General $\varepsilon$-representation for scalar one-loop Feynman integrals

TL;DR

This paper provides a comprehensive analysis of scalar one-loop Feynman integrals, deriving closed-form expressions in arbitrary dimensions and validating results numerically, which aids in higher-loop calculations.

Contribution

It introduces a systematic approach to express scalar one-loop integrals with all mass and invariant configurations in arbitrary dimensions using higher transcendental functions.

Findings

Derived closed-form expressions for all scalar one-loop integrals

Validated results with numerical checks using AMBRE/MB and LoopTools/FF

Facilitates higher-loop and multi-leg process calculations

Abstract

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms of higher transcendental functions. The integrals play a role as building blocks in general higher-loop or multi-leg processes. We also perform numerical checks of the calculations using AMBRE/MB and LoopTools/FF.