Wednesday, May 9, 2012

1205.1761 (A. Tawfik)

On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out and
QCD Critical Endpoint
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A. Tawfik
We calculate the first six non-normalized moments of particle multiplicity within the hadron resonance gas model. In terms of lower moments, general expressions for arbitrary higher moments are deduced, so that it is concluded that going from lower to higher moments is achievable through a series of lower moments and correlation functions. The thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials $\mu$, so that it was possible to evaluate them at the chemical freeze-out curve, which is characterized by constant $s/T^3$ at all values of $\mu$, where $s$ and $T$ are entropy density and temperature, respectively. It has been found that non-monotonic behavior reflecting dynamical fluctuation and strong correlations appears starting from the normalized third moment (skewness $S$). The signatures of non-monotonicity in the normalized fourth moment (kurtosis $\kappa$) and its products are very clear. Based on these findings, we introduce novel conditions describing the chemical freeze-out curve and the location of the QCD critical endpoint. The chemical freeze-out curve is described by $\kappa=3\,\chi^2$, where $\chi$ is the susceptibility in particle number. The location of QCD critical endpoint (at $T$- and $\mu$-axis) is found when $S_b=S_f$ or $\kappa_b=\kappa_f$, where the subscripts $b$ and $f$ refer to bosons and fermions, respectively. Accordingly, the QCD endpoint is positioned at $\mu\sim 350 $MeV and $T\sim162 $MeV.
View original: http://arxiv.org/abs/1205.1761

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