Alphabet of one-loop Feynman integrals

Abstract

In this paper, we present the universal structure of the alphabet of one-loop Feynman integrals. The letters in the alphabet are calculated using the Baikov representation with cuts. We consider both convergent and divergent cut integrals and observe that letters in the divergent cases can be easily obtained from convergent cases by applying certain limits. The letters are written as simple expressions in terms of various Gram determinants. The knowledge of the alphabet enables us to easily construct the canonical differential equations of the $d\log$ form and aids in bootstrapping the symbols of the solutions.

Comments: 13 pages, 2 figures; v3: published version in Chinese physics C