Centrality dependence of hadronization and chemical freeze out conditions at the LHC

Transcription

1 F. Becattini University of Florence Centrality dependence of hadronization and chemical freeze out conditions at the LHC F.B., M. Bleicher, E. Grossi, J. Steinheimer and R. Stock, arxiv: OUTLINE Introduction Centrality dependence The analysis Conclusions ECT* workshop on QCD and the statistical model

2 Dictionary Temperature Hadronization The process of hadron formation < > QCD phase transition LCEP = Latest Chemical Equilibrium Point of a hadron gas If hadronization occurs near or at chemical equilibrium, this is the point where chemical equilibrium ceases because of the collisions in an expanding hadron gas Chemical freeze out The (particle dependent) point where particle abundances freeze Kinetic freeze out The (approximate) point where elastic interactions cease

3 The picture Motivated by the investigations carried out at SPS energy in F.B., M. Bleicher, T. Kollegger, M. Mitrovski, T. Schuster and R. Stock, Phys. Rev. C 85 (2012) and the proton/pi anomaly observed at the LHC (see papers by Pratt, Aichelin, Steinheimer...) Hadronization occurs at (or implies) chemical equilibrium For small systems, no reinteractions For large systems, such as heavy ions, final state collisions may occur because of the large number of particles. Collisions distort the primordial equilibrium distribution

4 Picture's picture

5 Comparing reconstructed LCEP's with lattice QCD in central collisions F.B., M. Bleicher, T. Kollegger, T. Schuster, J. Steinheimer and R. Stock, Phys. Rev. Lett. 111 (2013) Lattice calculations from F. Karsch, J. Phys. G 38, (2011); S. Borsanyi et al., ibidem G. Endrodi, Z. Fodor, S. D. Katz and K. K. Szabo, JHEP 1104, 001 (2011) See also: The critical line of two flavor QCD at finite isospin or baryon densities from imaginary chemical potentials. P. Cea, L. Cosmai, M. D'Elia, A. Papa, F. Sanfilippo, Phys.Rev. D85 (2012)

6 Freeze out and centrality If the picture is correct, we should expect some centrality dependent effect Particle interactions in an expanding, approximately hydrodynamical system, cease when For a sphere, the expansion time is R/3(dR/dt) and if dr/dt ~ mean velocity, the above inequality becomes:

7 Freeze out and centrality (2) Therefore, freeze out occurs when with a density Therefore, the larger the multiplicity, the larger the freeze out radius and the lower the particle density. If one starts with a large number of particles at the hadronization, the system will take more time to decouple, and this will happen at a lower density. If nfo > nhad decoupling is instantaneous, otherwise it is not.

8 Freeze out and centrality (3) U. Heinz, G. Kestin, CPOD 2006 nucl th: Kinetic freeze out (at RHIC energy) DOES vary significantly as a function of centrality, whereas chemical does not. Interpretation: if kinetic decoupling occurs in the expanding hadron gas stage, it MUST depend on the geometry, roughly on Surface/Volume ratio. On the other hand, chemical seems NOT to depend, which is an indication that equilibrium is not achieved through hadronic collisions

9 Centrality dependence of chemistry STAR

10 Centrality dependence of chemistry (2) The rise the LHC difficult to reconcile with previously proposed pictures

11 Programme Estimate the effect of inelastic hadronic rescattering (with UrQMD) Run URQMD (isochronous CF particlization after all cells have fallen below 850 MeV/fm3) in the same centrality bins as those of the ALICE experiment For each particle species, calculate the modification factor = yield after cascade/cf yield Use the modification factors to correct the theoretical statistical model predicted yields

12 URQMD modification factors

13 The results Red: reconstructed LCEP Black: chemical freeze out

14 Example: most central collisions

15 The temperature shift Difference between CF and LCEP (assuming full correlation between the T errors of the two fits)

16 The fit quality

17 We must see the details at some point

18 Conclusions Centrality dependence of chemistry at the LHC provides further evidence Chemical freeze out chemical equilibrium ( hadronization) Corrections to the assumed chemically equilibrated yields improve fit quality and make the temperature more constant than otherwise found LCEP Temperature estimated to be 164(4) MeV at zero B We are looking forward to new and improved calculations of the modification factors to check if we can achieve an even better fit

19 Interpolation Fit with 4th 6th order polynomials, chisquare fit with non diagonal covariance matrix assuming 0.5 positive correlation coefficients. Variation of this coefficient to 0.9 does not change the final result significantly.

20 Major effects of excluding antibaryons: Essential recovery of original freeze-out point Much better fit quality

21 A closer look F.B., M. Bleicher, T. Kollegger, M. Mitrovski, T. Schuster and R. Stock, Phys. Rev. C 85 (2012) Is the agreement between SHM and data an indication of common freeze-out? If yes, we should see a deterioration of fit quality to a simulation including post-hadronization inelastic rescattering PROGRAMME

22 Main effect of hadronic rescattering (afterburner): antibaryon loss

23 Second step: fitting to SHM ( S) - Hydro only using exp. errors

24 Major effects of including afterburning: Lowering the output c.f.o. T by ~ 10 MeV Sizeable worsening of fit quality

25 Third step: fitting to SHM ( S) removing antibaryons Hydro Hydro+UrQMD

26 What does the data say?

27 SPS energy A recently published p yield by NA49 in Pb-Pb at 17.2 GeV turned out to be consistently lower than the predicted by SHM. Predicted: 6.86 (F.B., J. Manninen and M. Gazdzicki, Phys. Rev. C 73 (2006) ) Measured: 4.23±0.35 New fit to Pb-Pb mult's at 17.2 GeV Lower T, lower quality F. B., M. Bleicher, T. Kollegger, M. Mitrovski, T. Schuster and R. Stock Phys. Rev. C 85 (2012)

28 Possible explanation: the effect of post hadronization rescattering Effect of UrQMD afterburning on initial statistical hadronic yields from a hydro code See also S. Bass and A. Dumitr Phys. Rev. C 61 (2000) Residual distribution of a fit to hadronic yields excluding anti baryons: Similar pattern of deviations

29 LHC energy The p ( p)/π yield in PbPb at 2.76 TeV is lower than predicted by the statistical hadronization model by 40% (prediction by A. Andronic et al., J.Phys. G38 (2011) ) Advocated as an effect of post-hadronization rescattering: J. Steinheimer, J. Aichelin and M. Bleicher, Phys. Rev. Lett. 110 (2013) Y. Pan and S. Pratt, Baryon Annihilation in Heavy Ion Collisions arxiv: [nucl th] F. B., M. Bleicher, T. Kollegger, T. Schuster, J. Steinheimer and R. Stock, Hadron Formation in Relativistic Nuclear Collisions and the QCD Phase Diagram,'' arxiv: [nucl th].

30 Where did we start from? F.B., An introduction to the Statistical Hadronization Model, arxiv:

31 How to reconstruct hadronization conditions? Strictly speaking, the latest hadro chemical equilibrium point (LHCEP) Estimating the effect of the afterburning with an analytical calculation (e.g. Pratt) or a Monte-Carlo (UrQMD) Critical line = Hadronization Latest chemical equilibrium point Chemical freeze-out Kinetic freeze-out Corrected fit to ALICE data Higher T, much better quality