 Scalar triangle Feynman integral

ID: scalar-triangle-feynman-integral

Codex  0 Created 2026-10-14 Updated 2026-11-05

In mostly-minus signature, take

D_{j} = (ℓ + r_{j})^{2} - m^{2} + i 0

C = - \frac{i}{16 π ^{2}} \int_{x_{j} \geq 0} d x_{0} d x_{1} d x_{2} δ (1 - \sum_{j} x_{j}) [m^{2} - \sum_{i < j} x_{i} x_{j} (r_{i} - r_{j})^{2} - i 0]^{- 1} .

For massive internal lines this is ultraviolet finite in four dimensions. Physical external kinematics can still create threshold cuts, encoded by the Feynman i-epsilon prescription.

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