FLUCTUATIONS AND QCD PHASE TRANSITION

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FLUCTUATIONS AND QCD PHASE TRANSITION
Bedanga Mohanty Variable Energy Cyclotron Centre,
Kolkata

• OUTLINE
• What is fluctuation of a quantity ?
• What is the connection between fluctuation and
  phase transition ?
• Can fluctuation be a probe for QCD PT ?
• How does fluctuation for a typical observable
  evolve with time ?
• What are the proposed observable and
  corresponding the experimental results so far ?
• Summary

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I will try to keep it simple!
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FLUCTUATION IN A QUANTITY
Physical quantities which describe a macroscopic
body in equilibrium are almost always, very
nearly equal to their mean values. Nevertheless
deviations from mean values, though small do
occur quantities are said to fluctuate
---- Landau

It is of interest to know the probability
distribution of these deviations
Considering deviations in x to be small with mean
at 0
W (x) Constant e S(x)
X some physical quantity S(x) is the entropy
S(x) S(0) ½ bx2
W(x) dx sqrt(b/2p) e-1/2bx2 dx
The probability distribution of the various
values of fluctuation in x is a Gaussian
distribution
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FLUCTUATION AND PHASE TRANSITION
Thermodynamic quantities ? phase
transition It is of interest to calculate the
fluctuation of fundamental thermodynamic
quantities Condition the system must contain
sufficient number of particles
W (x) e (DPDV-DTDS/2T)
W (x) e DS
Consider V and T to be independent variable
DS change in the entropy in the fluctuation
W (x) exp - Cv(DT)2/2T2 (DP/DV)T (DV)2/2T
Fluctuations related to Sp. Heat and
compressibility
(DT)2/T2 1/Cv
(DN)2/N2 -(DV/DP)T(T/V2)
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FLUCTUATION FOR IDEAL GAS AND AT CRITICAL POINT
Ideal gas EOS - V NT/P Substituting
in
Critical Point Compressibility
(DV/DP)T of a substance becomes infinite
(DN)2/N2 -(DV/DP)T(T/V2)
(DN)2/N2 large
(DN)2 N
Fluctuation becomes large
Statistical fluctuation is Poissonian
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FLUCTUATION TO STUDY QCD PHASE TRANSITION

• 1. We should know what are the QCD phase
  transitions
• 2. Can one correlate fluctuations in
  thermodynamic
• variables to fluctuations in experimental
• observable
• 3. Does the experiments looking for QCD phase
• transition satisfy the various conditions we
  have discussed so far

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QCD PHASE TRANSITIONS
Tricritical point
PRL 81 (1998) 4816 Stephanov et al.
Analogy Critical Opalescence (as observed in a
CO2 liquid-gas transition)
NPA 663 (2000)183 Peter Braun-Munzinger

• QCD transitions
• Deconfinement
• Chiral symmetry restoration

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EXPERIMENTAL OBSERVABLE AND FLUCTUATION IN
THERMODYNAMICAL VARIABLES
Thermodynamic properties of matter
PRL 75 (1995) 1044 L. Stodolsky
(DpT)2/pT2 (DT)2/T2 1/Cv
PLB 430 (1998) 9 S. Mrowczynski
Study of thermodynamical quantities (or
fluctuations in experimental observables) can
shed light on possible existence of phase
transition and its nature
At tricritical point singularities in
thermodynamical observables large e-by-e
fluctuations in Expt. Obs.
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CHIRAL SYMMETRY RESTORATION

• Through search for disoriented
• chiral condensates
• Study and detection of DCC
• Nature of chiral phase transition
• Vacuum structure of strong interaction

Look at Ng vs. Nch correlation
A.A. Anselm et al., PLB 261(1991) 482 Rajagopal
et al NPB 404 (1993)577
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FLUCTUATIONS IN HEAVY-ION COLLISIONS
Gaussian
Large number
WA98
WA98
Fluctuation width
Exponential
WA98
NA49
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OBSERVABLES PROPOSED

• Event-by-event physics is an important tool
  to study thermalization and phase transition
  through anomalous fluctuations and correlations.
• What kind of fluctuations can be studied in
  relativistic heavy-ion collisions?
• Multiplicity fluctuation
• Net charge/Net baryon number fluctuation
• Particle ratio fluctuation
• Transverse momentum fluctuation
• Balance Functions

Rich field
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PAPERS PUBLISHED
Temperature fluctuations (Stodolsky (95), Shuryak
(98)) Phi-measure (Gazdzicki,
Mrowczynski(92)) Quantum statistics (Mrowczynski
(98)) Particle Ratios (Baym, Heiselbergy (99),
Stephanov (99), Jeon, Koch (99,00),
Mohanty,Nayak, Mahapatra (01)) Resonance gas
(Rajagopal, Shuryak, Stephanov (99), Jeon
koch (99))
Phase transitions, bubble formation (Baym,
Heiselberg (99), Rajagopal, Shuryak, Stephanov
(99), Heiselberg, Jackson (00)) Charge
fluctuations (Asakawa, Heinz, Mueller (00), Jeon,
Koch (00), Dumitru Pisarski (00), Stephanov,
Shuryak (00)) Baryon number fluctuations
(Asakawa, Heinz, Mueller (00), Gavin (00),
Mohanty, Alam, Nayak (03)) Balance functions
(Bass, Danielewicz, Pratt (00)) Review Article
(Heiselberg (00))
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MULTIPLICITY FLUCTUATION
Multiplicity fluctuation ?N

• NWM (Nuclear wounded model)
• A superposition of NN collisions.

Thermal model
Degree of thermalization
Heiselberg, Phys. Rept 351 (2001) 161
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MULTIPLICITY FLUCTUATION
Experimental result from NA49
Conclusion
Cannot distinguish between these two models at
NA49.
Mahapatra, Mohanty and Phatak IJMPA 17 (2002) 675
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MULTIPLICITY FLUCTUATIONS
Data agree fairly well with model calculations
Ref PRC 65 (2002) 054912
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PARTICLE RATIO FLUCTUATUIONS
Result from NA49

• pi/pi- ratio fluctuation
• similar to net charge
• fluctuation
• K/pi ratio fluctuation
• strange enhancement
• pi0/pi(pi-) ratio fluctuation
• chiral symmetry restoration

Large amplitude non-statistical fluctuation is
small.
PRL 86 (2001) 1965
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Ng vs. Nch FLUCTUATIONS
Results from data compared to mixed events and
simulation
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Ng vs. Nch FLUCTUATION
Only photons ? Only charged particles ? Both
? Both and correlated ?
Mixed events used to filter out contribution from
different sources to fluctuation

• Presence of individual
• Fluctuations in both
• Ng
• Nch

Ref PRC 64 (2001) 011901 (R)
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TRANSVERSE MOMENTUM FLUCTUATION
Result from NA49
Mean pT
Large amplitude non-statistical fluctuation is
small.
PLB 459 (1999) 679
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TRANSVERSE MOMENTUM FLUCTUATION
Gaussian
QM2002
Non Gaussian
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TRANSVERSE MOMENTUM FLUCTUATION
PRC 66 (2002) 024901
Event-by-event ltpTgt for data () and mixed event
()
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TRANSVERSE MOMENTUM FLUCTUATION
Non-statistical fluctuations increase the rms
width by 140.5
Gamma with increased rms Gamma ref. from
inclusive pT spectrum
183K top 15 central events using 70 of all
primary Particles. Both () and (-) charges h
lt 1, full f, 0.1 lt pT lt 2.0 GeV/c
QM2002
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FLUCTUATION NEW IDEAS
Fluctuation in conserved quantities net charge,
net baryon number or net strangeness number
Asakawa, et al.,PRL 85(2000)2072 JeonKoch PRL
85(2000)2076
Balance Functions
Bass, Danielewicz, Pratt, Phys. Rev. Lett. 85,
2689 (2000)
Tri-critical point
PRL 81 (1998) 4816 Stephanov et al.
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FLUCTUATION IN CONSERVED QUANTITY
Asakawa, et al.,PRL 85(2000)2072 JeonKoch PRL
85(2000)2076
Idea Given strong longitudinal expansion the
fluctuations of conserved quantities
will be preserved during
hadronisation and hadronic phase
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FLUCTUATION IN CONSERVED QUANTITY
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FLUCTUATION IN CONSERVED QUANTITY
QM2002
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FLUCTUATION IN CONSERVED QUANTITY
? ? 0.35, ???/2, 0.3 ? pT ? 2.0 GeV/c 10
most central collisions
PRL 89 (2002) 082301
v(Q) 0.965 0.007(stat.) 0.019 (syst.)?snn
130GeV v(Q) 0.969 0.006(stat.) 0.020
(syst.)?snn 200GeV
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EVOLUTION OF FLUCTUATION
Mohanty, Alam, Nayak PRC 67 (2003) 024904
Scenarios
Initial conditions and fluctuations

• QGP
• Hadron gas
• Hadron gas with mass variation
• mh mh(1-T2/Tc2)l
• 0 lt l lt 1

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EVOLUTION OF FLUCTUATION
Evolution Scenraios and fluctuations at
freeze-out (120 MeV)
EOS

• Ideal gas
• Hadron gas with all particles having mass up to
  2.5 GeV
• Lattice

DNb(ti)2/Nb
Mohanty, Alam, Nayak PRC 67 (2003) 024904
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BALANCE FUNCTIONS
Bass, Danielewicz, Pratt, Phys. Rev. Lett. 85,
2689 (2000)

• Motivated by the idea that hadrons
• are locally produced in (),(-) pairs.
• Early pairs separate due to Long. Exp.
• Later pairs correlated at small Dy

N - (Dy) Histogram of y(p) - y(p-) , for
all possible pairs within an event. This
histogram is summed over all events.
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BALANCE FUNCTIONS
Eprint nucl-ex/0301014 (PRL in press) STAR
Collaboration

• Separation decreases with centrality
• Requires delayed production of charge (delayed
  hadronization)
• Suggests creation of gluon-rich matter

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SUMMARY
Theory You see what I show
Experiment I think I hear it
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SUMMARY THEORY

• Net charge/Net baryon number fluctuation
• Space-time evolution was not properly
  considered!
• Particle ratio fluctuation
• 100 papers on DCC yet no dynamical model
  exists
• Lots of questions still remain unanswered !
• Balance Functions
• Most interesting to me! Still needs to be
  studied
• in greater detail
• Possibility of existence of a tri-critical point
  Exciting possibility to relate fluctuation
  to QCD phase diagram

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FINAL SUMMARY THEORY
Absence of evidence is not evidence of absence
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SUMMARY SPS (EXP)
Large amplitude non-statistical fluctuation is
small at SPS
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SUMMARY RHIC (EXP)
Non-statistical fluctuation observed!
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Is it signal or background !
QGP
Thanks
Bedanga