Towards quantitative precision in functional QCD I

TL;DR

This paper develops a systematic, automated functional renormalisation group scheme for QCD at finite density, including full effective potential and error analysis, validated against lattice and other functional results.

Contribution

It introduces a fully automated computational framework for fRG in QCD, incorporating a comprehensive error analysis and the full effective potential of the chiral order parameter.

Findings

Results agree well with lattice and other functional approaches.

First data on multi-scattering events of pions and sigma mode.

Validated the systematic convergence of the fRG scheme.

Abstract

Functional approaches are the only first principle QCD setup that allow for direct computations at finite density. Predictive power and quantitative reliability of the respective results can only be obtained within a systematic expansion scheme with controlled systematic error estimates. Here we set up such a scheme within the functional renormalisation group (fRG) approach to QCD, aiming for full apparent convergence. In the current work we test this setup, using correlation functions and observables in 2+1 flavour vacuum QCD as a natural benchmark case. While the current work includes many evolutionary improvements collected over the past two decades, we also report on three novel important developments: (i) A comprehensive systematic error analysis based on the modular nature of the fRG approach. (ii) The introduction of a fully automated computational framework, allowing for unprecedented access and improvement of the fRG approach to QCD. (iii) The inclusion of the full effective potential of the chiral order parameter. This also gives access to all-order scattering events of pions and to the full momentum dependence of correlation functions, which is a first application of the automated computational framework (ii). The results compare very well to other state-of-the-art results both from functional approaches and lattice simulations, and provide data on general multi-scattering events of pions and the sigma mode for the first time.