Numerical Contour Integration for Loop Integrals

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Abstract
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculations of the standard model. Examples of 3- and 4-point diagrams in 1-loop integrals and 2- and 3-point diagrams in 2-loop integrals with arbitrary masses are shown. Moreover it is shown that numerical evaluations of the Hypergeometric function, which often appears in the loop integrals, can be performed using the numerical contour-integration method.

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