FeynOnium: Using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories

TL;DR

FeynOnium is a new open-source software toolkit built on FeynCalc for automating symbolic calculations in nonrelativistic Effective Field Theories, especially for heavy quark systems, at tree- and 1-loop levels.

Contribution

It introduces a comprehensive framework and add-on for semi-automatic symbolic calculations in NREFTs, expanding FeynCalc's capabilities for Cartesian tensors, Pauli matrices, and nonstandard loop integrals.

Findings

Successfully reproduces known results in heavy quark EFTs

Supports calculations at tree- and 1-loop levels

Open-source and extendable for other nonrelativistic systems

Abstract

We present new results on FeynOnium, an ongoing project to develop a general purpose software toolkit for semi-automatic symbolic calculations in nonrelativistic Effective Field Theories (EFTs). Building upon FeynCalc, an existing Mathematica package for symbolic evaluation of Feynman diagrams, we have created a powerful framework for automatizing calculations in nonrelativistic EFTs (NREFTs) at tree- and 1-loop level. This is achieved by exploiting the novel features of FeynCalc that support manipulations of Cartesian tensors, Pauli matrices and nonstandard loop integrals. Additional operations that are common in nonrelativistic EFT calculations are implemented in a dedicated add-on called FeynOnium. While our current focus is on EFTs for strong interactions of heavy quarks, extensions to other systems that admit a nonrelativistic EFT description are planned for the future. All our codes are open-source and publicly available. Furthermore, we provide several example calculations that demonstrate how FeynOnium can be employed to reproduce known results from the literature.