Abstract
We summarize our results for light (pseudo-)scalar mesons at finite chemical potential and vanishing temperature. We extract the meson bound state wave functions, masses, and decay constants up to the first-order phase transition from the homogeneous Bethe-Salpeter equation and confirm the validity of the Silver-Blaze property. For this purpose, we solve a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of QCD in Landau gauge.
Highlights
The QCD phase diagram and the properties of hadrons in medium are strongly connected
The properties of pseudoscalar and scalar meson degrees of freedom are tied to dynamical chiral symmetry breaking and its restoration and play an important role in the vicinity of second-order phase transitions: they account for the effective long-range degrees of freedom and control the universal behavior
At zero temperature and small chemical potential, QCD displays the so-called Silver-Blaze property: observables are unaffected by chemical potential as long as the baryon chemical potential μB is not large enough to create physical excitations
Summary
The QCD phase diagram and the properties of hadrons in medium are strongly connected. We approach QCD with the nonperturbative functional method of Dyson-Schwinger equations (DSEs) and extend previous bound state calculations for pion and sigma mesons to finite chemical potential and vanishing temperature. To this end, we use a variant of a well-studied truncation scheme that includes the backcoupling of the quark onto the gluon, see Ref. We obtain a rainbow-ladder like truncation which greatly simplifies the associated interaction kernel in the BSE, cf below The effects on the critical end point are not too drastic and the additional approximations are justified
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