Asymptotics of the banana Feynman amplitudes at the large complex structure limit

TL;DR

This paper confirms that the leading asymptotics of the l-loop Banana Feynman amplitude at the large complex structure limit are described by the Gamma class of a specific Fano hypersurface, linking numerical observations with theoretical proof.

Contribution

The paper provides a theoretical confirmation of the numerical observation that the asymptotics are governed by the Gamma class of a Fano hypersurface, using a Gamma-conjecture type result.

Findings

Asymptotic behavior matches the Gamma class description

Numerical observations are theoretically validated

Links Feynman amplitudes with algebraic geometry concepts

Abstract

Recently B\"onisch-Fischbach-Klemm-Nega-Safari discovered, via numerical computation, that the leading asymptotics of the l-loop Banana Feynman amplitude at the large complex structure limit can be described by the Gamma class of a degree (1,...,1) Fano hypersurface F in (P^1)^{l+1}. We confirm this observation by using a Gamma-conjecture type result for F.