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How to Measure Specific Heat Using Event-by-Event Average $p_T$ Fluctuations | | M. J. Tannenbaum
; PHENIX Collaboration
; | | Date: |
1 Dec 2005 | | Abstract: | 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 $M_{p_T}$, the event-by-event average $p_T$, by $F_{p_T}$, 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:
[ F_{p_T}=sigma^{
m data}_{M_{p_T}}/sigma^{
m random}_{M_{p_T}}-1simeq(< n > -1) sigma^2_{T}/< T>^2 ]
Combining this with the Gavai, {it et al.},cite{Gavai05} and Korus, {it et al.},cite{Korus} definitions of the specific heat per particle, a simple relationship is obtained:
[ c_v/T^3={mean{n}over mean{N_{tot}}} {1over F_{p_T}} ]
$F_{p_T}$ is measured with a fraction $mean{n}/mean{N_{tot}}$ of the total particles produced, a purely geometrical factor representing the fractional acceptance, $sim 1/33$ in PHENIX. Gavai, {it et al.} predict that $c_v/T^3=15$, which corresponds to $F_{p_T}sim 0.20$% in PHENIX, which may be accessible by measurements of $M_{p_T}$ in the range $0.2leq p_Tleq 0.6$ GeV/c. In order to test the Gavai, {it et al.} prediction that $c_v/T^3$ is reduced in a QGP compared to the ideal gas value (15 compared to 21), precision measurements of $F_{p_T}$ in the range 0.20% for $0.2leq p_Tleq 0.6$ GeV/c may be practical. | | Source: | arXiv, nucl-ex/0512004 | | Services: | Forum | Review | PDF | Favorites | |
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