arXiv subjects

Marco Klann

Publications and source records attributed to Marco Klann.

2 recordsLinked to original sources

arXiv2026

Graphical Functions by Examples

Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and have enabled major advances, including the highest-loop results currently known in several quantum field theories. Their role extends to conformal field theory, and recent algorithmic developments now allow many graphical functions to be computed automatically. This review, based on graduate-level lectures held by O.S. in 2025/26 at the University of Hamburg, introduces the central ideas behind graphical functions, covering periods, Feynman residues, and the treatment of regular and singular cases in both integer and non-integer dimensions. It also discusses connections to momentum space and self-duality, and provides guidance for further study, offering a coherent entry point into a topic not addressed in standard textbooks.

hep-th↗

arXiv2026

Heavy-quark production in deep-inelastic scattering -- Mellin moments of structure functions

We compute Mellin moments of the heavy-quark structure functions in deep-inelastic scattering at next-to-leading order in quantum chromodynamics, retaining their full dependence on the heavy-quark mass. Using the optical theorem and the operator product expansion, we derive analytic results for fixed Mellin moments $N = 2$ to $22$ of the structure functions $F_2$ and $F_L$. Our results reproduce the known expressions in the relevant asymptotic limits, in particular for virtualities of the exchanged photon $Q^2$ much larger than the heavy-quark mass squared $m^2$, and are in agreement with existing parametrisations of the next-to-leading-order coefficient functions. The computational set-up developed in this work also provides a direct pathway toward extending these calculations to next-to-next-to-leading order.

hep-ph↗