Search results for " 14J81"

showing 2 items of 2 documents

Bhabha Scattering and a special pencil of K3 surfaces

2018

We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.

Algebra and Number Theory14C22 14J28 34L25 14J81010308 nuclear & particles physicsPhysics::Medical PhysicsGeneral Physics and Astronomy01 natural sciencesApéry's constantLattice (module)Theoretical physicsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics010306 general physicsAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)Bhabha scatteringMathematics
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Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering

2019

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.

High Energy Physics - TheoryMathematics - Algebraic GeometryMathematics::Algebraic GeometryHigh Energy Physics - Theory (hep-th)Mathematics - Number TheoryHigh Energy Physics::PhenomenologyFOS: MathematicsFOS: Physical sciences14C22 11G50 14J81 14J28 11G05Number Theory (math.NT)Algebraic Geometry (math.AG)
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