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Ladders and rainbows in the minimal subtraction scheme

Paul-Hermann Balduf*

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Phys. Rev. D 111, 116009 – Published 11 June, 2025

DOI: https://doi.org/10.1103/kxln-26db

Abstract

In dimensional regularization with D=D0−2ε, the minimal subtraction (MS) scheme is characterized by counterterms that only consist of singular terms in ε. We develop a general method to compute the infinite sums of massless ladder or rainbow Feynman integrals in MS at D0. Our method is based on relating the MS-solution to a kinematic solution at a coupling-dependent renormalization point. If the ε-dependent Mellin transform of the kernel diagram of the insertions can be computed in closed form, we typically obtain a closed form expression for the all-order solution in MS. As examples, we consider Yukawa theory and ϕ4 theory in D0=4, and ϕ3 theory in D0=6.

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Phys. Rev. D 111, 116009– Published 11 June, 2025
  • Received 17 March 2025
  • Accepted 5 May 2025
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