论文标题
对称降低高型单环积分和最大切割
Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
论文作者
论文摘要
我们得出了有用的还原公式，这些公式表达具有大量外部动量的单环feynman积分，就较低的积分而言，携带易于衍生的运动学系数，这些系数在外部动量中是对称的。这些公式适用于与外部动量的尺寸至少要高两个外腿的积分，并以两个可能的基础表示：一个由后代积分的子集组成，其外部腿少，另一个由一组完整的微型降低剂积分组成，仅与外部力矩的尺寸相比，仅由一个多腿组成。在3+1个维度中，可以计算运动学不变性的紧凑表示形式，这很容易适合旋转器或痕量表示。还原公式与d维单位性削减有着密切的关系，因此为计算完整的（全epsilon）表达式提供了以任意多重性散射的路径。
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external momenta. These formulae apply for integrals with at least two more external legs than the dimension of the external momenta, and are presented in terms of two possible bases: one composed of a subset of descendant integrals with one fewer external legs, the other composed of the complete set of minimally-descendant integrals with just one more leg than the dimension of external momenta. In 3+1 dimensions, particularly compact representations of kinematic invariants can be computed, which easily lend themselves to spinor-helicity or trace representations. The reduction formulae have a close relationship with D-dimensional unitarity cuts, and thus provide a path towards computing full (all-epsilon) expressions for scattering at arbitrary multiplicity.
