Searching for the QCD critical point in nuclear collisions

Transcription

1 Critical Point and Onset of Deconfinement, Florence, 3-6 July 2006 Searching for the QCD critical point in nuclear collisions F.K. Diakonos

2 Outline. Observational critical QCD - basic predictions 2. CMC Generator for critical events 3. Reconstruction of the critical sigma sector (CMC) 4. SPS A + A data analysis - preliminary results 5. Summary and Conclusions

3 . Observational Critical QCD Hot condensate of isoscalar particles critical sigmas is formed in A + A collisions freezing out at the immediate neighbourhood of the QCD critical point (µ c, T c ). Critical opalescence of QCD matter Strong power-laws in transverse momentum correlation functions of critical sigmas Power-law exponents determined through universality class: φ p 2(p )/3 p = 2,3,.. (Ising 3 D) critical isoscalar condensate with monofractal geometry in transverse momentum space

4 Dipions (π +, π ) originating from the decay of critical sigmas with invariant mass close to the two-pion threshold carry the imprints of the critical fractal geometry Intermittency analysis in the transverse momentum space of these dipions determines the exponent φ 2 The geometrical characteristics of the critical isoscalar condensate are simulated through Critical Monte Carlo (CMC) events. N.G. Antoniou et al, Nucl. Phys. A 693, 799 (200); Nucl. Phys. A 76, 49 (2005).

5 2. CMC Generator for critical events The geometrical properties of the critical σ-condensate are incorporated in the Critical Monte Carlo (CMC) event generator: Sigma particles organized in clusters in transverse momentum space with maximal size 0 MeV Each cluster is self-similar characterized by the fractal correlation dimension D F = 2 3 The total number of clusters depends on the size A of the colliding nuclei The technique of truncated Lévy random walks is used for the generation of the sigma momenta within a cluster The self-similar geometry of the sigma clusters is revealed in intermittency analysis calculating the factorial moments in transverse momentum space of the σ-sector

6 However sigmas are not directly observable with ratio 2 3 a pair of opposite charged pions provided: M σ > 2m π decay to The geometrical pattern of the original sigma clusters kinematically distorted in the pion sector! 3 3 F 2 (M) 2 2 =0.68(0) M 2

7 3. Reconstruction of the critical sigma sector (CMC) Form event-by-event dipions with invariant mass in the kinematical window: with ǫ 2m π. 4m 2 π (p π + + p π ) 2 (2m π + ǫ) 2 () Isoscalar content of the events involving reconstructed dipions: ւ ց Real (critical) sigmas Fake sigmas Use small values of ǫ ( O( MeV )) n π + π 2 to enhance the weight of real over fake sigmas Substract (if possible) background effects due to fake sigmas

8 Types of correlations between reconstructed dipions real σ - real σ real σ - fake σ fake σ - fake σ critical sector simulated by simulated by hybrid events mixed and hybrid events To construct hybrid events: Form the ensemble of mixed events (in the sector of charged pions) Construct for each real event containing charged pions, in one to one correspondence, a hybrid event with the same multiplicity by choosing: with probability q a track from the real event and with probability q a track from a mixed event For q = : hybrid events mixed events

9 Use the substraction: F 2 (M, q) = F 2 (M, q) F2 h (M, q) to extract the critical sector of correlated dipions: F 2 (M, q) M 2φ 2(q) Modify q in a window near q = (q [0.5,.0]) to achieve optimum cancellation (maximum φ 2, R 2 ) of the background (at q = q ) 0 F 2 (M,q * ) 2 (q* )=0.66(02) q * = M 2

10 4. Analysis of A + A NA49 data - preliminary results Performing the above analysis in A + A systems (NA49-SPS) at E L = 58 AGeV : A Number of events run period reconstruction window p m π + π [280,320] MeV C m π + π [280,289] MeV Si m π + π [280,282] MeV Pb m π + π [280,280.2] MeV For all systems: (i) approximately the same total number of tracks of charged pions (ii) n π + π.5 within the corresponding reconstruction window

11 <n + ->=.5, q * =0.8 <n + ->=.5, q * =0.7 p+p C+C F 2 (M) 2 =0.24(03), R 2 =0.70, 2 = =0.44(02), R 2 =0.87, 2 =0.86 0, , 0 00 Si+Si <n + ->=.5, q * =.0 Pb+Pb <n + ->=.5, q * =0.7 2 =0.65(03), R 2 =0.93, 2 =0.6 0, =0.62(04), R 2 =0.92, 2 =0.24 0, 0 00 M 2

12 Clear signature of strong, self-similar dipion correlations in the reconstruction window for C + C, Si + Si and Pb + Pb systems φ 2 for Si + Si and Pb + Pb system close to the critical value 2 3 However in the considered reconstruction window Coulomb (π +, π ) and possible sigma (dipion) correlations entangled Use reconstruction window: (2m π + ǫ ) 2 m 2 π + π (2m π + ǫ 2 ) 2 with ǫ 4 MeV (Q 50 MeV ) and 2m π ǫ 2 > ǫ analysis restricted in subspace with suppressed Coulomb correlations

13 Scan for ǫ and use ǫ 2 to achieve n π + π 2 p+p, m in [284,298] MeV, <n >=. 2 =0.27(02), 2 =0.69, R 2 =0.65 C+C, m in [287,289] MeV, <n >=. =0.54(05), 2 =0.78, R 2 =0.6 2 F 2 (M) 0,8 critical QCD prediction q=0.9 0, q=0.8 0, ,6 0,4 C+C Si+Si q=0.7 Si+Si, m in [304,305] MeV, <n >=2 2 =0.63(07), 2 =0.46, R 2 =0.68 Pb+Pb, m in [284,284.] MeV, <n >=3. =0.04(02), 2 =0.63, R 2 = ,2 p+p Pb+Pb 0,0 q=0.7 0 A 0, , M 2

14 Coulomb (π + π ) correlations in the reconstruction windows suppressed! C 2 (Q).3.2. p+p.3.2. C+C Si+Si. Pb+Pb Q (GeV)

15 Behaviour of Si + Si NA49-SPS system similar to CMC Not reproducible through HIJING events for Si + Si at 58 AGeV CMC for Si+Si at 58 AGeV Si+Si at 58 AGeV 20 HIJING for Si+Si at 58 AGeV 5 2 =0.63(07), R2 =0.68 F 2 (M) =0.68(03), R2 = M 2

16 5. Conclusions A method of analysis to look for isoscalar critical fluctuations in A + A data is developed Within this method the disentanglement between Coulomb (π +, π ) correlations and sigma correlations in the reconstructed dipion sector is possible Applying this method to NA49 data a clear signature for the presence of unconventional correlations in the Si + Si and C + C system at 58 AGeV is obtained The size of these correlations, especially for the Si + Si system, measured in terms of the critical index φ 2 is close to the theoretical expectation for an A+A collision system freezing out close to the QCD critical point

17 The errors in the above analysis are relatively large and higher statistics (unfortunately not available at the present stage) are needed for a more accurate calculation of φ 2 Our results support the need for an extented exploration of the QCD phase diagram in the neighbourhood of the freezing-out conditions of the lighter systems at energies close to the maximum SPS energy 58 AGeV