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

A simple way to visualize event-by-event average p(T) fluctuations is by assuming that each collision has a different temperature parameter (inverse p(T) slope) and that the ensemble of events has a temperature distribution about the mean, < T >, with standard deviation sigma(T). PHENIX characterizes the non-random fluctuation of M-pT, the event-by-event P average p(T), by F-pT, the fractional difference of the standard deviation of the data from that of a random sample obtained PT with mixed events. This can be related to the temperature fluctuation: F-pT = sigma(data)(MpT)/sigma(random)(MpT) -1 similar or equal to (< n > - 1)sigma(5/)(T)< 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: c(v)/T-3 = (< n >/< N-tot >)-(1/F-pT) is measured with a fraction < n >/ N-tot) of the total particles produced, a purely geometrical factor representing the fractional acceptance, similar to 1/33 in PHENIX. Gavai et al. [5] predict that c(v)/T-3 = 15, which corresponds to F-pT similar to 0.20% in PHENIX, which may be accessible by measurements of M-pT in the range PT 3 PT 0.2 <= P-T <= 0.6 GeV/c. In order to test the Gavai et al. prediction that cv/T-3 is reduced in a QGP compared to the ideal gas value (15 compared to 21), precision measurements of F-pT in the range 0.20% for 0.2 <= P-T <= 0.6 GeV/c may be practical.