6533b85dfe1ef96bd12bf152

RESEARCH PRODUCT

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

Marco BesierBartosz NaskręckiDino FestiMichael J. Harrison

subject

Surface (mathematics)Algebra and Number TheoryRank (linear algebra)ScatteringHigh Energy Physics::PhenomenologyFibrationStructure (category theory)General Physics and AstronomyLattice (discrete subgroup)K3 surfaceTheoretical physicsMathematics::Algebraic GeometryDiscriminantMathematical PhysicsMathematics

description

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.

https://doi.org/10.4310/cntp.2020.v14.n4.a4