The Massless Higher-Loop Two-Point Function
The Massless Higher-Loop Two-Point Function
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无质量高环两点函数
DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
F. Brown
中科院分区：
文献类型：
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作者：
F. Brown
介绍了一种以参数形式解析计算无质量费曼积分的新方法。通过对该方法的分析，得出了原始费曼图G求值为多个zeta值的判据。该准则仅依赖于G的拓扑结构，并且可以通过算法进行检查。作为推论，我们证明了Bierenbaum和Weinzierl的结果，即无质量2环2点函数可以用多个zeta值表示，并将其推广到3、4和5环的情况。我们发现，在这个范围内，平面图的泰勒展开式的系数可求多个zeta值，而交叉数为1的非平面图可求多个单位六根的和。我们的方法对于通过在一条边打开二部图k3,4而得到的交叉数为2的五个环图来说是失败的。
We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph G to evaluate to multiple zeta values. The criterion depends only on the topology of G, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless 2-loop 2-point function is expressible in terms of multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We find that the coefficients in the Taylor expansion of planar graphs in this range evaluate to multiple zeta values, but the non-planar graphs with crossing number 1 may evaluate to multiple sums with 6th roots of unity. Our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite graph K3,4 at one edge.