Root is an object-oriented analysis framework
developed by Rene Brun at CERN.
PHOBOS started actively experimenting with ROOT in January 1996.
We adopted this as our official framework in July 1996, putting us on the leading edge
of this very large wave.
Some nice documentation can be found at:
The Root Primer Page: includes a nice Paw->Root command conversion table
Phat stands for Phobos
Analysis Toolkit.
It is a version of root with PHOBOS-specific
code linked in. The word "phat" in American English slang means outstanding or
excellent
with connotations of being hip and cutting edge. See for instance here or here (R-rated
sites!).