Feynman integrals at large loop order and the $\log$-$Γ$ distribution
Michael Borinsky, Andrea Favorito
公開日: 2025/3/10
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.