论文标题
评估具有四个或五个繁殖器的三环自能量主积分
Evaluation of three-loop self-energy master integrals with four or five propagators
论文作者
论文摘要
我获得了由三或五个具有通用质量的传播器的三环自能力主积分满足的身份，包括相对于每个平方质量和外部动量不变的衍生物。然后，这些身份是根据相应的重新归一化的主积分重铸的，从而通过微分方程方法对其进行直接的数值评估。提供了一些基准示例。用于获得衍生身份的方法仅依赖于零件关系集成所隐含的一般形式，而无需实际按照零件减少程序进行通常的集成。作为副产品，我发现一个简单的公式将主体积分扩展到外部动量不变的任意顺序，这是根据相应真空积分的已知衍生物的扩展。
I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These identities are then recast in terms of the corresponding renormalized master integrals, enabling straightforward numerical evaluation of them by the differential equations approach. Some benchmark examples are provided. The method used to obtain the derivative identities relies only on the general form implied by integration by parts relations, without actually following the usual integration by parts reduction procedure. As a byproduct, I find a simple formula giving the expansion of the master integrals to arbitrary order in the external momentum invariant, in terms of known derivatives of the corresponding vacuum integrals.
