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

## TL;DR

This paper investigates a K3 surface arising from two-loop electroweak-QCD corrections to Drell--Yan scattering, analyzing its geometric properties and elliptic fibrations to connect geometry with physical phenomena.

## Contribution

It provides a detailed geometric analysis of the K3 surface, including its Picard lattice and elliptic fibrations, linking complex geometry with particle physics corrections.

## Key findings

- Computed Picard lattice rank and discriminant using two methods
- Classified elliptic fibrations and identified the Shioda--Inose structure
- Connected geometric features to physical corrections in Drell--Yan scattering

## Abstract

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. Moreover, we point out the physical relevance of our results.