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<p>We find empirically that the value of Feynman integrals follows a log-Γ 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 <i>ϕ</i><sup>4</sup> 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.</p>

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Feynman integrals at large loop order and the log-Γ distribution

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月23日

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  • Michael Borinsky,
  • Andrea Favorito

摘要

We find empirically that the value of Feynman integrals follows a log-Γ 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 ϕ4 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.