Modern Feynman Diagrammatic One-Loop Calculations

TL;DR

This paper introduces advanced Feynman diagram techniques for efficient and stable one-loop amplitude calculations in multi-leg processes, addressing numerical challenges near singular kinematics, with application to a complex proton-proton collision process.

Contribution

It presents a semi-algebraic method combining multiple techniques for fast, stable one-loop amplitude computations, avoiding spurious Gram determinants near singularities.

Findings

Achieved stable amplitude calculations near singular kinematics.

Demonstrated the method on the $pp\to b\bar{b}b\bar{b}+X$ process.

Improved computational efficiency in multi-leg one-loop calculations.

Abstract

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\to b\bar{b}b\bar{b}+X$.