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 Apery--Fermi pencil, that was related to Apery'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.

中文翻译：

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Bhabha 散射和 K3 表面的特殊铅笔

我们研究了 Bhabha 散射中 $2$-loop 图中出现的 K3 表面铅笔。通过详细分析铅笔的一般成员和特殊成员的皮卡德格，我们确定了这支铅笔与著名的阿佩里——费米铅笔有关，这与阿佩里通过工作证明$\zeta(3)$的非理性有关F. Beukers、C. Peters 和 J. Stienstra。同一支铅笔奇迹般地出现在不同且看似无关的物理环境中。