Pion Interferometry and RHIC Physics

1. Pion InterferometryandRHIC Physics John G. Cramer Department of PhysicsUniversity of WashingtonSeattle, 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

2. Part 1 About RHIC The Relativistic Heavy Ion Collider and STAR Solenoidal Tracker At RHIC at BNL Brookhaven NationalLaboratory John G. Cramer

3. Brookhaven/RHIC/STAR Overview Systems: Au + Au CM Energies: 130 GeV/A 200 GeV/A1st Collisions: 06/13/2000 Location: BrookhavenNationalLaboratory, Long Island,NY TandemVan de Graaff AGS Yellow Ring Blue Ring RHIC Booster Ring John G. Cramer

4. 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. John G. Cramer

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

6. Central Au +Au Collision at sNN = 130 GeV Run: 1186017, Event: 32, central colors ~ momentum: low-- -high John G. Cramer

7. Part 2 RHIC Physics Expectations John G. Cramer

8. A Metaphor for RHIC Physics Understanding John G. Cramer

9. Surprises from RHIC • The “Hydro Paradox”: Relativistic hydrodynamic calculations work surprisingly well, while cascade string-breaking models have problems. • Strong absorption of high pT pions: There is evidence for strong “quenching” of high momentum pions. • The “HBT Puzzle”: The ratio of the source radii Rout/Rside is ~1, while the closest model predicts 1.2, and most models predict 4 or more. RLong 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 theRHIC HBT Puzzle. John G. Cramer

10. 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 … John G. Cramer

11. Part 3 The Hanbury-BrownTwiss Effect andBose-Einstein Interferometry John G. Cramer

12. A Happy Coincidence of Scales For the Hanbury-Brown Twiss Effect to work, we must have ab/lL » 1, wherea = size of object,b = separation of detectorsl = wavelength of correlated particlesL = object-detector distance Stars:a = 2 Rsun = 1.5 x 109 mL = 10 light years = 1017 m l = 500 nm = 5 x 10-7 m Therefore, need b = lL/a = 33 m (OK!) Pions:a = 10 fmL = 1 m l = 4.4 fm Therefore, need b = lL/a = 44 cm (OK!) So the same technique can be used on stars and on RHIC collision fireballs! John G. Cramer

13. The Hanbury-Brown-Twiss Effect Coherent interference between incoherent sources! S(x,p)=S(x)S(p) For non-interacting identical bosons: The “bump” results fromthe Bose-Einstein statistics ofidentical pions (Jp=0-). Width of the bump in theith momentum direction isproportional to 1/Ri. John G. Cramer

14. Bertsch-Pratt Momentum Coordinates x (long) (out, side) John G. Cramer

15. A Bose-Einstein Correlation “Bump” This 3D histogram is STARdata that has been corrected forCoulomb repulsion ofidentical p-p- pairs andis a projection slice nearqlong=0 . The central “bump” resultsfrom Bose-Einstein statisticsof identical pions (Jp=0-). John G. Cramer

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

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

18. Part 4 The RHIC HBT Puzzle John G. Cramer

19. “Naïve” picture (no space-momentum correlations): Rout2 = Rside2+(bpairt)2 One step further: Hydro calculation of Rischke & Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV. Looking for a “soft spot” Small Rout/Rsideonly forTQGP=Tf (unphysical)). Pre-RHIC HBT Predictions Rside Rout John G. Cramer

20. The RHIC HBT Puzzle • 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 John G. Cramer

21. dN/dt time The RHIC HBT Puzzle • 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 (RO/RS) • evolution duration (RL) Heinz & Kolb, hep-ph/0204061 John G. Cramer

22. centrality λ 0.6 0.4 0.2 6 6 RO (fm) RS (fm) 4 4 1.2 6 RL (fm) RO / RS 1 4 0.8 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 <kT> GeV/c HBT at 200 GeV • HBT radii increase with increasing centrality • HBT radii decrease with kT (flow) • RO / RS~ 1 (short emission time) problem persists STAR PRELIMINARY John G. Cramer

23. centrality λ 0.6 0.4 0.2 6 6 RO (fm) RS (fm) 4 4 1.2 6 RL (fm) RO / RS 1 4 0.8 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 <kT> GeV/c HBT at 200 GeV • HBT radii increase with increasing centrality • HBT radii decrease with kT (flow) • RO / RS~ 1 (short emission time) problem persists • Longitudinal radius • Modified Sinyukov fit • M. Herrmann and G.F. Bertsch, Phys. Rev. C51 (1995) 328 • <tfo>central ≈ 9 fm/c • <tfo>peripheral ≈ 7 fm/c • Tfo = 90MeV/c (spectra) STAR PRELIMINARY John G. Cramer

24. 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 liketo fill the gapwith future RHIC runs. John G. Cramer

25. Conclusions from HBT Analysis • The pion-emissionsource size is smaller than expected, with little growth from a factor of 10 increase in collision energy from the CERN SPS. • The time from initial collision to emission is also about the same as observed at the SPS, about 9 fm/c. • The emission duration is also very short, at most 1-2 fm/c. • 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! John G. Cramer

26. Part 5 Pion Phase Space Density and Entropy John G. Cramer

27. 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 Dp3Dx3 = h3. • The source-averaged phase space density is áf(p)ñ º ∫[f(p,x)]2 d3x / ∫f(p,x) d3x, i.e., the local phase space density averaged over thef-weighted source volume. Because of Liouville’s Theorem, for free-streaming particles áf(p)ñ 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. John G. Cramer

28. Entropy: Calculation & Expectations • Entropy – The pion entropy per particle Sp/Np and the total pion entropy at midrapidity dSp/dy can be calculated from áf(p)ñ. 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. 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. 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. hep-ph/0212302 nucl-th/0104023 Can Entropy provide the QGP “Smoking Gun”?? John G. Cramer

29. Pion Phase Space Density at Midrapidity The source-averaged phase space density áf(mT)ñ is the dimensionless number of pions per 6-dimensional phase space cell h3, as averaged over the source. At midrapidity áf(mT)ñ is given by the expression: Average phasespace density HBT “momentumvolume” Vp PionPurityCorrection Momentum Spectrum Jacobianto make ita Lorentzscalar John G. Cramer

30. RHIC Collisions as Functions of Centrality Frequency of Charged Particlesproduced in RHIC Au+Au Collisions At RHIC we can classifycollision events by impact parameter, based on charged particle production. of sTotal Participants Binary Collisions John G. Cramer

31. Corrected HBT Momentum Volume Vp /l½ 50-80% Centrality 40-50% Peripheral 30-40% Fits assuming: Vpl-½=A0 mT3a (Sinyukov) 20-30% 10-20% 5-10% 0-5% Central STAR Preliminary mT - mp (GeV) John G. Cramer

32. Global Fit to Pion Momentum Spectrum • We make a global fit of the uncorrected pion spectrum vs. centrality by: • Assuming that the spectrumhas the form of an effective-TBose-Einstein distribution: • d2N/mTdmTdy=A/[Exp(E/T) –1] • and • Assuming that A and T have aquadratic dependence on thenumber of participants Np:A(p) = A0+A1Np+A2Np2T(p) = T0+T1Np+T2Np2 STAR Preliminary John G. Cramer

33. Interpolated Pion Phase Space Density áfñat S½ = 130 GeV HBT points with interpolated spectra Note failure of “universal” PSDbetween CERN and RHIC. } NA49 Central STAR Preliminary Peripheral John G. Cramer

34. Fits to Interpolated Pion Phase Space Density HBT points using interpolated spectra fittedwith Blue-Shifted Bose Einstein function Central STAR Preliminary Warning: PSD in the region measured contributes only about 60% to the average entropy per particle. Peripheral John G. Cramer

35. Converting Phase Space Density to Entropy per Particle (1) Starting from quantum statistical mechanics, we define: +0.2% An estimate of the average pion entropy per particle áS/Nñ can be obtainedfrom a 6-dimensional space-momentum integral over the local phase spacedensity f(x,p): O(f) O(f3) O(f4) +0.1% dS6(Series)/dS6 1.000 To perform the space integrals, we assume that f(x,p) = áf(p)ñg(x),where g(x) = Ö23 Exp[-x2/2Rx2-y2/2Ry2-z2/2Rz2], i.e., that the source hasa Gaussian shape based on HBT analysis of the system. Further, we make theSinyukov-inspired assumption that the three radii have a momentum dependenceproportional to mT-a. Then the space integrals can be performed analytically.This gives the numerator and denominator integrands of the above expressionfactors of RxRyRz = Reff3mT-3a.(For reference, a~½) -0.1% O(f2) -0.2% f John G. Cramer

36. Converting Phase Space Density to Entropy per Particle (2) The entropy per particle áS/Nñ then reduces to a momentum integralof the form: (6-D) (3-D) (1-D) We obtain a from the momentum dependence of Vpl-1/2 and performthe momentum integrals numerically using momentum-dependent fits to áfñor fits to Vpl-1/2 and the spectra. John G. Cramer

37. Entropy per Pion from Two Fit Methods Peripheral STAR Preliminary Black = Combined fits to spectrum and Vp/l1/2 Red = BSBE1: Const Green = BSBE2:~ bT Blue = BSBE3: Odd 7th order Polynomial in bT Central John G. Cramer

38. Thermal Bose-Einstein Entropy per Particle The thermal estimate of the p entropy per particle can beobtained by integrating a Bose-Einstein distribution over3D momentum: mp/mp T/mp mp= 0 mp= mp Note that the thermal-model entropy per particle usually decreases with increasing temperature T and chemical potential mp. John G. Cramer

39. Entropy per Particle S/N with Thermal Estimates STAR Preliminary Peripheral Solid line and points show S/Nfrom spectrum and Vp/l1/2 fits. For T=110 MeV, S/N impliesa pion chemical potential ofmp=44.4 MeV. Dashed line indicates systematicerror in extracting Vp from HBT. Central Dot-dash line shows S/N from BDBE2 fits to áfñ John G. Cramer

40. Total Pion Entropy dSp/dy STAR Preliminary Dashed line indicates systematicerror in extracting Vp from HBT. P&P Why is dSp/dylinear with Np?? Solid line is a linear fit through (0,0)with slope = 6.58 entropy unitsper participant Dot-dash line indicates dS/dy fromBSBEx fits to interpolated <f>. P&P Entropy content ofnucleons + antinucleons John G. Cramer

41. Initial Entropy Density: ~(dSp/dy)/Overlap Area Initial collision overlap area is roughlyproportional to Np2/3 Initial collision entropy is roughlyproportional to freeze-out dSp/dy. Therefore, (dSp/dy)/Np2/3should be proportionalto initial entropydensity, a QGPsignal. Solid envelope =Systematic errors in Np STAR Preliminary Data indicates that the initialentropy density does grow withcentrality, but not very rapidly. Our QGP “smoking gun” seems to beinhaling the smoke! John G. Cramer

42. Conclusions from PSD/Entropy Analysis • The source-averaged pion phase space density áfñ is very high, in the low momentum region roughly 2´ that observed at the CERN SPS for Pb+Pb at ÖSnn=17 GeV. • The pion entropy per particle Sp/Np is very low, implying a significant pion chemical potential (mp~44 MeV) at freeze out. • The total pion entropy at midrapidity dSp/dy grows linearly with initial participant number Np, with a slope of ~6.6 entropy units per participant. (Why?? Is Nature telling us something?) • For central collisions at midrapidity, the entropy content of all pions is ~5´ greater than that of all nucleons+antinucleons. • 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. John G. Cramer

43. Overall Conclusions The useful theoretical models that has served us so well at the AGSand SPS for heavy ion studies have now been overloaded with a largevolume of puzzlingnew data from HBTanalysis at RHIC. Things are a bitup in the air. We need moretheoretical helpto meet the challengeof understandingwhat is going on inthe RHIC regime. In any case, thisis a very excitingtime for the STARexperimentalistsworking at RHIC! John G. Cramer

44. The End John G. Cramer