numerical integration and note that further study is required to fully understand their impact on the high-precision computation.
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by Elise de Don... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2405.13286.pdfDeeper Inquiries