Holonomic techniques for massive 3-loop form factors: the gluonic case
Year: 2026
Type: preprint
Abstract: Massive three-loop form factors for vector, axial-vector, scalar, and pseudoscalar currents are vital for precision collider phenomenology. Extending the quarkonic framework to the more complex gluonic case, in Ref. (arXiv:2609.22034 [hep-ph]) we computed these contributions widely using advanced computer algebra, automated guessing, and large-scale PSLQ searches. Here, we outline the core strategy of the large-moment method and illustrate its main challenges, including solving record-sized recurrences and differential equations. Our high-precision evaluation provides an exact analytic representation around $s=0$ in terms of MZVs. We achieved a complete analytic series expansion around $s=\pm\infty$ for the first time, which depends on MZVs and three constants out of higher number spaces, along with reliable analytic continuations across $s \in (-\infty, \infty)$, serving as a landmark benchmark for modern symbolic computation.
Source: arXiv (Cornell University)
Institutions: TU Dortmund University, Deutsches Elektronen-Synchrotron DESY
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214030750
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