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Reduction formalism for dimensionally regulated one-loop N-point integrals

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abstract

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4-2\epsilon) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N=6. Further a tensor reduction method for N-point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order \epsilon for N>=5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N=6.

fields

hep-ph 1

years

2025 1

verdicts

CONDITIONAL 1

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  • Positive Integrands from Feynman Integrals in the Minkowski Regime hep-ph · 2025-06-30 · conditional · none · ref 90 · internal anchor

    A method for converting Minkowski-regime Feynman parameter integrals into sums of real, positive integrands with complex prefactors, eliminating contour deformation and speeding up numerical evaluation.