NUKLEONIKA 2006, 51(Suppl. 3):s93-s97
Michael J. Tannenbaum
for the PHENIX Collaboration
Brookhaven National Laboratory, Upton, NY 11973-5000, USA
A simple way to visualize event-by-event average pT fluctuations is by assuming that each collision
has a different temperature parameter (inverse pT slope) and that the ensemble of
events has a temperature distribution about the mean, <T>, with standard deviation sT.
PHENIX characterizes the non-random fluctuation of MpT,
the event-by-event average pT, by FpT, the fractional
difference of the standard deviation of the data from that of a random sample obtained with mixed events.
This can be related to the temperature fluctuation: FpT =
sMpTdata/sMpTrandom – 1 =~ (<n> - 1)sT2/<T>2.
Combining this with the Gavai et al. [5] and Korus et al. [6] definitions of the specific heat
per particle, a simple relationship is obtained: cv/T3 = (<n>/<Ntot>)×(1/FpT).
FpT is measured with a fraction <h>/<Ntot>
of the total particles produced, a purely geometrical factor representing the fractional acceptance,
~1/33 in PHENIX. Gavai et al. [5] predict that cv/T3 = 15,
which corresponds to FpT ~ 0.20% in PHENIX, which may be accessible
by measurements of MpT in the range
0.2 £ pT £ 0.6 GeV/c.
In order to test the Gavai et al. prediction that cv/T3
is reduced in a QGP compared to the ideal gas value (15 compared to 21), precision measurements
of FpT in the range 0.20% for 0.2 £ pT
£ 0.6 GeV/c may be practical.