Bhabha Scattering and a special pencil of K3 surfaces

Dino Festi; Duco van Straten

Bhabha Scattering and a special pencil of K3 surfaces

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arxiv 1809.04970 v2 pith:5IH5VBGL submitted 2018-09-13 math.AG

Dino Festi , Duco van Straten This is my paper · ORCID

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keywords pencilbhabhascatteringspecialsurfacesanalysingappearedappears

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abstract

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.

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