Communications in Number Theory and Physics

Volume 14 (2020)

Number 4

Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering

Pages: 863 – 911



Marco Besier (Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Germany; and PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany)

Dino Festi (Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Germany)

Michael Harrison (School of Mathematical Sciences, University of Nottingham, United Kingdom; and MAGMA Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, NSW, Australia)

Bartosz Naskręcki (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland)


We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell–Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda–Inose structure.

The second-named author was supported by the grant SFB/TRR 45 in Mainz.

Received 30 September 2019

Accepted 16 April 2020

Published 2 October 2020