Ladders and rainbows in the minimal subtraction scheme
Paul-Hermann Balduf · Physical review. D/Physical review. D. · 2025
In dimensional regularization with D = D 0 − 2 ε , 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 D 0 . 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 ϕ 4 theory in D 0 = 4 , and ϕ 3 theory in D 0 = 6 .