  We compute the dimuon-excess invariant mass distribution at the rho-meson
peak in the context of relativistic heavy-ion collisions at SPS energies. The
temperature, T, and chemical potential, mu, dependent parameters describing the
rho-meson --its width, mass and leptonic decay constant-- are determined from
finite energy QCD sum rules. Results show that the rho-meson width increases
whereas its mass and leptonic decay constant decrease near the (chemical
potential-dependent) critical temperature T_c(mu) for chiral symmetry
restoration/quark-gluon deconfinement. As a consequence, starting from T_c(mu),
for a short lived cooling the main effect is a broadening of the dimuon
distribution. However, when the evolution brings the system to a lower
freeze-out temperature, with the rho-meson parameters approaching their vacuum
values, the dimuon distribution shows a broad peak centered at the vacuum
rho-meson mass. For even lower freeze-out temperatures the peak becomes less
prominent since the thermal phase space factor suppresses the distribution for
larger values of the invariant dimuon mass, given that the average temperature
is smaller. The dimuon distribution exhibits a non-trivial behavior with mu.
For small mu values the distribution broadens with increasing mu becoming a bit
steeper at low invariant masses for larger values of mu. Our results are in
very good agreement with data from the NA60 Collaboration.
