Transcript Lysbilde 1 - Istituto Nazionale di Fisica Nucleare

Measures of charged particle fluctuations
(in high energy heavy-ion collisions)
Joakim Nystrand
University of Bergen
Bergen, Norway
• Charged particle fluctuation measures.
• Behaviour of these measures in various non-dynamical
scenarios.
• Simple dynamical (toy) models.
• Conclusions and comparison with some experimental
results.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Event-by-event fluctuations of charged particles:
Example variable
1. Net-charge
2. Strangeness
3. Baryon number
4. Multiplicity
Q = n+ – n–
K/π
(p+p)/(π+ + π–)
nch = n+ + n–
I assume that the physics motivation for studying fluctuations
in these quantities is well known to this audience, if not, see
1. S. Jeon, V. Koch Phys. Rev. Lett. 85 (2000) 2076.
2. M. Asakawa, U. Heinz, B. Müller Phys. Rev. Lett. 85 (2000) 2072.
3. H. Heiselberg, A.D. Jackson Phys. Rev. C 63 (2001) 064904.
4. M. Gazdzicki, Eur. Phys. J. C 8 (1999) 131.
5. S. Mrowczynski, Phys. Lett. B 459 (1999) 13.
……
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Net charge fluctuations
Measured in one event:
n+ positive and n– negative particles
nch = n+ + n– , Q = n+ – n– , R = n+/n–
V(Q), V(R) – variance of Q and R.
< > - average over events
4 measures of fluctuations:
V ( Q)
v ( Q) 
 n ch 
v(R)  V(R)  n ch 
S.Jeon, V.Koch PRL 85 (2000) 2076.


1
Q
 Q 

n ch 
 n ch  
 n ch 

 n
n 

 dyn  

  n   n  
2
2
S. Mrowczynski, Phys. Rev. C 66 (2002)
024904; a modification of the Φ measure
 1
1 

 

  n   n  
C.Pruneau, S.Gavin,
S.Voloshin, Phys. Rev. C 66
(2002) 044904.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Goal of this study  Investigate the behaviour of these
measures in a set of scenarios (simplified → semirealistic)
First scenario (simplest possible) :
Generate Nch particles, + or – with equal prob. and assume
that we detect a fraction pa of them.
Expectations
v(Q) = Γ = 1
v(R) = 4 asymptotically
v=0
● Nch = 1000
□ Nch = 200
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Add charge conservation  Assume first that N+ = N– = Nch/2
(these are the global multiplicities)
Expectations
v(Q), Γ, v(R):
→ 0 as pa → 1
(no fluctuations if we
measure the whole event)
In general,
prev. res.  (1 – pa)
ν = – 4/Nch (indep. of pa)
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Add excess of positive particles (but no charge conservation)
 Let N+ = p+ Nch and N– = p– Nch and introduce ε = p+ – p–
Expectations
v(Q) = 1 – paε2
V(R) = 4 + 16ε + O(ε2)
Γ = 1 – ε2
ν=0
●ε=0
□ ε = 0.1
∆ ε = 0.2
 Major problem when studying fluctuations in a ratio,
strong, linear dependence of R on ε (applies to n+/n– and
to K/π)
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Combine charge conservation with excess of positive particles,
and add fluctuations in the global multiplicity.
 Nch = 1000, Nch = 900-1100, Nch = 800-1200 ; ε = 0.2
Expectations
Only v(Q) depends on the
variation in global mult.
v(Q) = 1 – pa + pa ε2 v(Nch)
Slight shift in ν with charge
conservation and ε0
ν = –4 / <Nch> (1- ε2)
 Dependence of v(Q) on global multiplicity variation
problematic.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Experimental efficieny and background tracks
For a detector that on average finds a fraction pe of the
tracks passing through it, the probability to detect exactly nd
tracks out of ntrue is given by a binomial distribution.
 In this context, equivalent to reducing the acceptance
pa → pa · pe .
Introducing a certain fraction, fbg, of uncorrelated background
tracks. Keeping charge conservation and with Nch=1000 and ε=0.
Reduces the slopes of v(Q), v(R), and Γ by a factor (1-fbg).
Constant reduction for ν; ν = – 4 (1-fbg) / <Nch>.
● fbkg = 0
□ fbkg = 0.2
∆ fbkg = 0.4
Summary non-dynamical scenarios
1. A variation of the exp. acceptance, pa, or efficiency, pe
 A reduction in v(Q), v(R), and Γ by a factor (1 – pa· pe)
 ν is unaffected by pa and pe.
2. v(R) has a complicated behavior for small acceptances
and depends strongly on the asymmetry, <N+/N–> or
<K/π>  1.
3. All 4 measures are affected by an uncorrelated
background.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Add some dynamics 
decay of neutral resonances, for example 0 → π+ π–.
Generate particles with one phase space variable , which
could correspond to azimuthal angle,  = φ/2π.
Assume acceptance in other variables (y, pT) is complete,
or at least wide.
Let fres be the fraction of particles emanating from resonance
decays and Δ=1/24 be the opening angle of the daughters.
Varying fres
● fres = 0
□ fres = 0.3
∆ fres = 0.6
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Varying Δ
● Δ = 1/12
□ Δ = 1/24
∆ Δ = 1/72
Conclusions:
* Clear deviations from the purely stochastic behavior are
seen in all variables when resonance correlations are included.
* Deviations are seen at small acceptances, but note that
this requires that the coverage in the other variables (y, pT) is
complete (or at least wide).
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
A simplified model of the hadronization from a
Quark-Gluon Plasma could be done along the same lines:
Hadronization only into pions (π+ π– π0). Angular distribution
between pions from same quark pair distributed with width
Δ.
● Δ = 1/6
□ Δ = 1/12
∆ Δ = 1/36
Dividing out the (1-pa) dependence
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Relevance of these studies to real data (?)
Au+Au @ sNN1/2 = 62 GeV
0-5%
10-20%
30-40%
70-80%
STAR Data (preliminary/work in
progress), C. Pruneau 2nd Wkshp on
the Critical Point (Bergen 2005)
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
The large-scale variations for certain variables are often
dominated by statistical, non-dynamical fluctuations.
nch is used here to
select the centrality.
K. Adcox et al. (PHENIX) Phys. Rev. Lett. 89 (2002) 082301.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Conclusions
• Avoid studying fluctuations in particle ratios
(n+/n–) or (K/π), or at least be extremely careful.
• The variation of ν with Δφ sensitive probe of
dynamical fluctuations.
Hard to directly interpret measured ν vs. Δφ
but
Any reasonable resonance cocktail (0, f0, K0S, …)
with correct momentum distributions (including
collective flow) should be able to reproduce the
behavior of ν vs. Δφ.
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand
Some notes and references
1. The net-charge results are from J. Nystrand, E. Stenlund,
H. Tydesjö Phys. Rev. C 68 (2003) 034902.
2. Some more details and derivations of the analytical expectations in
H. Tydesjö Lic. and Phd. Theses, available at
http://www.hep.lu.se/staff/tydesjo/theses.html
3. Similar studies by J. Zaranek Phys. Rev. C 66 (2002) 044902;
S. Mrowczynski, Phys. Rev. C 66 (2002) 024904.
Some quotes about statistics
1. He uses statistics as a drunken man uses lamp-posts – for
support rather than illumination. (A. Lang)
2. If your experiment needs statistics, you ought to have done
a better experiment. (E. Rutherford)
3. Then there is the man who drowned crossing a stream with
an average depth of six inches. (W.I.E. Gates).
Correlations and Fluctuations in Relativistic Nuclear Collisions, Florence, Italy, July 7-9 2006
Joakim Nystrand