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

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.

Non-relativistic and potential non-relativistic effective field theories for scalar mediators

“…For the latter we employed Mathematica packages FeynArts [110], FeynRules [111] and FeynCalc [112][113][114]. The automation of nonrelativistic calculations was significantly simplified by making use of FeynCalc 9.3 and the FeynOnium [115] extension that allow for algebraic manipulations of Cartesian tensors and Pauli matrices. Furthermore, an experimental interface to QGRAF [116] diagram generator was added to the development version of the FeynHelpers [117] extension.…”

A Challenge for Discrimination of Color-Singlet versus Color-Octet Quarkonium Production

“…[56] and Ref. [57]. However, the desired highlydifferential nature of the likelihood on phase space may be very challenging to achieve at next-to-leading order, due to the curse of dimensionality and the difficulty of real and virtual divergence cancellation.…”

P-wave quarkonium wavefunctions at the origin in the $$ \overline{\mathrm{MS}} $$ scheme

“…commutes with Pauli matrices with 3-dimensional indices, while it anticommutes with ones carrying d − 4-dimensional indices. The Pauli matrix algebra in d − 1 spatial dimensions can be done easily by using the Mathematica package FeynCalc with the FeynOnium addon [42][43][44][45]. In the spin triplet case, we apply the decomposition of the rank-2 tensor carrying indices i and j from σ i rk δZ kj E into the trace, antisymmetric, and symmetric traceless parts, following eqs.…”