  We update our previous results for (pseudo-)scalar mesons at zero temperature
and finite quark chemical potential and generalize the investigation to include
(axial-)vector mesons. We determine bound-state properties such as meson masses
and decay constants up to chemical potentials far in the first-order
coexistence region. To extract the bound-states properties, we solve the
Bethe-Salpeter equation and utilize Landau-gauge quark and gluon propagators
obtained from a coupled set of (truncated) Dyson-Schwinger equations with
N$_\textup{f}=2+1$ dynamical quark flavors at finite chemical potential and
vanishing temperature. For multiple (pseudo-)scalar and (axial-)vector mesons,
we observe constant masses and decay constants for chemical potentials up to
the coexistence region of the first-order phase transition thus verifying
explicitly the Silver-Blaze property of QCD. Inside the coexistence region the
pion becomes more massive and its decay constants decrease, whereas
corresponding quantities for the (axial-)vector mesons remain (almost)
constant.
