1. Multiplicity Fluctuations in Hadron-Resonance Gas
Viktor Begun
Bogolyubov Institute for Theoretical Physics
Kiev, Ukraine
Viktor Begun

2. Multiplicity fluctuations
Scaled variance
- Event-by-event
- Statistical averaging:
GCE, CE, MCE
Non-relativistic case
(discussed in textbooks):
Relativistic Gas:
!!!
Viktor Begun

3. The beginning: CE vs GCE
grand canonical limit
They are different!
V.B., M.Gaździcki,
M.Gorenstein, O.Zozulya,
Phys. Rev. C70, (2004)
canonical limit
Viktor Begun

4. Particle number distributions
g.m.c.e.
Viktor Begun

5. Some recent publications on fluctuations in GCE, CE and MCE:
V.B., M.Gorenstein, M.Hauer, V.Konchakovski, O.Zozulya, nucl-th\ , Phys. Rev. C, in print.
G. Torrieri, nucl-th/
V.B., and M. I. Gorenstein, Phys. Rev. C 73, (2006)
G. Torrieri, S. Jeon and J. Rafelski, AIP Conf. Proc. 828, 55 (2006)
G. Torrieri, S. Jeon and J. Rafelski, nucl-th/
G. Torrieri, S. Jeon and J. Rafelski, Rom. Rep. Phys. 58, 031 (2006)
M. Gazdzicki, J. Phys. Conf. Ser. 27, 154 (2005)
F. Becattini, A. Keranen, L. Ferroni and T. Gabbriellini, Phys. Rev. C 72, (2005)
V.B., M. I. Gorenstein, A. P. Kostyuk and O. S. Zozulya, J.Phys.G32, (2006)
G. Torrieri, S. Jeon and J. Rafelski, nucl-th/
J. Cleymans, K. Redlich and L. Turko, J. Phys. G 31, 1421 (2005)
J. Cleymans, K. Redlich and L. Turko, Phys. Rev. C 71, (2005)
V.B., M. I. Gorenstein and O. S. Zozulya, Phys. Rev. C 72, (2005)
A. Z. Mekjian, Nucl. Phys. A 761, 132 (2005)
A. Keranen, F. Becattini, V.B., M. I. Gorenstein, O.S. Zozulya, J. Phys. G, (2005)
V.B., M. I. Gorenstein, A. P. Kostyuk and O. S. Zozulya, Phys. Rev. C 71, (2005)
F. Becattini and L. Ferroni, Eur. Phys. J. C 38, 225 (2004)
Viktor Begun

6. Effect of Resonance Decays
GCE
S.Jeon, V.Koch,
Phys.Rev.Lett. 83 (1999)
V.B., M.Gorenstein, M.Hauer,
V.Konchakovski, O.Zozulya,
nucl-th\
CE, MCE
Viktor Begun

7. Line of the chemical freeze-out
<E>/<N> = 1GeV → T(μB)
S = 0 → μS
Q/B = 0.4 → μQ
THERMUS — S. Wheaton, J. Cleymans, J. Phys. G (2005)
J. Cleymans and K. Redlich, Phys. Rev. Lett. 81, 5284 (1998)
J. Cleymans, H. Oeschler, K. Redlich, S. Wheaton, Phys. Rev. C 73, (2006)
F. Becattini, J. Manninen, M. Ga´zdzicki, Phys. Rev. C 73, (2006)
Viktor Begun

8. The prediction of CE hadron gas model
< 1 ?!
Small acceptance
Resonance decays
V.B., M.Gorenstein, M.Hauer,
V.Konchakovski, O.Zozulya,
nucl-th\
Viktor Begun

9. < 1 !!! See talk of B. Lungwitz, Correlations and Fluctuations
in Relativistic Nuclear Collisions,
Florence, July
Viktor Begun

10. Summary Scaled variances are different in different ensembles,
even in thermodynamic limit:
( ωCE(Q=0) = 1/2, ωGMCE(m=0) = 1/4, ωMCE(m=0,Q=0) = 1/8 )
The analytical formulae for the
resonance decay contribution in CE has been found
The prediction for the energy dependence of the scaled variances in the most central Pb+Pb collisions has been done
A comparison of the statistical model for hadron-resonance gas in CE with NA49 data was discussed
GCE is not valid for scaled variances,
even for “small” part of the system!
Viktor Begun