FeynOnium: using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories
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Springer
Received: July 3, Revised: September 17, Accepted: October 22, Published: November 25,
2020 2020 2020 2020
Nora Brambilla,a,b Hee Sok Chung,a Vladyslav Shtabovenkoc,d,a and Antonio Vairoa a
Technische Universität München, Physik-Department, James-Franck-Str. 1, 85748 Garching, Germany b Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, 85748 Garching, Germany c Institut für Theoretische Teilchenphysik (TTP), Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany d Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China
E-mail: [email protected], [email protected], [email protected], [email protected] 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. Keywords: Effective Field Theories, Perturbative QCD ArXiv ePrint: 2006.15451
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)130
JHEP11(2020)130
FeynOnium: using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories
Contents 1 Introduction
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2 Nonrelativistic QCD and potential nonrelativistic QCD
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3 Existing approaches to automatic EFT calculations
5 7 7 9 10
5 Installation and usage 5.1 Installation 5.2 Basic nonrelativistic calculations 5.3 Dirac algebra 5.4 Pauli algebra 5.5 Loop calculations 5.6 FeynOnium
15 15 16 19 19 21 24
6 Examples 6.1 Euler-Heisenberg Lagrangian 6.2 Heavy Baryon Effective Theory 6.3 Dimension six 4-fermion operators in NRQCD (unequal mass case) 6.4 J/ψ → 3γ decay in NRQCD ¯ → γγ decays in NRQCD 6.5 QQ 6.6 Inclusive hadronic decays of P -wave quarkonia in NRQCD 6.7 Relativistic corrections to quarkonium light-cone distribution amplitudes 6.8 One-loop running of the chromoelectric dipole interaction in pNRQCD
26 27 29 29 31 32 33 35 37
7 Summary
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A Useful formulas for Pauli algebra
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B Tensors and matrices in FeynCalc B.1 Lorentz and Cartesian tensors in the internal (FCI) notation B.2 Lorentz an
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