A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry

TL;DR

This paper explores how dual conformal symmetry helps determine the structure of multi-loop Feynman integrals, especially their symbol alphabet and properties, with a focus on two-loop four-external-mass integrals with uniform transcendental weights.

Contribution

It derives two-loop four-external-mass Feynman integrals with UT weights using dual conformal symmetry and elucidates the symbol structure from related integrals, advancing understanding of their algebraic properties.

Findings

All symbol letters can be obtained from dual conformal integrals by sending a dual point to infinity.

Properties like first two entries and Steinmann relations are consistent with dual conformal integral properties.

The approach simplifies the analysis of complex multi-loop Feynman integrals.

Abstract

Multi-loop Feynman integrals are key objects for the high-order correction computations in high energy phenomenology. These integrals with multiple scales, may have complicated symbol structures. We show that the dual conformal symmetry sheds light on the alphabet and symbol structures of multi-loop Feynman integrals. In this paper, first, as a cutting-edge example, we derive the two-loop four-external-mass Feynman integrals with uniform transcendental (UT) weights, based on the latest developments on UT integrals. Then we show that all the symbol letters can be nicely obtained from those of closely-related dual conformal integrals, by sending a dual point to infinity. Certain properties of the symbol such as first two entries and extended Steinmann relations are also studied from analogous properties of dual conformal integrals.