Toward quantitative precision for QCD at large densities

QCD at large density reveals a rich phase structure, ranging from a potential critical end point and inhomogeneous phases or moat regimes to color superconducting ones with competing order effects. Resolving this region in the phase diagram of QCD with functional approaches requires a great deal of quantitative reliability already for a qualitative access. In the present work, we systematically extend the functional renormalization group approach to low-energy QCD by setting up a fully self-consistent approximation scheme in a low-energy effective quark-meson theory. In this approximation, all pointlike multiscattering events of the mesonic pion and the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>σ</a:mi></a:math> mode are taken into account in terms of an effective potential as well as all higher quark-antiquark-mesonic scattering orders. As a first application we compute the phase structure of QCD including its low temperature, large chemical potential part. The quantitative reliability of the approximation and systematic extensions is also discussed.