
We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{_0}$ function. The approach can be employed to evaluate the coefficient of arbitrary power of $\varepsilon$ in the expansion of a scalar integral, where $D=4-2\varepsilon$ denotes the time-space dimension.
Latex, 68 pages
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, FOS: Physical sciences, QC770-798, Feynman diagrams
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, FOS: Physical sciences, QC770-798, Feynman diagrams
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 16 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
