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<p>Since Feynman integrals (FIs) at higher spacetime dimensions are free of infrared and collinear divergences — and their ultraviolet divergences can be systematically subtracted — this allows us to construct a wide range of locally finite Feynman integrals. Especially, we propose a method named <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>R</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overline{R} \)</EquationSource> </InlineEquation>-operation to subtract out ultraviolet divergences that at the same time preserves infrared and collinear safety of the original FI. By expressing these locally finite FIs in terms of master integrals and imposing constraints on their <i>ϵ</i>-expanded forms, we reduce the <i>ϵ</i>-expanded master integrals to a minimal basis. We provide an automated package to identify such constraints, offering a tool useful for high-order perturbative computations.</p>

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Reduction of ϵ-expanded Feynman integrals

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月13日

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  • Yan-Qing Ma,
  • Cong-Hao Qin,
  • Ao Tan,
  • Kai Yan

摘要

Since Feynman integrals (FIs) at higher spacetime dimensions are free of infrared and collinear divergences — and their ultraviolet divergences can be systematically subtracted — this allows us to construct a wide range of locally finite Feynman integrals. Especially, we propose a method named R ¯ \( \overline{R} \) -operation to subtract out ultraviolet divergences that at the same time preserves infrared and collinear safety of the original FI. By expressing these locally finite FIs in terms of master integrals and imposing constraints on their ϵ-expanded forms, we reduce the ϵ-expanded master integrals to a minimal basis. We provide an automated package to identify such constraints, offering a tool useful for high-order perturbative computations.