6533b857fe1ef96bd12b4f2d

RESEARCH PRODUCT

Bhabha Scattering and a special pencil of K3 surfaces

Dino FestiDuco Van Straten

subject

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

description

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.

yearjournalcountryeditionlanguage
2018-09-13
http://arxiv.org/abs/1809.04970