At the sqrt(sNN)=200 GeV top beam energy of the Relativistic Heavy Ion
Collider (RHIC), collisions of two 197-Au nuclei result in dense and
strongly interacting systems of partons at high temperatures, T, and
low baryo-chemical potentials, muB. In central collisions, these
systems hadronize at (muB,T) values near (~20,~160) MeV via a
crossover-type transition. Systems formed at larger values of the
baryo-chemical potential may undergo a first-order transition. This
implies the possible existence of a critical point. Nuclear systems
passing through such a critical point are expected to exhibit
divergences of the thermodynamic susceptibilities and correlation
lengths that are analogous to those seen in many liquids. The
observation of a Quantum ChromoDynamic (QCD) critical point would
transform the phase boundaries in (muB,T) space. Increasing the
baryo-chemical potential in Lattice QCD calculations is
computationally difficult, but it can be accomplished experimentally
by reducing the beam energy. In the year 2010 and 2011 runs, the RHIC
provided Au+Au collisions at seven beam energies ranging from 7.7 to
200 GeV, which spanned a range of muB from ~20 to ~420 MeV. The
spectra and event-by-event multiplicities of numerous species of
charged hadrons were measured in the wide and azimuthally complete
acceptance of the Solenoidal Tracker at RHIC (STAR) experiment. The
(muB,T) values at chemical freeze-out for the different beam energies
and collision centralities can be inferred from the spectra. The
shapes of the event-by-event multiplicity distributions, quantified by
their statistical moments, mean, variance, skewness, and kurtosis, are
expected to diverge non-monotonically as a result of the divergence of
the correlation length expected if the system has passed close to the
critical point. In this talk, we will present the status of the STAR
Collaboration's exploration of the QCD phase diagram. This will
include the study of the identified particle yield ratios to extract
the (muB,T) values, and the statistical moments of the multiplicity
distributions of several different species of charged hadrons. The
particle identification is performed using the ionization energy loss
in the Time Projection Chamber and the information from the then newly
installed Time of Flight system. The moments values will be compared
to the "baseline" behavior implied by the Hadron Resonance Gas model
and Poisson statistics.