2. STAR Pion Interferometry and RHIC Physics John G. Cramer Department of Physics University of Washington Seattle, Washington, USA John G. Cramer Department of Physics University of Washington Seattle, Washington, USA Invited Talk presented at IX Mexican Workshop on Particles and Fields Physics Beyond the Standard Model Universidad de Colima, Colima, Mexico November 19, 2003 Invited Talk presented at IX Mexican Workshop on Particles and Fields Physics Beyond the Standard Model Universidad de Colima, Colima, Mexico November 19, 2003

3. STAR November 19, 2003 John G. Cramer2 Part 1 About RHIC The Relativistic Heavy Ion Collider and STAR Solenoidal Tracker At RHIC at BNL Brookhaven National Laboratory About RHIC The Relativistic Heavy Ion Collider and STAR Solenoidal Tracker At RHIC at BNL Brookhaven National Laboratory

4. STAR November 19, 2003 John G. Cramer3 Systems: Au + Au CM Energies: 130 GeV/A 200 GeV/A 1 st Collisions: 06/13/2000 Location: Brookhaven National Laboratory, Long Island, NY Brookhaven/RHIC/STAR Overview AGS Tandem Van de Graaff RHIC Blue Ring Yellow Ring Booster Ring

5. STAR November 19, 2003 John G. Cramer4 What does RHIC do? RHIC accelerates gold nuclei in two beams to about 100 Gev/nucleon each (i.e., to kinetic energies that are over 100 times their rest mass-energy) and brings these beams into a 200 GeV/nucleon collision. Four experiments, STAR, PHENIX, PHOBOS, and BRAHMS study these collisions. In the year 2000 run, RHIC operated at a collision energy of 130 Gev/nucleon. In 2001-2 it operated at 200 GeV/nucleon.

6. STAR November 19, 2003 John G. Cramer5 ZDC Barrel EMC Endcap EMC Magnet B=  0.5 T ZDC FTPCs Vertex Position Scintillators (TOF) Trigger Barrel (TOF) Time Projection Chamber Silicon Vertex Tracker RICH 2 m 4 m 24 sectors x 5692 r  pads x 350 t bins = 47,812,800 pixels y  1 The STAR Detector

7. STAR November 19, 2003 John G. Cramer6 Run: 1186017, Event: 32, central colors ~ momentum: low - - - high Central Au +Au Collision at  s NN = 130 GeV

8. STAR November 19, 2003 John G. Cramer7 Part 2 RHIC Physics Expectations

9. STAR November 19, 2003 John G. Cramer8 A Metaphor for RHIC Physics Understanding

10. STAR November 19, 2003 John G. Cramer9 Surprises from RHIC 1.The “Hydro Paradox”: Relativistic hydrodynamic calculations work surprisingly well, while cascade string-breaking models have problems. 2.Strong absorption of high p T pions: There is evidence for strong “quenching” of high momentum pions. 3.The “HBT Puzzle”: The ratio of the source radii R out /R side is ~1, while the closest model predicts 1.2, and most models predict 4 or more. R Long is smaller than is consistent with boost invariance. In essence, all models on the market have been falsified by HBT. In the remainder of this talk we will focus on the RHIC HBT Puzzle.

11. STAR November 19, 2003 John G. Cramer10 In Search of the Quark-Gluon Plasma (QGP) A pion gas should have few degrees of freedom. A quark-gluon plasma should have many degrees of freedom and high entropy. Entropy should be roughly conserved during the fireball’s evolution. Hence, look in phase space for evidence of: Large source size, Long emission lifetime, Extended expansion, Large net entropy …

12. STAR November 19, 2003 John G. Cramer11 The Hanbury-Brown Twiss Effect and Bose-Einstein Interferometry Part 3

13. STAR November 19, 2003 John G. Cramer12 A Happy Coincidence of Scales For the Hanbury-Brown Twiss Effect to work, we must have ab/ L  1, where a = size of object, b = separation of detectors = wavelength of correlated particles L = object-detector distance Stars: a = 2 R sun = 1.5 x 10 9 m L = 10 light years = 10 17 m = 500 nm = 5 x 10 -7 m Therefore, need b = L/a = 33 m (OK!) Pions: a = 10 fm L = 1 m = 4.4 fm Therefore, need b = L/a = 44 cm (OK!) So the same technique can be used on stars and on RHIC collision fireballs!

14. STAR November 19, 2003 John G. Cramer13 The Hanbury-Brown-Twiss Effect For non-interacting identical bosons: S(x,p)=S(x)S(p) Coherent interference between incoherent sources! The “bump” results from the Bose-Einstein statistics of identical pions (J  =0  ). Width of the bump in the i th momentum direction is proportional to 1/R i.

15. STAR November 19, 2003 John G. Cramer14 Bertsch-Pratt Momentum Coordinates (long) (out, side) x

16. STAR November 19, 2003 John G. Cramer15 A Bose-Einstein Correlation “Bump” This 3D histogram is STAR data that has been corrected for Coulomb repulsion of identical     pairs and is a projection slice near q long =0. The central “bump” results from Bose-Einstein statistics of identical pions (J  =0  ).

17. STAR November 19, 2003 John G. Cramer16 “traditional” HBT axis STAR HBT Matrix (circa Nov. 2000) Year 1 From the beginning - study correlations of nonidentical particles and resonance production Goal: reconstruct complete picture with full systematics Year 1 ?? Year 2Analysis In progress

18. STAR November 19, 2003 John G. Cramer17 STAR HBT Matrix (circa 2003) “traditional” HBT axis Analysis in progress published 3 Correlations (accepted PRL) asHBT Phase space density Correlations with Cascades dAu, pp Cascades submitted Not shown:

19. STAR November 19, 2003 John G. Cramer18 The RHIC HBT Puzzle Part 4

20. STAR November 19, 2003 John G. Cramer19 Pre-RHIC HBT Predictions “Naïve” picture (no space-momentum correlations):  R out 2 = R side 2 +(  pair  ) 2 One step further:  Hydro calculation of Rischke & Gyulassy expects R out /R side ~ 2- >4 @ k t = 350 MeV.  Looking for a “soft spot”  Small R out /R side only for T QGP =T f (unphysical)). R out R side

21. STAR November 19, 2003 John G. Cramer20 p-space observables well-understood within hydrodynamic framework → hope of understanding early stage x-space observables not well-reproduced correct dynamical signatures with incorrect dynamic evolution? Heinz & Kolb, hep-ph/0204061 The RHIC HBT Puzzle

22. STAR November 19, 2003 John G. Cramer21 time dN/dt p-space observables well-understood within hydrodynamic framework → hope of understanding early stage x-space observables not well-reproduced correct dynamical signatures with incorrect dynamic evolution? Over-large timescales are modeled? emission/freezeout duration (R O /R S ) evolution duration (R L ) Heinz & Kolb, hep-ph/0204061 The RHIC HBT Puzzle

23. STAR November 19, 2003 John G. Cramer22 R O (fm) R L (fm) λ R S (fm) R O / R S GeV/c centrality 6 6 6 4 4 4 1 1.2 0.8 0.2 0.4 0.6 0.2 0.3 0.4 0.5 STAR PRELIMINARY HBT radii increase with increasing centrality HBT radii decrease with k T (flow) R O / R S ~ 1 (short emission time) problem persists HBT at 200 GeV

24. STAR November 19, 2003 John G. Cramer23 HBT radii increase with increasing centrality HBT radii decrease with k T (flow) R O / R S ~ 1 (short emission time) problem persists Longitudinal radius Modified Sinyukov fit M. Herrmann and G.F. Bertsch, Phys. Rev. C51 (1995) 328 central ≈ 9 fm/c peripheral ≈ 7 fm/c T fo = 90MeV/c (spectra) HBT at 200 GeV R O (fm) R L (fm) λ R S (fm) R O / R S GeV/c centrality 6 6 6 4 4 4 1 1.2 0.8 0.2 0.4 0.6 0.2 0.3 0.4 0.5 STAR PRELIMINARY

25. STAR November 19, 2003 John G. Cramer24 HBT Source Radius Excitation Function Source radii from HBT interferometry do not show a significant increase between CERN energies and RHIC energies. However, we would still like to fill the gap with future RHIC runs.

26. STAR November 19, 2003 John G. Cramer25 Conclusions from HBT Analysis 1.The pion-emission source size is smaller than expected, with little growth from a factor of 10 increase in collision energy from the CERN SPS. 2.The time from initial collision to emission is also about the same as observed at the SPS, about 9 fm/c. 3.The emission duration is also very short, at most 1-2 fm/c. 4.These results imply an explosive system with a very hard equation of state. We were expecting to bring the nuclear liquid to a gentle boil. Instead, it is exploding in our face!

27. STAR November 19, 2003 John G. Cramer26 Part 5 Pion Phase Space Density and Entropy Pion Phase Space Density and Entropy

28. STAR November 19, 2003 John G. Cramer27 Phase Space Density: Definition & Expectations Phase Space Density - The phase space density f(p,x) plays a fundamental role in quantum statistical mechanics. The local phase space density is the number of pions occupying the phase space cell at (p,x) with 6-dimensional volume  p 3  x 3 = h 3. The source-averaged phase space density is  f(p)  ∫[f(p,x)] 2 d 3 x / ∫f(p,x) d 3 x, i.e., the local phase space density averaged over the f-weighted source volume. Because of Liouville’s Theorem, for free-streaming particles  f(p)  is a conserved Lorentz scalar. At RHIC, with about the same HBT source size as at the CERN SPS but with more emitted pions, we expect an increase in the pion phase space density over that observed at the SPS.

29. STAR November 19, 2003 John G. Cramer28 hep-ph/0212302 Entropy: Calculation & Expectations Entropy – The pion entropy per particle S  /N  and the total pion entropy at midrapidity dS  /dy can be calculated from  f(p) . The entropy S of a colliding heavy ion system should be produced mainly during the parton phase and should grow only slowly as the system expands and cools. Entropy is conserved during hydrodynamic expansion and free- streaming. Thus, the entropy of the system after freeze-out should be close to the initial entropy and should provide a critical constraint on the early- stage processes of the system. nucl-th/0104023 A quark-gluon plasma has a large number of degrees of freedom. It should generate a relatively large entropy density, up to 12 to 16 times larger than that of a hadronic gas. At RHIC, if a QGP phase grows with centrality we would expect the entropy to grow strongly with increasing centrality and participant number. Can Entropy provide the QGP “Smoking Gun”??

30. STAR November 19, 2003 John G. Cramer29 Pion Phase Space Density at Midrapidity The source-averaged phase space density  f(m T )  is the dimensionless number of pions per 6-dimensional phase space cell h 3, as averaged over the source. At midrapidity  f(m T )  is given by the expression: Momentum Spectrum HBT “momentum volume” V p Pion Purity Correction Jacobian to make it a Lorentz scalar Average phase space density

31. STAR November 19, 2003 John G. Cramer30 RHIC Collisions as Functions of Centrality 50-80%30-50%20-30%10-20%5-10%0-5% At RHIC we can classify collision events by impact parameter, based on charged particle production. Participants Binary Collisions Frequency of Charged Particles produced in RHIC Au+Au Collisions of  Total

32. STAR November 19, 2003 John G. Cramer31 Corrected HBT Momentum Volume V p / ½ STAR Preliminary Central Peripheral m T - m  (GeV) 0-5% 5-10% 10-20% 20-30% 30-40% 40-50% 50-80% Centrality Fits assuming: V p  ½ =A 0 m T 3  (Sinyukov)

33. STAR November 19, 2003 John G. Cramer32 Global Fit to Pion Momentum Spectrum We make a global fit of the uncorrected pion spectrum vs. centrality by: (1)Assuming that the spectrum has the form of an effective- T Bose-Einstein distribution: d 2 N/m T dm T dy=A/[Exp(E/T) –1] and (2)Assuming that A and T have a quadratic dependence on the number of participants N p : A(p) = A 0 +A 1 N p +A 2 N p 2 T(p) = T 0 +T 1 N p +T 2 N p 2 STAR Preliminary

34. STAR November 19, 2003 John G. Cramer33 Interpolated Pion Phase Space Density  f  at S ½ = 130 GeV Central Peripheral NA49 STAR Preliminary Note failure of “universal” PSD between CERN and RHIC. } HBT points with interpolated spectra

35. STAR November 19, 2003 John G. Cramer34 Fits to Interpolated Pion Phase Space Density Central Peripheral STAR Preliminary Warning: PSD in the region measured contributes only about 60% to the average entropy per particle. HBT points using interpolated spectra fitted with Blue-Shifted Bose Einstein function

36. STAR November 19, 2003 John G. Cramer35 Converting Phase Space Density to Entropy per Particle (1) Starting from quantum statistical mechanics, we define: To perform the space integrals, we assume that f(x,p) =  f(p)  g(x), where g(x) =  2 3 Exp[  x 2 /2R x 2  y 2 /2R y 2  z 2 /2R z 2 ], i.e., that the source has a Gaussian shape based on HBT analysis of the system. Further, we make the Sinyukov-inspired assumption that the three radii have a momentum dependence proportional to m T . Then the space integrals can be performed analytically. This gives the numerator and denominator integrands of the above expression factors of R x R y R z = R eff 3 m T   (For reference,  ~½) An estimate of the average pion entropy per particle  S/N  can be obtained from a 6-dimensional space-momentum integral over the local phase space density f(x,p): O(f) O(f 2 ) O(f 3 )O(f 4 ) f dS 6 (Series)/dS 6 +0.2%  0.2%  0.1%  0.1% 

37. STAR November 19, 2003 John G. Cramer36 Converting Phase Space Density to Entropy per Particle (2) The entropy per particle  S/N  then reduces to a momentum integral of the form: We obtain  from the momentum dependence of V p -1/2 and perform the momentum integrals numerically using momentum-dependent fits to  f  or fits to V p -1/2 and the spectra. (6-D) (3-D) (1-D)

38. STAR November 19, 2003 John G. Cramer37 Entropy per Pion from Two Fit Methods Central Peripheral STAR Preliminary Green = BSBE 2 : ~  T Red = BSBE 1 : Const Blue = BSBE 3 : Odd 7 th order Polynomial in  T Black = Combined fits to spectrum and V p / 1/2

39. STAR November 19, 2003 John G. Cramer38   = 0   = m  Thermal Bose-Einstein Entropy per Particle The thermal estimate of the  entropy per particle can be obtained by integrating a Bose-Einstein distribution over 3D momentum:   /m  T/m  Note that the thermal-model entropy per particle usually decreases with increasing temperature T and chemical potential  .

40. STAR November 19, 2003 John G. Cramer39 Entropy per Particle S/N with Thermal Estimates Central Peripheral STAR Preliminary Dashed line indicates systematic error in extracting V p from HBT. Dot-dash line shows S/N from BDBE 2 fits to  f  Solid line and points show S/N from spectrum and V p / 1/2 fits. For T=110 MeV, S/N implies a pion chemical potential of   =44.4 MeV.

41. STAR November 19, 2003 John G. Cramer40 Total Pion Entropy dS  /dy STAR Preliminary Dashed line indicates systematic error in extracting V p from HBT. Dot-dash line indicates dS/dy from BSBE x fits to interpolated. Solid line is a linear fit through (0,0) with slope = 6.58 entropy units per participant Entropy content of nucleons + antinucleons P&P Why is dS  /dy linear with N p ??

42. STAR November 19, 2003 John G. Cramer41 Initial collision overlap area is roughly proportional to N p 2/3 Initial collision entropy is roughly proportional to freeze-out dS  /dy. Therefore, ( dS  /dy)/N p 2/3 should be proportional to initial entropy density, a QGP signal. Initial Entropy Density: ~(dS  /dy)/Overlap Area Data indicates that the initial entropy density does grow with centrality, but not very rapidly. Solid envelope = Systematic errors in N p Our QGP “smoking gun” seems to be inhaling the smoke! STAR Preliminary

43. STAR November 19, 2003 John G. Cramer42 Conclusions from PSD/Entropy Analysis 1.The source-averaged pion phase space density  f  is very high, in the low momentum region roughly 2  that observed at the CERN SPS for Pb+Pb at  S nn =17 GeV. 2.The pion entropy per particle S  /N  is very low, implying a significant pion chemical potential (   ~44 MeV) at freeze out. 3.The total pion entropy at midrapidity dS  /dy grows linearly with initial participant number N p, with a slope of ~6.6 entropy units per participant. (Why?? Is Nature telling us something?) 4.For central collisions at midrapidity, the entropy content of all pions is ~5  greater than that of all nucleons+antinucleons. 5.The initial entropy density increases with centrality, but forms a convex curve that shows no indication of the dramatic increase in entropy density expected with the onset of a quark- gluon plasma.

44. STAR November 19, 2003 John G. Cramer43 The useful theoretical models that has served us so well at the AGS and SPS for heavy ion studies have now been overloaded with a large volume of puzzling new data from HBT analysis at RHIC. Things are a bit up in the air. We need more theoretical help to meet the challenge of understanding what is going on in the RHIC regime. In any case, this is a very exciting time for the STAR experimentalists working at RHIC! Overall Conclusions

45. STAR November 19, 2003 John G. Cramer44 The End