Scalar diquarks in the QCD vacuum
While QCD fundamentally only depends on the values of the strong coupling and the quark masses, it exhibits a rich nonperturbative structure at low energies, where composite fields emerge as the relevant degrees of freedom. In this work, we present a first-principles framework that captures the transition from fundamental QCD to its low-energy sector in vacuum. It builds on the dynamical hadronization technique within the functional renormalization group approach to two-flavor QCD. In this framework, the low-energy constants relevant for effective models, including effective masses and coupling strengths, naturally emerge from the underlying renormalization group flow without introducing free parameters beyond those of QCD itself. We investigate the dynamical emergence of the pion, the $\sigma$-meson and the scalar diquark in both imaginary and real time, and determine a set of QCD low-energy constants which can be used to fix the free parameters of models of dense quark matter with a two-flavor color superconducting phase. In particular, this includes previously unknown properties of the scalar diquark. Our results provide important microscopic input for constraining color superconducting phases, which are expected to play a key role in our understanding of dense neutron star matter.