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arXiv · 2503.07803

Feynman integrals at large loop order and the $\log$-$\Gamma$ distribution

Michael Borinsky·Andrea Favorito
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Abstract

We find empirically that the value of Feynman integrals follows a $\log$-$\Gamma$ distribution at large loop order. This result opens up a new avenue towards the large-order behavior in perturbative quantum field theory. Our study of the primitive contribution to the scalar $\phi^4$ beta function in four dimensions up to 17 loops provides accompanying evidence. Guided by instanton considerations, we discuss the extrapolation of this contribution to all loop orders.

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Michael Borinsky, Andrea Favorito. 2025-03-10. Feynman integrals at large loop order and the $\log$-$\Gamma$ distribution. https://doi.org/10.1007/jhep09(2025)182

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