1. 1 F.Antinori – Bergen, March`05 – Freeze-out at the SPS Freeze-out conditions in nuclear collisions at the SPS Federico Antinori INFN Padova - Italy

2. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 2Contents Introduction Introduction Particle spectra (kinetic freeze-out) Particle spectra (kinetic freeze-out) Particle rates (chemical freeze-out) Particle rates (chemical freeze-out) Messages from freeze-out Messages from freeze-out (and other “special features” at the SPS...) So, where do we stand? (my take...) So, where do we stand? (my take...) So, what next? (my take...) So, what next? (my take...) Conclusions Conclusions

3. 3 F.Antinori – Bergen, March`05 – Freeze-out at the SPS Freeze-out?

4. 4Freeze-out? to speak of “freeze-out” one needs: to speak of “freeze-out” one needs: a “collective” system a “collective” system with some degree of uniformity in its space-time evolution with some degree of uniformity in its space-time evolution freeze-out  interactions cease freeze-out  interactions cease inelastic interactions  “chemical” freeze-out  particle rates inelastic interactions  “chemical” freeze-out  particle rates elastic interactions  “kinetic” freeze-out  particle spectra elastic interactions  “kinetic” freeze-out  particle spectra can we describe the freeze-out conditions using a relatively small number of parameters? can we describe the freeze-out conditions using a relatively small number of parameters?

5. 5 F.Antinori – Bergen, March`05 – Freeze-out at the SPS Particle spectra

6. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 6 Transverse mass spectra Indeed, transverse mass spectra are close to thermal: Indeed, transverse mass spectra are close to thermal: e.g.: NA57 53% central e.g.: NA57 53% central...but thermal spectra, by themselves, do not imply thermalization or collectivity!...but thermal spectra, by themselves, do not imply thermalization or collectivity!

7. 7 Inverse slope systematics The inverse slope, or “apparent temperature” T increases with the particle mass The inverse slope, or “apparent temperature” T increases with the particle mass does not happen in pp does not happen in pp Collective transverse flow? Collective transverse flow? for a common transverse flow velocity v T, and for, one indeed expects: for a common transverse flow velocity v T, and for m T < 2m, one indeed expects: apparent temperature freeze-out temperature transv. flow velocity [NA44, QM`96]

8. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 8 Blast wave model e.g.: NA49 158 GeV, 10% cent’y (20% for  ); constant velocity profile (n=0) constant velocity profile (n=0) [Schnedermann et al.: Phys. Rev. C48 (1993) 2462] more refined treatment: m T distribution described as combined result of thermal motion (T) and collective transverse expansion (  ) more refined treatment: m T distribution described as combined result of thermal motion (T) and collective transverse expansion (  )

9. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 9 Blast wave vs energy 20 GeV 30 GeV 158 GeV 40 GeV Freeze-out ~ independent of  s T ~ 120 – 130 MeV T ~ 120 – 130 MeV  ~ 0.45  ~ 0.45 NA49 7 – 10 % most central

10. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 10 Blast wave vs centrality NA57 158 GeV Centrality classes: 0  40 to 53 % most central 0  40 to 53 % most central 1  23 to 40 % most central 1  23 to 40 % most central 2  11 to 23 % most central 2  11 to 23 % most central 3  4.5 to 11 % most central 3  4.5 to 11 % most central 4  4.5 % most central 4  4.5 % most central With increasing centrality: With increasing centrality: Transverse flow velocity increases Transverse flow velocity increases Freeze-out temperature decreases Freeze-out temperature decreases  careful when combining different centralities! 1  contours n=1 [NA57: J. Phys. G 30 (2004) 823]

11. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 11 Fit to singly strange particles p  nta  e ... ? n=1 So, what happens: multi-strange particles freeze out earlier? multi-strange particles freeze out earlier? everything flows the same way? everything flows the same way? NA57

12. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 12 Is the  special? m T -m 0 [GeV/c 2 ] 012 200 300 400 T [MeV] Local inverse slope Inverse slope depends on m T range used to fit the spectrum Measured  slopes below blast wave expectation

13. 13 Kinetic freeze-out from HBT HBT + h -, d spectra HBT + h -, d spectra [NA49: Eur. Phys. J. C 2 (1998) 661] [B.Tomášik et al., nucl-th/9907096] Blast wave analysis of spectra Blast wave analysis of spectra 1  contours n=1 central Pb-Pb T ~ 120 MeV T ~ 120 MeV  ~.5  ~.5 } (central Pb-Pb)

14. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 14 v2?v2?v2?v2? some discrepancy between NA45 and NA49 some discrepancy between NA45 and NA49 v 2 not at hydro limit? v 2 not at hydro limit? v 2 well below hydro limit for T f = 120 MeV v 2 well below hydro limit for T f = 120 MeV but NA57: T f increases for peripheral events but NA57: T f increases for peripheral events 1  contours n=1 T f = 146 ± 17 MeV for (11-23)% centrality; NA45 data (13-26)% T f = 146 ± 17 MeV for (11-23)% centrality; NA45 data (13-26)% so hydro limit perhaps not too far... so hydro limit perhaps not too far... [Snellings et al.: nucl-ex/0305001] [NA45: Phys. Rev. Lett. 92 (2004) 032301]

15. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 15 Kinetic freeze-out collective expansion + thermal motion collective expansion + thermal motion ~ independent of  s for central collisions ~ independent of  s for central collisions but pronounced centrality dependence but pronounced centrality dependence some room for deviation from kinetic freeze-out systematics for multi-strange particles, expecially  (early freeze-out?) some room for deviation from kinetic freeze-out systematics for multi-strange particles, expecially  (early freeze-out?) v2 not too far from hydro limit? v2 not too far from hydro limit?

16. 16 F.Antinori – Bergen, March`05 – Freeze-out at the SPS Particle rates

17. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 17 Collective behaviour? The particle composition of the system in Pb-Pb is very different from that of proton – induced collisions! The particle composition of the system in Pb-Pb is very different from that of proton – induced collisions!

18. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 18 Thermal fits if abundances determined by thermodynamical equilibrium  particle ratios described by two parameters: T, µ B if abundances determined by thermodynamical equilibrium  particle ratios described by two parameters: T, µ B two chemical potentials eliminated using strangeness neutrality and isospin conservation two chemical potentials eliminated using strangeness neutrality and isospin conservation + strong resonance decays, account for products of weak decays, finite size and excluded volume corrections,... + strong resonance decays, account for products of weak decays, finite size and excluded volume corrections,... does this work with the data? does this work with the data?

19. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 19 Thermal fits not too bad! not too bad! e.g.: Braun-Munzinger & Stachel @ top SPS high degree of thermal equilibration even for rare, multi-strange particles high degree of thermal equilibration even for rare, multi-strange particles

20. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 20 particle species mix indeed essentially described by two parameters particle species mix indeed essentially described by two parameters remarkable! remarkable! but let’s have a closer look... but let’s have a closer look...

21. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 21 ssss 4π yield ratios sometimes preferred for thermal fits 4π yield ratios sometimes preferred for thermal fits to be safe in case strangeness ends up too far away in rapidity from where originally produced to be safe in case strangeness ends up too far away in rapidity from where originally produced use one set of (T, µ B ) for full rapidity... use one set of (T, µ B ) for full rapidity... in this case  s ~ 0.7 - 0.8 must be introduced in this case  s ~ 0.7 - 0.8 must be introduced strangeness undersaturation factor: strangeness undersaturation factor: for each particle, a factor  s N(s+s) e.g.: [Becattini et al.: hep-ph/0310049]

22. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 22 qqqq see e.g.: [Becattini et al.: hep-ph/0310049]  q controls overall abundance of light q, q  q controls overall abundance of light q, q w.r.t. previous, additional factor  q B for baryons w.r.t. previous, additional factor  q B for baryons  2 /dof comes very close to one  2 /dof comes very close to one (but with an additional parameter...) same at RHIC; see : [Rafelski & Letessier: hep-ph/0309030] 158 A GeV/c Pb-Pb: 158 A GeV/c Pb-Pb:  q = 1.6 (fixed to best)  s = 0.929 ± 0.027 pentaquark (if ) production (if statistical) would be particularly sensitive to need for  q ! pentaquark (if ) production (if statistical) would be particularly sensitive to need for  q ! additional  q 2 factor for Θ + w.r.t. other models additional  q 2 factor for Θ + w.r.t. other models e.g.: [Letessier et al.: hep-ph/0310188, Becattini et al.: hep-ph/0310049] E

23. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 23Resonances? e.g.: Λ(1520) deviates from sistematics (~ 1/2) [Markert: J. Phys. G 28 (2002) 1753] e.g.: Λ(1520) deviates from sistematics (~ 1/2) [Markert: J. Phys. G 28 (2002) 1753]  rescattering of decay prod’s? regeneration of resonances also possible? regeneration of resonances also possible?  chemical composition changes after chemical freeze-out... ? actually, how is this accounted for in thermal models? actually, how is this accounted for in thermal models? Fit to NA49 data hep-ph/0310049 [Becattini et al.: hep-ph/0310049]

24. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 24 T systematics we don’t seem to be able to get a system of hadrons with a temperature beyond T max ~ 170 MeV we don’t seem to be able to get a system of hadrons with a temperature beyond T max ~ 170 MeV sounds like Hagedorn... sounds like Hagedorn... filled: AA open: elementary [Satz: Nucl.Phys. A715 (2003) 3c]

25. 25 T vs µ B systematics the extracted freeze-out points at SPS (and RHIC) lay very close to the predicted QGP phase boundary the extracted freeze-out points at SPS (and RHIC) lay very close to the predicted QGP phase boundary

26. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 26 Freeze-out vs centrality? how does the (T, µ B ) point move with centrality? how does the (T, µ B ) point move with centrality? that would be an interesting analysis! that would be an interesting analysis!

27. 27 Canonical vs Grand Canonical Energy penalty to create a strange particle: Energy penalty to create a strange particle: Canonical: Canonical: computed taking into account also energy to create companion to ensure conservation of strangeness Grand Canonical limit: Grand Canonical limit: just due to creation of particle itself. The rest of the system acts as a reservoir and “picks up the slack” removal of canonical suppression in nucleus-nucleus removal of canonical suppression in nucleus-nucleus increases with strangeness increases with strangeness ~ observed enhancements ~ observed enhancements detailed centrality dependence not reproduced (but very crude modelling...) detailed centrality dependence not reproduced (but very crude modelling...) [Hamieh et al.: Phys. Lett. B486 (2000) 61]

28. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 28 Does this explain the observed enhancement pattern? a system in eq., if it is large enough, is in GC eq., but being large in itself is not a sufficient condition for being GC! a system in eq., if it is large enough, is in GC eq., but being large in itself is not a sufficient condition for being GC! if AA colls. were just a superposition of pp, they would have to be treated canonically all the same! if AA colls. were just a superposition of pp, they would have to be treated canonically all the same! the system must also know it is large... the system must also know it is large... it must know that an Ω + generated here can be compensated by, say, an Ω - on the other side of the fireball! it must know that an Ω + generated here can be compensated by, say, an Ω - on the other side of the fireball! what counts is the correlation volume what counts is the correlation volume “Canonical Suppression is removed!” “Canonical Suppression is removed!” an observation, not an explanation an observation, not an explanation

29. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 29 Hadronic transport Hadronic transport codes: Hadronic transport codes: do reasonably well on singly strange particles do reasonably well on singly strange particles but fail to reproduce the production of multi-strange particles at SPS and RHIC but fail to reproduce the production of multi-strange particles at SPS and RHIC see for instance: see for instance: [Soff et al.: Phys. Lett. B471 (1999) 89], [Soff et al.: Phys. Lett. B471 (1999) 89], [C.Greiner: nucl-th/0208080 and references there], [C.Greiner: nucl-th/0208080 and references there], [STAR: nucl-ex/0307024], [STAR: nucl-ex/0307024], [Huovinen & Kapusta: nucl-th/0310051] [Huovinen & Kapusta: nucl-th/0310051] they get closer if: they get closer if: masses are reduced towards chiral values masses are reduced towards chiral values or string tension is enhanced with respect to ee/pp/pA enhanced contribution from inelastic scattering during expansion enhanced contribution from inelastic scattering during expansion Activity is still ongoing: Activity is still ongoing: e.g.: [Capella: nucl-th/0303045; Subrata Pal et al.: nucl-th/0106074] e.g.: [Capella: nucl-th/0303045; Subrata Pal et al.: nucl-th/0106074] hadronic models are getting more and more exotic... hadronic models are getting more and more exotic... [Huovinen & Kapusta: nucl-th/0310051]

30. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 30 Freeze-out messages From particle spectra: From particle spectra: collective behaviour collective behaviour collective transverse flow collective transverse flow elliptic flow elliptic flow From particle rates: From particle rates: collective behaviour collective behaviour strangeness conserved over large volume strangeness conserved over large volume chemical composition ~ as expected for chemical equilibrium chemical composition ~ as expected for chemical equilibrium even for rare multi-strange particles (order-of-magnitude enhancement!) even for rare multi-strange particles (order-of-magnitude enhancement!) “historic” QGP signature “historic” QGP signature not reproduced by hadronic transport not reproduced by hadronic transport

31. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 31 Peripheral More “special features” of HIC @ SPS J/  suppression: the other “historic” QGP signature J/  suppression: the other “historic” QGP signature enhancement of intermediate-mass dileptons enhancement of intermediate-mass dileptons enhancement of low- mass dileptons enhancement of low- mass dileptons NA50

32. 32 RHIC: disappearance of the away- side jet in central collisions RHIC: disappearance of the away- side jet in central collisions SPS? SPS? qualitatively: similar pattern qualitatively: similar pattern quantitatively, within these errors: quantitatively, within these errors: consistent with acoplanarity broadening consistent with acoplanarity broadening no evidence for suppression of away- side yield no evidence for suppression of away- side yieldAway-side? NA45 peripheral NA45 central widthyield

33. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 33 R AA at the SPS? Original WA98 result for   Original WA98 result for   [WA98: EPJC 23 (2002) 225] no pp data: used compiled reference no pp data: used compiled reference New analysis by D.d’Enterria: [QM`04 and nucl-ex/0403055] New analysis by D.d’Enterria: [QM`04 and nucl-ex/0403055] used different pp reference, including more data samples  used different pp reference, including more data samples 

34. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 34 R AA from WA98 with new reference for 3 centralities: R AA from WA98 with new reference for 3 centralities: suppression in central collisions at SPS? suppression in central collisions at SPS? yellow band: Cronin and shadowing, but no quenching yellow band: Cronin and shadowing, but no quenching [Vitev & Gyulassy: Phys. Rev. Lett. 89 (2002) 252301]

35. 35 F.Antinori – Bergen, March`05 – Freeze-out at the SPS My own take on all this... - where do we stand? - what next?

36. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 36 Where do we stand? SPS: SPS: first pieces of evidence for deconfinement first pieces of evidence for deconfinement hyperon enhancements hyperon enhancements J/  suppression J/  suppression large deviation from pp behaviour in dilepton spectra large deviation from pp behaviour in dilepton spectra what does this mean? what does this mean? RHIC: RHIC: new impressive pieces of evidence new impressive pieces of evidence strong collectivity (v 2 @ hydro limit) strong collectivity (v 2 @ hydro limit) jet quenching jet quenching indications of “recombination” phenomenology indications of “recombination” phenomenology no evidence RHIC matter different from SPS matter no evidence RHIC matter different from SPS matter

37. 37 “what next”: i) investigate onset SPS and RHIC: SPS and RHIC: evidence for a collective, strong interacting, system evidence for a collective, strong interacting, system signatures of deconfinement signatures of deconfinement AGS: AGS: also signs of collective behaviour also signs of collective behaviour but no evidence of deconfinement but no evidence of deconfinement (of course absence of evidence  evidence of absence!) hints for interesting behaviour at low SPS E: hints for interesting behaviour at low SPS E:

38. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 38 a) confirm NA49 results a) confirm NA49 results (independent confirmation is a must in our business!) further SPS running? further SPS running? FAIR? FAIR? FT-RHIC? FT-RHIC? b) correlate excitation of strangeness with that of other QGP observables b) correlate excitation of strangeness with that of other QGP observables fluctuations? fluctuations? dileptons? dileptons? J/  ? J/  ?...... easier said than done!  a very tall order for FAIR!

39. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 39 “what next”: ii) probe the medium what are the properties of the system created in the collision? what are the properties of the system created in the collision?  study medium with high energy probes parton energy loss parton energy loss in-medium fragmentation in-medium fragmentation  high  s frontier: RHIC, LHC! my favourite observable: heavy flavour! my favourite observable: heavy flavour!

40. 40 Heavy Flavours c, b produced in early stages of collision, then conserved (neglecting annihilation) c, b produced in early stages of collision, then conserved (neglecting annihilation)  ideal probes of bulk, strongly interacting phase energy loss? energy loss? thermal production? thermal production? no extra production at hadronization no extra production at hadronization  ideal probes of fragmentation independent string fragmentation vs recombination independent string fragmentation vs recombination QUARK-GLUON PLASMA AND PRODUCTION OF LEPTONS, PHOTONS AND PSIONS IN HADRONIC COLLISIONS E.Shuryak, Yadernaya Fizika 28 (1978) 403

41. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 41 Heavy flavour energy loss? Energy loss for heavy flavours is expected to be reduced: i)Casimir factor light hadrons originate predominantly from gluon jets, heavy flavoured hadrons originate from heavy quark jets light hadrons originate predominantly from gluon jets, heavy flavoured hadrons originate from heavy quark jets C R is 4/3 for quarks, 3 for gluons C R is 4/3 for quarks, 3 for gluons ii)dead-cone effect gluon radiation expected to be suppressed for  < M Q /E Q gluon radiation expected to be suppressed for  < M Q /E Q [Dokshitzer & Karzeev, Phys. Lett. B519 (2001) 199] [Armesto et al., Phys. Rev. D69 (2004) 114003] Casimir coupling factor transport coefficient of the medium average energy loss distance travelled in the medium  R.Baier et al., Nucl. Phys. B483 (1997) 291 (“BDMPS”)

42. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 42 e.g.: D 0  K -  + in ALICE expected performance expected performance S/B ≈ 10 % S/B ≈ 10 % S/  (S+B) ≈ 40 (1 month Pb-Pb running) S/  (S+B) ≈ 40 (1 month Pb-Pb running) statistical. systematic. p T - differential  similar performance in pp (wider primary vertex spread) (wider primary vertex spread)

43. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 43 R AA (D 0 ) in ALICE Low p T (< 6–7 GeV/c) Nuclear shadowing ‘High’ p T (6–15 GeV/c) expected performance (1 month Pb-Pb, 9 months p-p) expected performance (1 month Pb-Pb, 9 months p-p)  such measurements allow to study medium properties!

44. F.Antinori – Bergen, March`05 – Freeze-out at the SPS 44Conclusions Freeze out is interesting! Freeze out is interesting! collective system, strong expansion, ~ chemical equilibrium collective system, strong expansion, ~ chemical equilibrium SPS: SPS: indications of partonic behaviour: indications of partonic behaviour: hyperon enhancements hyperon enhancements J/  suppression J/  suppression threshold behaviour at low energy SPS limit? threshold behaviour at low energy SPS limit? RHIC: further evidence of partonic behaviour: RHIC: further evidence of partonic behaviour: parton energy loss parton energy loss indication for kinetic parton recombination indication for kinetic parton recombination Next steps: Next steps: investigate onset (ambitious new programme!) investigate onset (ambitious new programme!) probe medium (my bet: heavy flavour will be a fundamental tool) probe medium (my bet: heavy flavour will be a fundamental tool)