  In the initial years of operation, experiments at the Relativistic Heavy Ion
Collider (RHIC) have identified a new form of matter formed in nuclei-nuclei
collisions at energy densities more than 100 times that of a cold atomic
nucleus. Measurements and comparison with relativistic hydrodynamic models
indicate that the matter thermalizes in an unexpectedly short time, has an
energy density at least 15 times larger than needed for color deconfinement,
has a temperature about twice the critical temperature predicted by lattice
QCD, and appears to exhibit collective motion with ideal hydrodynamic
properties - a "perfect liquid" that appears to flow with a near-zero viscosity
to entropy ratio - lower than any previously observed fluid and perhaps close
to a universal lower bound. However, a fundamental understanding of the medium
seen in heavy-ion collisions at RHIC does not yet exist. The most important
scientific challenge for the field in the next decade is the quantitative
exploration of the new state of nuclear matter. That will require new data that
will, in turn, require enhanced capabilities of the RHIC detectors and
accelerator. In this report we discuss the scientific opportunities for an
upgraded RHIC facility - RHIC II - in conjunction with improved capabilities of
the two large RHIC detectors, PHENIX and STAR. We focus solely on heavy flavor
probes. Their production rates are calculable using the well-established
techniques of perturbative QCD and their sizable interactions with the hot QCD
medium provide unique and sensitive measurements of its crucial properties
making them one of the key diagnostic tools available to us.
