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Variable Energy Cyclotron Centre, Kolkata

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1 Variable Energy Cyclotron Centre, Kolkata
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 Bedanga Mohanty

2 I will try to keep it simple!
Bedanga Mohanty

3 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 Bedanga Mohanty

4 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) Bedanga Mohanty

5 FLUCTUATION FOR IDEAL GAS AND AT CRITICAL POINT
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 Bedanga Mohanty

6 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 Bedanga Mohanty

7 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 Bedanga Mohanty

8 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. Bedanga Mohanty

9 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 Bedanga Mohanty

10 Gaussian Large number Fluctuation ~ width Exponential
FLUCTUATIONS IN HEAVY-ION COLLISIONS Gaussian Large number WA98 WA98 Fluctuation ~ width Exponential WA98 NA49 Bedanga Mohanty

11 Rich field 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 Bedanga Mohanty

12 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))……………………… Bedanga Mohanty

13 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 Bedanga Mohanty

14 MULTIPLICITY FLUCTUATION
Experimental result from NA49 Conclusion Cannot distinguish between these two models at NA49. Bedanga Mohanty

15 MULTIPLICITY FLUCTUATIONS
Data agree fairly well with model calculations Ref : PRC 65 (2002) Bedanga Mohanty

16 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 Bedanga Mohanty

17 Ng vs. Nch FLUCTUATIONS Results from data compared to mixed events and simulation Bedanga Mohanty

18 Only charged particles ?
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) (R) Bedanga Mohanty

19 TRANSVERSE MOMENTUM FLUCTUATION
Result from NA49 Mean pT Large amplitude non-statistical fluctuation is small. PLB 459 (1999) 679 Bedanga Mohanty

20 TRANSVERSE MOMENTUM FLUCTUATION
QM2002 Bedanga Mohanty

21 TRANSVERSE MOMENTUM FLUCTUATION
PRC 66 (2002) Event-by-event <pT> for data (+) and mixed event (+) Bedanga Mohanty

22 TRANSVERSE MOMENTUM FLUCTUATION
Non-statistical fluctuations increase the rms width by % 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| < 1, full f, 0.1 < pT < 2.0 GeV/c QM2002 Bedanga Mohanty

23 FLUCTUATION : NEW IDEAS
Fluctuation in conserved quantities : net charge, net baryon number or net strangeness number Asakawa, et al.,PRL 85(2000)2072; Jeon&Koch 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. Bedanga Mohanty

24 FLUCTUATION IN CONSERVED QUANTITY
Asakawa, et al.,PRL 85(2000)2072; Jeon&Koch PRL 85(2000)2076 Idea : Given strong longitudinal expansion the fluctuations of conserved quantities will be preserved during hadronisation and hadronic phase Bedanga Mohanty

25 FLUCTUATION IN CONSERVED QUANTITY
Bedanga Mohanty

26 FLUCTUATION IN CONSERVED QUANTITY
QM2002 Bedanga Mohanty

27 FLUCTUATION IN CONSERVED QUANTITY
||  0.35, =/2, 0.3  pT  2.0 GeV/c 10% most central collisions PRL 89 (2002) v(Q) = ± 0.007(stat.) – (syst.)snn = 130GeV v(Q) = ± 0.006(stat.) ± (syst.)snn = 200GeV Bedanga Mohanty

28 EVOLUTION OF FLUCTUATION
Mohanty, Alam, Nayak PRC 67 (2003) Scenarios Initial conditions and fluctuations QGP Hadron gas Hadron gas with mass variation mh* = mh(1-T2/Tc2)l 0 < l < 1 Initial /Scenario Values QGP HAD HAD* geff 37 15 24 Ti (MeV) 196 264 226 m (MeV) 132 340 105 [DNb(ti)]2/S 0.014 0.029 0.061 [DNb(ti)]2/Nb 0.56 1.16 2.46 Bedanga Mohanty

29 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 EOS/Secnario QGP HAD HAD* S cs2 = 1/3 1.0 1.3 P cs2 = 0.18 Lattice 2.0 2.8 2.5 RI 1.46 C 1.96 H 3.17 [DNb(ti)]2/Nb Mohanty, Alam, Nayak PRC 67 (2003) Bedanga Mohanty

30 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 Interesting pair + - N+ - (Dy) = Histogram of | y(p+) - y(p-) |, for all possible pairs within an event. This histogram is summed over all events. Bedanga Mohanty

31 BALANCE FUNCTIONS Eprint : nucl-ex/ (PRL in press) STAR Collaboration Pions Separation decreases with centrality Requires delayed production of charge (delayed hadronization) Suggests creation of gluon-rich matter Bedanga Mohanty

32 Theory : You see what I show
SUMMARY Theory : You see what I show Experiment : I think I hear it Bedanga Mohanty

33 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 Bedanga Mohanty

34 Absence of evidence is not evidence of absence
FINAL SUMMARY – THEORY Absence of evidence is not evidence of absence Bedanga Mohanty

35 SUMMARY – SPS (EXP) Large amplitude non-statistical fluctuation is small at SPS Bedanga Mohanty

36 SUMMARY – RHIC (EXP) Non-statistical fluctuation observed!
Bedanga Mohanty

37 Is it signal or background !
QGP Thanks Bedanga Bedanga Mohanty

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