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Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

机译:在等质量情况下两环日出图Master积分的精确数值评估

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摘要

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10(15) is achieved for arbitrary real values of the momentum transfer.
机译:我们在Fortran中提供了一个双精度例程,用于对等质量两环日出图的两个主积分(MI)进行精确,快速的数值评估,以便在d = 2和d = 4维中进行任意动量传递。该例程执行通过求解MI的奇异点对应的微分方程而获得的加速幂级数展开。对于最坏情况的展开,最多使用22个项,相对于动量传递的任意实数值,其相对精度优于10(15)中的一部分。

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