1. Search for the Critical Point of Strongly Interacting Matter at the CERN SPS G.Melkumov (JINR Dubna) for NA49 collaboration Tatranská Štrba, June 27th - July 1st, 2011

2. Pb+Pb at SPS energies: Energy density exceeds the critical value ( ≈ 1 GeV / fm 3 ) Signatures for deconfinement –radial & anisotropic flow –strangeness enhancement –J/Ψ,Ψ’ yield suppression –di-lepton enhancement & ρ 0 modification QCD prediction of quark-gluon deconfinement Search for the onset of deconfinement by the energy scan at the SPS Comprehensive study of the phase diagram of strongly interacting matter

3. Hadron measurements in large acceptance (y CM > y > y beam ) Tracking by large- volume TPCs in SC magnet field PID by dE/dx,TOF, decay topology, invariant mass NA49 experiment at CERN SPS Centrality determination by Forward Calorimeter Operating 1994-2002; p+p, C+C, Si+Si and Pb+Pb interactions at center of mass energy 6.3 – 17.3 GeV for N+N interaction

4. PID by TOF + dE/dx Tracking and particle identification Tracking PID by dE/dx

5. What is the energy threshold for deconfinement  (the lowest energy sufficient to create a partonic system)  Motivation: Statistical Model of the Early Stage (SMES) Gaździcki, Gorenstein, Acta Phys. Polon. B30, 2705 (1999) “kink” “horn” “step” entropy S  4 N  HG cont. QGP HG cont. QGP HG QGP mixed phase mixed phase 1 st order phase transition to QGP between top AGS and top SPS energies  s NN  7 GeV number of internal degrees of freedom (NDF) increases HG   QGP (activation of partonic degrees of freedom) total entropy and total strangeness are the same before and after hadronization (cannot decrease QGP  HG) mass of strangeness carriers decreases HG   QGP (m , K,... > m s ) constant temperature and pressure in mixed phase Search for the onset of deconfinement

6. Pions measure early stage entropy. In SMES: /N w ~ NDF 1/4  A+A data change from "suppression" (AGS) to "enhancement" at low SPS energies  Change of slope around 30A GeV; slope in A+A increases from ≈1 (AGS) to ≈ 1.3 (top SPS+RHIC) - consistent with increase x 3 in NDF  No change of slope in p+p data Full phase space (4  ) Pion energy dependence - 4π yields M. Gazdzicki and M. Gorenstein, Acta Phys.Pol. B30 (1999) 2705 Final NA49 results on the onset of deconfinemet: C.Alt et al., PRC77,024903 (2008)

7. Pion yield per participant NA49,C.Alt et al.,PRC77,024903(2008) central PbPb/AuAu π yield related to entropy production steeper increase in A+A suggests 3-fold increase of initial d.o.f E s related to strangeness/entropy ratio plateau consistent with prediction for deconfinement (SMES model, M.Gazdzicki and M.Gorenstein, Acta Phys. Pol.30,2705(1999)) Onset of deconfinement Kink Horn Ratio of strange particles to pions

8. Peaks sharply at the SPS SMES explanation: - entropy, number of s, s quarks conserved from QGP to freeze-out - ratio of (s + s) / entropy rises rapidly with T in the hadron gas - E s drops to the predicted constant QGP level above the threshold of deconfinement : hadronic mixedpartonic AGS SPS Strangeness to entropy ratio Proposed as measure of strangeness to entropy ratio (SMES) E s shows distinct peak at 30A GeV Described (predicted) by model assuming phase transition (SMES)

9.  Consistent with approximately constant temperature and pressure in mixed phase (latent heat)(softest point of EoS)  Hydrodynamical model with deconfinement phase transition starting at lower SPS energies describes data M. Gorenstein et al., Phys. Lett. B 567 (2003) 175 S. Hama et al., Braz. J. Phys. 34 (2004) 322 Kaon inverse slope parameter The step-like feature observed at SPS energies, not seen for p+p collisions and in models without phase transition Hydro+PT Step

10. Rapid changes of hadron production properties at low SPS energy most naturally explained by onset of deconfinement NA49,C.Alt et al.,PRC77,024903(2008); M.Gazdzicki et al.,arXiv:1006.1765 NA49,C.Alt et al., PRC77,024903 (2008) Shape of transverse mass spectra (H.Petersen and M.Bleicher, nucl-th/0611001) SPheRIO Softening of transverse (step) and longitudinal (minimum of c s ) features of EoS due to mixed phase (soft point of EoS) Onset of deconfinement Step Dale Estimate of sound velocity

11. Landau hydro-dynamical model (E.Shuryak,Yad.Fiz.16, 395(1972)) Minimum of sound velocity c s (softest point of EoS) around 30A GeV → sound velocity can be derived from measurements H.Petersen and M.Bleicher, nucl-th/0611001 width of rapidity distribution sound velocity More signals : Estimate of sound velocity Dale

12. 200 400 T(MeV) HornStep SPS(NA49), RHIC(STAR) and LHC(ALICE) Verification of SPS(NA49) results by RHIC(STAR) and LHC(ALICE) Horn- and Step- like features in hadron gas ->mixed phase->QGP transitions

13. QCD considerations suggest a 1 st order phase boundary ending in a critical point Hadro-chemical freeze-out points are obtained from statistical model fits to measured particle yields T and μ B approach phase boundary and estimated critical point at SPS SPS RHIC critical end point Fodor,Katz JHEP 04,50(2004) Exploration of phase diagram Evidence of the onset of deconfinement from rapid changes of hadron production properties Search for indications of the critical point as a maximum in fluctuations

14. Quark number susceptibilities

15. Y.Hatta and T.Ikeda, PRD67,014028 (2003) M.Asakawa et al.,PRL 101,122302(2008) Effects (singularities) at critical point effects of critical point are expected over a range of T,µ B hydro predicts that evolution of the system is attracted to critical point  =  B /3 The presence of the critical point can deform the trajectories describing the evolution of the expanding fireball in the (T,  B ) phase diagram For a given chemical freeze-out point three isentropic trajectories (n B /s = const.) are shown We do not need to hit precisely the critical point because a large region can be affected

16.  pT - measures transverse momentum fluctuations on event-by-event basis  - measures multiplicity fluctuations on event-by-event basis If A+A is a superposition of independent N+N  pT (A+A) =  pT (N+N)  (A+A) =  (N+N) +  part  pT is independent of N part fluctuations - mean multiplicity of hadrons from a single N+N  part - fluctuations in N part  is strongly dependent on N part fluctuations For a system of independently emitted For Poissonian multiplicity distribution particles (no inter-particle correlations)  pT = 0  =1 Event-by-event multiplicity & transverse momentum fluctuations

17. Search for the critical point A (system size)  s NN I.Kraus et al., Phys.Rev.C76, 064903 (2007) (2006)F.

18.  No significant energy dependence at SPS energies CP 1 location:   (CP 1 ) = 360 MeV T (CP 1 )  147 (chemical freeze-out temperature for Pb+Pb at   = 360 MeV) base-lines for CP 1 predictions (curves) are mean  pT and  values for 5 energies Data show no evidence for critical point fluctuations Event-by-event & multiplicity fluctuations NA49 T.Anticic et al., PRC79,044904 (2009) NA49 C.Alt et al., PRC78,034914 (2008) M. Stephanov, K.Rajagopal,E.Shuryak, PRD60,114028(1999) Y.Hatta and T.Ikeda, PRD67,014028(2003) CP estimates based on: Energy dependence for central Pb+Pb collisions

19. Maximum of  pT and  observed for C+C and Si+Si CP 2 location:   (CP 2 )  250 MeV =   (A+A at 158A GeV) T (CP 2 ) = 178 MeV = T chem (p+p) CP 2 predictions (curves) normalized to reproduce  pT and  value for central Pb+Pb collisions Data are consistent with the CP 2 predictions System size dependence of fluctuatios Pb+Pb - PRC78,034914 (2008) CC,SiSi - B.Lungwitz (PhD) Pt data: PRC70,034902 (2004) pp - PRC75,064904 (2007) data:

20. St. Mrówczyki Phys. Lett. B465, 8 (1999 ) Single particle variable - inclusive avarage Event variable (summation runs over particles in a given event) - averaging over events Higher moments: Higher moments of fluctuation M.A.Stepanov, Phys.Rev.Lett. 102, 032301 ( 2009 ) Advantage: the amplitude of critical point peak is proportional to higher powers of the correlation length. Examples for second and fourth moments: Higher moments have been advertised as a probe for the phase transition and critical point effects Higher moments of measure (K.Grebieszkow, M.Bogusz) Definition: So far we were using second moment:  (2) pT 1. In a superposition model  (2) pT (A+A) =  (2) pT (N+N) 2. For independently emitted particles  (2) pT = 0 According to S. Mrówczyński Phys. Lett. B465, 8 (1999) only the 3 rd moment preserves the above (1. and 2.) properties of the 2 nd moment (higher moments not). In particular only  (2) pT and  (3) pT are intensive as thermodynamic quantities.

21. Φ pT (3) : 3 rd moment fluctuations Φ pT (3) has strongly intensive property like Φ pT (S.Mrowczynski,Phys.Lett.B465,8(1999)) NA49 preliminary Pb+Pb 7% central Systematic errors are large No indication of CP fluctuations K.Grebieszkow and M.Bogusz, NA49 preliminary Higher moments are expected to be more sensitive to fluctuations

22. C. R. Allton, Phys. Rev. D68 (2003), 014507 quark number susceptibility:  q ≡ ∂n q /∂μ q, T 0 – critical temperature for μ q = 0 (  B = 3  q ) Baryon density fluctuations appear to diverge for some critical value of the baryochemical potential For strongly interacting matter long range baryon density fluctuations expected A picture supported by lattice calculations Critical phenomena and density fluctuations Critical phenomena give rise to density fluctuations which obey the power laws. These power laws describe the density fluctuations of zero mass sigma particles abundantly produced in AA collisions at CP as well as the density fluctuations of net-baryons. The critical fluctuations (power laws) in sigma and proton sectors is motivated by the hypothesis that sigma and net-protons densities are a magnitudes of the order parameters for the second order phase transition associated with the QCD CP.

23. Intermittency in low mass π + π - pair density critical point predicted to lead to power-law density fluctuations of σ field observation via density fluctuations of low mass π + π - pairs in p T space power law behavior of F 2 (M) factorial moment expected (intermittency) N.Antoniou et al.,Nucl.Phys.A693,799(2001);A761,149(2005) NA49 data indicate intermittency signal for Si+Si ( T.Anticic et al., PRC81,064907(2010 )). Similar critical fluctuations for Si+Si interactions observed in proton sector. QCD Critical point close to freeze-out point of Si+Si system ?

24. T.Anticic et al., PRC70, 034902 (2004) C.Alt et al., PRC75, 064904 (2007) C.Alt et al,. PRC78, 034914 (2008) T.Anticic et al., PRC79, 044904 (2009) B.Lungwitz, NA49 thesis (2008) first hint on the hill of fluctuations? Critical point search in fluctuations first hint on the hill of fluctuations?

25. New data to be registered by NA61 Critical point of strongly interacting matter by an observation of a hill of fluctuations in two dimensional plane (energy)-(system size) The critical point should lead to an increase of multiplicity and transverse momentum fluctuations NA61  Search for the QCD critical point

26. 10 20 30 40 80 158 energy (A GeV) In+In C+C S+S New data to be registered by NA61 p+p Establish the system size dependence of the anomalies observed in Pb+Pb collisions-further test interpretation as due to the onset of deconfinement 10 20 30 40 80 158 energy (A GeV) It is expected that the ''horn'' like structure should be the same for S+S and Pb+Pb collisions and then rapidly disappear for smaller systems ? NA61  Study of the onset of deconfinement

27. NA49 extrapolation Ion physics program NA61 Scan in energy and system size A Search for hill of fluctuations as signature of critical point Study onset of deconfinement: disappearance of “horn” etc. T µBµB Pb+Pb

28. 13 20 30 40 80 158 Xe+La energy (A GeV) Pb+Pb Be+C Ar+Ca NA61 ion program p+p p+Pb NA49 (1996-2002) 2009/10/11 2010/11/12 2014 2012/14 2015 P p+p 158 TT STAR (2008-10) Au+Au T -test of secondary ion beams P -pilot data taken Progress and revised plans in data taking NA61

29. Summary Onset of deconfinement indicated in inclusive observables in central Pb+Pb colisions at lower SPS energies of about 30A GeV: Results are not reproduced by hadron-string models (RQMD, UrQMD, HSD). Described (predicted) by model assuming phase transition (SMES) No indications of the critical point in the energy dependence of multiplicity and mean transverse momentum fluctuations in central Pb+Pb collisions System size dependence of the critical point at 158A GeV shows: a maximum of mean p T and multiplicity fluctuations in the complete p T range  consistent with the predictions an increase (from p+p up to Pb+Pb) of mean p T fluctuations in the low p T region; high p T particles show no fluctuation signal  Higher moment of Pt fluctuations measure : analysis of the 3 rd moment of Pt fluctuations for the energy and system size dependence is in progress A detailed energy and system-size scan is necessary to investigate the properties of the onset of deconfinement and to establish the existence of the critical point  NA61/SHINE