Periods and Feynman integrals

TL;DR

This paper proves that all coefficients of Laurent series for multi-loop Feynman integrals in dimensional regularisation are periods when evaluated in the Euclidean region with rational ratios of invariants and masses.

Contribution

It establishes that under specific conditions, the Laurent series coefficients of multi-loop integrals are periods, linking Feynman integrals to number theory.

Findings

Laurent series coefficients are periods in the specified setting

Results connect Feynman integrals with algebraic geometry and number theory

Provides a mathematical foundation for understanding the nature of Feynman integral coefficients

Abstract

We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this case all coefficients of the Laurent series are periods.