Advanced techniques solve complex equations in particle physics calculations
Holonomic techniques for massive 3-loop form factors: the gluonic case
Symbolic Computation
Summary
Calculations involving how particles like gluons behave are very complex but important for understanding particle collisions precisely. The authors extended previous methods used for quarks to handle the more difficult gluon case using powerful computer tools. They managed to find exact mathematical expressions and series expansions that describe these particles’ behaviors across a wide range of conditions. This work provides a valuable benchmark for future symbolic computations in high-energy physics.
What this means in practice
- •For collider phenomenology teams: Use exact gluon form factor expansions to improve precision in particle collision models.
- •For symbolic computation developers: Incorporate large-moment methods to solve similarly complex equations in computer algebra systems.
Authors
J. Blümlein, A. De Freitas, P. Marquard, J. Obrovsky, C. Schneider
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.