1. How to measure E-by-E fluctuations of identified particles
Anar Rustamov for the NA49 and NA61/SHINE Collaborations
NICA/JINR-FAIR Bilateral Workshop
“Matter at highest baryon densities in the laboratory and in space”
Frankfurt Institute for Advanced Studies (FIAS), April 2 – 4, 2012
Outline:
Phase diagrams
Critical point
E-by-E fluctuations
Identity method
Application to data
Summary and outlook

2. Phases of matter phase diagram of water
Hypothetical phase diagram of strongly interacting matter
phase diagram of water
(electromagnetically interacting matter)
first order liquid-gas phase transition line
ends in a second order critical point
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

3. Critical point, fluctuations
Smoluchowski, Annalen der Physik, 25, 1908.
Einstein, Annalen der Physik, 33, 1910.
Large fluctuations near the critical point leads to well-known phenomena of Critical Opalescence
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

4. Predicted signals Initial Stage Early Stage (ES) Freeze-Out (FO)
Phys. Rev. D 82, (2010)
Initial Stage
Early Stage (ES)
Freeze-Out (FO)
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

5. Selected fluctuation measures
Multiplicity fluctuations
Poisson case:
Chemical (particle composition) fluctuations
NA49:
STAR:
Independent Poisson distributions:
Some other measures
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

6. Particle ratio fluctuations
K/p and K/π results from NA49 and STAR are
significantly different at low energies.
What is the reason for this discrepancy ?
Acceptance effects
Centrality selection
Bias in the used methods ?
Wrong results ?
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

7. NA49 particle identification
Charge
Momentum vector
Mass
Production point π p K e e π K p p
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

8. NA49 fluctuation analysis
Event mixing is used to remove:
Artificial correlations
2. Statistical fluctuations
For each particle from inclusive fit define:
PDFs of dE/dx:
PDFs of momentum:
using Maximum Likelihood method
extract e-b-e particle ratios,
Introduces artificial correlations!
No analytical derivation!
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

9. Identity method “in a nutshell”
Phys. Rev. C 83, (2011) ,Phys. Rev. C 84, (2011)
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

10. Identity method, defining the problem
Available information:
Inclusive dE/dx spectra
Mean multiplicities
dE/dx value for every track
Given this information we want to
estimate moments of the unknown
multiplicity distributions
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

11. Identities (3-particle example)
Calculated
for each event
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

12. W distributions (simulation)π K p
Wπ, nπ
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

13. W distributions (simulation)
Wπ, nπ π K p
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

14. W distributions (simulation)
Wπ, nπ π K p
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

15. W distributions (simulation)
Wπ, nπ π K p
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

16. Is there a relation between moments of W quantities and unknown multiplicity distributions
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

17. Identity method, second moments
Main idea is to find a relation between known moments of the W quantities and unknown moments of multiplicity distributions. For example in case of 2 particle types (p, k)
Known in term of inclusive dE/dx distributions
Known in term of inclusive dE/dx distributions
Phys. Rev. C 83, (2011)
Phys. Rev. C 84, (2011)
(2- component system)
(n- component or matrix method)
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

18. Identity method, second moments
Complete example in case of 2 particle types, p and k
(in general works for any number of particle species)
3 equations, 3 unknowns
Phys. Rev. C 84, (2011)
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

19. Identity method, third moments
Main idea is to find a relation between known moments of the W quantities and unknown moments of multiplicity distributions. For example in case of 2 particle types (p, k)
ready for publication
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

20. Application to the data
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

21. NA49 data set
Reaction
P [GeV/c]
s1/2 [GeV]
F [GeV1/2]
0-3.5%
Pb + Pb 20
6.271
1.918 30
7.621
2.233 40
8.766
2.471 80
12.325
3.101
158
17.27
3.812
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

22. W distributions (experiment)
With Simple-4-Gaussian dE/dx fits
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

23. Perfect agreement with both, published results of NA49, and STAR !
NA49, Pb+Pb, 0-3.5% (identity method)
NA49, Pb+Pb, 0-3.5% (e-by-e fit)
STAR, Au+Au, 0-5%
preliminary
Error calculation for identity method: ongoing
Statistical errors are expected to be similar to those from e-by-e fit
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

24. Increasing trend at low energies reported by NA49 is confirmed
NA49, Pb+Pb, 0-3.5% (identity method)
NA49, Pb+Pb, 0-3.5% (e-by-e fit)
STAR, Au+Au, 0-5%
preliminary
Error calculation for identity method: ongoing
Statistical errors are expected to be similar to those from e-by-e fit
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

25. Increasing trend at low energies reported by NA49 is confirmed
NA49, Pb+Pb, 0-3.5% (identity method)
NA49, Pb+Pb, 0-3.5% (e-by-e fit)
STAR, Au+Au, 0-5%
preliminary
Error calculation for identity method: ongoing
Statistical errors are expected to be similar to those from e-by-e fit
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

26. The differences are still there
preliminary
preliminary
NA49 (identity method)
NA49 (e-by-e fit)
STAR
Independent analysis of NA49 data by different method confirms
p/pi k/p and k/pi energy dependence published by NA49
What is the reason for this difference in k/p and k/pi?
Acceptance effects
Centrality selection
Bias in the used methods
Wrong results?
NA49 (checked)
STAR results can be verified with the identity method
preliminary
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

27. NA61 Road Map Tchem [MEV] μB [MEV] p+p
Be+Be
p+p
C+C
Si+Si
Pb+Pb
Tchem [MEV]
μB [MEV]
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

28. NA61 Road Map
/12
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

29. Summary and Outlook Summary
A new unbiased approach to study multiplicity fluctuations of identified particles has been developed
Identity method allows to study higher cumulants predicted to better probe the critical point
The method was used to verify published NA49 results.
It is programmed in a separate package which can be compiled under the ROOT and used in any experiments
Outlook
The Identity method can also be applied to STAR data
It will also be used for the NA61/SHINE data
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

30. Phase diagram Spontaneous symmetry braking:
Chiral symmetry SU(2)L x SU(2)R
order parameter:
Center symmetry Z(3) (of SU(3)C)
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

31. Critical point, fluctuations
Large fluctuations near the critical point leads to well-known phenomena of Critical Opalescence
I order phase transition
II order phase transition
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,

32. Multi-4-Gaussian dE/dx fit
A. Rustamov, NICA/JINR-FAIR Workshop, FIAS,