How to measure specific heat using event-by-event average pT fluctuations

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, , with standard deviation σT. 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 σMpT(data)/σMpT(random)-1∼ ( - 1)σT2/. Combining this with the Gavai et al. and Korus et al. definitions of the specific heat per particle, a simple relationship is obtained: cν/T3 = (/)·(1/FpT). FpT is measured with a fraction <η>/ of the total particles produced, a purely geometrical factor representing the fractional acceptance, ∼ 1/33 in PHENIX. Gavai et al. predict that cν/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 cν/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. (author)