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arXiv · 1809.04970

Bhabha Scattering and a special pencil of K3 surfaces

Dino Festi·Duco van Straten
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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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Dino Festi, Duco van Straten. 2018-09-13. Bhabha Scattering and a special pencil of K3 surfaces. https://arxiv.org/abs/1809.04970

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