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arXiv 0803.3147hep-phhep-th
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单圈振幅的多项式结构

Polynomial Structures in One-Loop Amplitudes

Ruth Britto, Bo Feng, Gang Yang

备注：
44 pages, title changed to be closer to content, section 2.1 extended to section 2.1 and 2.2 to be more self-contained, references added, typos corrected, the final version to appear in JHEP
发表信息：
JHEP 0809:089,2008
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摘要：

一般的单圈散射振幅可以用主积分展开。主积分的系数可以通过两步过程从树级输入中获得。首先，使用已知的公式来写出（4- 2 π）维主积分的系数;这些公式依赖于一个额外的变量u，它编码了维度位移。其次，将（4- 2 π）维主积分的u相关系数转换为维数移位主积分的显式系数。这个过程要求系数的初始公式对u具有多项式依赖性。在这里，我们给出一个证明的情况下，无质量传播的这个属性。证据是建设性的。因此，作为副产品，我们产生不同的代数表达式的标量积分系数，其中多项式属性是显而易见的。在这些公式中，盒子和五边形的贡献被明确地分开。

英文摘要：

A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2epsilon)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2epsilon)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

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