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On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations
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An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.
Forward citations
Cited by 2 Pith papers
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Numerical computation of Fox functions
A numerical toolkit, based on Sinc methods plus contiguity shifts of lambda, is presented for evaluating multivariate Fox functions representing Feynman integrals.
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Feynman Fox integrals in the physical region
A recipe is given that expresses physical-region Feynman integrals as Fox functions on vertical Mellin-Barnes contours with the correct cut structure, but the claimed imaginary-part correctness is not yet verified.
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