Master integrals for semi-inclusive cuts of massless four-loop propagators

2025/03/25 by Magerya, Vitaly, Fekésházy, Levente · 1 citation
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2503.19837

Abstract

We present the analytic calculation of all master integrals for 3-, 4-, and 5-particle semi-inclusive cuts of four-loop massless propagators by means of differential equations. We fix the integration constants by reducing the semi-inclusive integrals to their fully inclusive counterparts with the Integration-By-Parts (IBP) method. We validate our results by calculating the next-to-next-to-next-to-leading order (N3LO) semi-inclusive e⁺e^- → X cross-section and integrating directly over the differential variable. We provide the results in a machine-readable form. The presented integrals are essential for the direct calculation of NNLO time-like splitting functions and N3LO coefficient functions, which play a crucial role in precision QCD calculations.

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