Pion Interferometry and RHIC Physics STAR John G. Cramer Department of Physics University of Washington Seattle, Washington, USA Invited Talk presented at IX Mexican Workshop on Particles and Fields Physics.
Download ReportTranscript Pion Interferometry and RHIC Physics STAR John G. Cramer Department of Physics University of Washington Seattle, Washington, USA Invited Talk presented at IX Mexican Workshop on Particles and Fields Physics.
Pion Interferometry and RHIC Physics STAR 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 Part 1 About RHIC The Relativistic Heavy Ion Collider and STAR Solenoidal Tracker At RHIC at BNL Brookhaven National Laboratory STAR November 19, 2003 2 John G. Cramer Brookhaven/RHIC/STAR Overview Systems: Au + Au p p CM Energies: 130 GeV/A 200 GeV/A Tandem Van de Graaff AGS 1st Collisions: 06/13/2000 Location: Brookhaven National Laboratory, Long Island, NY STAR Yellow Ring Blue Ring RHIC Booster Ring November 19, 2003 3 John G. Cramer 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. STAR November 19, 2003 4 John G. Cramer The STAR Detector y1 24 sectors x 5692 rf pads x 350 t bins = 47,812,800 pixels Time Projection Chamber 2m FTPCs ZDC ZDC Vertex Position Scintillators (TOF) Endcap EMC 4m Trigger Barrel (TOF) Barrel EMC Magnet B= 0.5 T Silicon Vertex Tracker RICH STAR November 19, 2003 5 John G. Cramer Central Au +Au Collision at sNN = 130 GeV Run: 1186017, Event: 32, central colors ~ momentum: low - - - high STAR November 19, 2003 6 John G. Cramer Part 2 RHIC Physics Expectations STAR November 19, 2003 7 John G. Cramer A Metaphor for RHIC Physics Understanding STAR November 19, 2003 8 John G. Cramer 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 pT pions: There is evidence for strong “quenching” of high momentum pions. 3. 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 the RHIC HBT Puzzle. STAR November 19, 2003 9 John G. Cramer 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 … STAR November 19, 2003 10 John G. Cramer Part 3 The Hanbury-Brown Twiss Effect and Bose-Einstein Interferometry STAR November 19, 2003 11 John G. Cramer A Happy Coincidence of Scales For the Hanbury-Brown Twiss Effect to work, we must have ab/lL 1, where a = size of object, b = separation of detectors l = wavelength of correlated particles L = object-detector distance Stars: a = 2 Rsun = 1.5 x 109 m17 L = 10 light years = -7 10 m l = 500 nm = 5 x 10 m Therefore, need b = lL/a = 33 m (OK!) Pions: a = 10 fm L=1m 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! STAR November 19, 2003 12 John G. Cramer The Hanbury-Brown-Twiss Effect Coherent interference between incoherent sources! 1 X S(x,p)=S(x)S(p) Source y 2 For non-interacting identical bosons: The “bump” results from the Bose-Einsteinpstatistics of identical pions (J =0 ). Width of the bump in the ith momentum direction is proportional to 1/Ri. STAR November 19, 2003 13 John G. Cramer Bertsch-Pratt Momentum Coordinates C(qout , qside , qlong ) 2 2 2 2 2 2 2 1 l exp( -R out qout - Rside qside - R long qlong - 2R ol qout qlong ) 1 K (P P ) T 2 T1 T2 Q QT QL p1 p2 QS p1 November 19, 2003 p2 x beam direction beam direction (long) STAR QO QT (out, side) 14 John G. Cramer A Bose-Einstein Correlation “Bump” This 3D histogram is STAR data that has been corrected for Coulomb repulsion of identical p p pairs and is a projection slice near qlong=0 . The central “bump” results from Bose-Einstein pstatistics of identical pions (J =0-). STAR November 19, 2003 15 John G. Cramer STAR HBT Matrix (circa Nov. 2000) Goal: reconstruct complete picture with full systematics p+ p- + - 0 p p ++ p+ 0 p+ f 0 Sergei's HBT matrix Year 1 Year 1 ?? Year 2 p Y1 p Y1 ? Y2 Analysis In progress From the beginning - study correlations of nonidentical particles and resonance production STAR November 19, 2003 16 “traditional” HBT axis John G. Cramer STAR HBT Matrix (circa 2003) p+ p- + - 0 p p ++ p+ 0 p+ f - Analysis in progress 0 Sergei's HBT matrix published p Y1 Y1 ? submitted Not shown: Y2 3p Correlations (accepted PRL) asHBT Phase space density Correlations with Cascades dAu, pp Cascades STAR November 19, 2003 17 p “traditional” HBT axis John G. Cramer Part 4 The RHIC HBT Puzzle STAR November 19, 2003 18 John G. Cramer Pre-RHIC HBT Predictions “Naïve” picture (no space-momentum correlations): Rout2 = Rside2+(bpairt)2 Rside Rout One step further: Hydro calculation of Rischke & Gyulassy expects Rout/Rside ~ 2>4 @ kt = 350 MeV. Looking for a “soft spot” Small Rout/Rside only for TQGP=Tf (unphysical)). STAR November 19, 2003 19 John G. Cramer 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 STAR November 19, 2003 20 John G. Cramer 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 dN/dt CYM & LGT PCM & clust. hadronization NFD NFD & hadronic TM string & hadronic TM STAR PCM & hadronic TM time November 19, 2003 21 John G. Cramer HBT at 200 GeV centrality λ • HBT radii increase with increasing centrality 0.6 • HBT radii decrease with kT (flow) 0.4 0.2 6 6 4 4 6 1.2 4 1 0.8 0.2 0.3 0.4 0.5 STAR 0.2 0.3 0.4 0.5 <kT> GeV/c November 19, 2003 22 John G. Cramer RO / RS RL (fm) STAR PRELIMINARY RS (fm) RO (fm) • RO / RS ~ 1 (short emission time) problem persists HBT at 200 GeV centrality λ • HBT radii increase with increasing centrality 0.6 • HBT radii decrease with kT (flow) 0.4 • Modified Sinyukov fit <tfo>central ≈ 9 fm/c <tfo>peripheral ≈ 7 fm/c Tfo = 90MeV/c (spectra) 6 6 4 4 6 1.2 4 1 0.8 0.2 0.3 0.4 0.5 STAR 0.2 0.3 0.4 0.5 <kT> GeV/c November 19, 2003 23 John G. Cramer RO / RS M. Herrmann and G.F. Bertsch, Phys. Rev. C51 (1995) 328 RL (fm) RL t fo T K 2 mT / T mT K1 mT / T STAR PRELIMINARY RS (fm) Longitudinal radius 0.2 RO (fm) • RO / RS ~ 1 (short emission time) problem persists 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. STAR November 19, 2003 24 John G. Cramer 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! STAR November 19, 2003 25 John G. Cramer Part 5 Pion Phase Space Density and Entropy STAR November 19, 2003 26 John G. Cramer 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 p3x3 = h3. The source-averaged phase space density is f(p)∫[f(p,x)]2 d3x / ∫f(p,x) d3x, 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. STAR November 19, 2003 27 John G. Cramer Entropy: Calculation & Expectations Entropy – The pion entropy per particle Sp/Np and the total pion entropy at midrapidity dSp/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. A quark-gluon plasma has a Entropy is conserved largeduring number of degrees of hydrodynamic freedom. It should generate a expansion and freerelatively large Thus, entropy streaming. thedensity, up to 12 to 16 times than that entropy of thelarger system of aafter hadronic gas. should freeze-out be close to the initial At RHIC,and if ashould QGP phase entropy grows with centrality provide a critical we would expect the entropy toearlygrow constraint on the strongly increasing stagewith processes of thecentrality and system. participant number. hep-ph/0212302 nucl-th/0104023 Can Entropy provide the QGP “Smoking Gun”?? STAR November 19, 2003 28 John G. Cramer Pion Phase Space Density at Midrapidity The source-averaged phase space density f(mT) is the dimensionless number of pions per 6-dimensional phase space cell h3, as averaged over the source. At midrapidity f(mT) is given by the expression: 3 2 λ(c π ) 1 1 d N f (m T ) E π 2 π m T dm T dy R S R O R L λ Average phase space density STAR Jacobian Momentum Spectrum to make it a Lorentz scalar November 19, 2003 29 HBT “momentum Pion volume” Vp Purity Correction John G. Cramer RHIC Collisions as Functions of Centrality At RHIC we can classify collision events by impact parameter, based on charged particle production. Frequency of Charged Particles produced in RHIC Au+Au Collisions 50-80% 30-50% 20-30% 10-20% 5-10% 0-5% of sTotal Participants Binary Collisions STAR November 19, 2003 30 John G. Cramer Corrected HBT Momentum Volume Vp /l½ 50-80% 2000 Centrality 1500 40-50% Peripheral GeV3 1000 700 106 Vp 500 30-40% Fits assuming: Vp l-½=A0 mT3a (Sinyukov) 20-30% 10-20% 5-10% 0-5% 300 Central 200 150 0.05 0.1 0.15 0.2 mT - mp (GeV) STAR November 19, 2003 31 0.25 0.3 Vp λ (c π )3 λ R SR O R L John G. Cramer Global Fit to Pion Momentum Spectrum 1000 500 100 d2N 2 mTdmTdy 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: d2N/mTdmTdy=A/[Exp(E/T) –1] and (2) Assuming that A and T have a quadratic dependence on the number of participants Np: 50 A(p) = A0+A1Np+A2Np2 T(p) = T0+T1Np+T2Np2 A0 A1 A2 T0 T1 T2 STAR Value 31.1292 21.9724 -0.019353 0.199336 -9.23515E-06 2.10545E-07 10 Error 14.5507 0.749688 0.003116 0.002373 2.4E-05 6.99E-08 November 19, 2003 5 0.1 0.2 0.3 mT 32 0.4 0.5 0.6 m John G. Cramer Interpolated Pion Phase Space Density f at S½ = 130 GeV HBT points with interpolated spectra 0.4 NA49 f 0.3 0.2 } Note failure of “universal” PSD between CERN and RHIC. Central 0.1 Peripheral 0.1 STAR November 19, 2003 0.2 mT m 33 0.3 0.4 John G. Cramer Fits to Interpolated Pion Phase Space Density HBT points using interpolated spectra fitted with Blue-Shifted Bose Einstein function 0.5 Central fp 0.2 0.1 0.05 Warning: PSD in the region measured contributes only about 60% to the average entropy per particle. 0.05 STAR 0.1 November 19, 2003 0.15 mT m GeV 34 Peripheral 0.2 0.25 John G. Cramer Converting Phase Space Density to Entropy per Particle (1) Starting from quantum statistical mechanics, we define: f f ( x , p); dS6 - f Log ( f ) ( f 1) Log ( f 1) - f Log ( f ) f 12 f 2 - 16 f 3 965 f 4 ... +0.2% An estimate of the average pion entropy per 3particle S/N can be obtained O(f) O(f )over the local phase space O(f4) from a 6-dimensional space-momentum integral density f(x,p): 0.1% dS6(Series)/dS6 dp 3dx 3dS ( p , x ) 6 - S N1.000 3 3 dp dx f ( p, x ) - dp 3dx 3[- f Log ( f ) f 12 f 2 - 16 f 3 965 f 4 - - dp 3dx 3 f To perform the space integrals, we assume that f(x,p) = f(p) g(x), 3 2 2 2 2 2 2 where g(x) = 2 Exp[-x /2Rx -y /2Ry -z /2Rz ], i.e., that the source has -0.1%shape based on HBT analysis of the system. Further, we make the a Gaussian Sinyukov-inspired -a assumption that the three radii have a momentum dependence proportional to mT . Then the space can be performed analytically. O(f2integrals ) This gives the numerator3 and-3adenominator integrands of the above expression factors-0.2% of RxRyRz = Reff mT . (For reference, a~½) f STAR November 19, 2003 35 John G. Cramer Converting Phase Space Density to Entropy per Particle (2) The entropy per particle S/N then reduces to a momentum integral of the form: dp dx dS 6 ( p, x ) - S N 3 3 dp dx f ( p, x ) 3 3 (6-D) - 3 - dp mT -3a [- f Log f f 1 2 3 - 0 dpT pT mT 1-3a 5- Log ( 8 ) 2 dp mT -3a f 2 0 dpT pT mT 3 f 3 5 24 2 f 4 ] (3-D) f (8) [- f Log f 12 f 5- Log f 2 -9 4 1-3a 2 - 9 43 f 3 245 2 f 4 ] f We obtain a from the momentum dependence of Vpl-1/2 and perform the momentum integrals numerically using momentum-dependent fits to f -1/2 or fits to Vpl and the spectra. STAR November 19, 2003 36 John G. Cramer (1-D) Entropy per Pion from Two Fit Methods 4.6 Peripheral 4.4 4 Green = BSBE2: ~ bT Blue = BSBE3: Odd 7th order Polynomial in bT S N 4.2 Black = Combined fits to spectrum and Vp/l1/2 Red = BSBE1: Const 3.8 Central 3.6 50 STAR 100 November 19, 2003 150 200 Np participants 37 250 300 350 John G. Cramer Thermal Bose-Einstein Entropy per Particle The thermal estimate of the p entropy per particle can be obtained by integrating a Bose-Einstein distribution over 3D momentum: S/N 0 mT pT dpT [( f BE 1) Ln( f BE 1) - f BE Ln( f BE )] 0 0.2 0.4 0.6 0.8 1. 1.2 1.4 1.6 1.8 2. mT pT dp f BE 10 mp/mp 0. 7.37481 5.13504 4.46843 4.16727 4.00256 3.90175 3.83522 3.78887 3.75521 3.72997 0.3 5.86225 4.33169 3.89106 3.70431 3.61107 3.56032 3.53137 3.51456 3.50489 3.49958 8 0.6 4.30277 3.45065 3.23476 3.16747 3.15191 3.15728 3.17146 3.18916 3.20786 3.22638 0.9 2.43181 2.25166 2.28837 2.36967 2.45851 2.54375 2.62195 2.69244 2.75553 2.8119 mp = 0 6 4 2 mp = mp 0 STAR 1 Exp[( mT - mp ) / T ] - 1 SN T/mp where f BE 0.5 1 Note that the thermal-model entropy per particle usually decreases with increasing temperature T and chemical potential mp. November 19, 2003 38 1.5 Tm 2 2.5 John G. Cramer 3 Entropy per Particle S/N with Thermal Estimates 4.6 4.4 Peripheral BPB T 90 MeV Solid line and points show S/N from spectrum and Vp/l1/2 fits. 4.2 S N T 120 MeV For T=110 MeV, S/N implies a pion chemical potential of mp=44.4 MeV. 4 Dashed line indicates systematic error in extracting Vp from HBT. T 200 MeV 3.8 3.6 Central Landau Limit: m 0 Dot-dash line shows S/N from BDBE2 fits to f 3.4 50 STAR 100 November 19, 2003 150 200 N p participants 39 250 300 John G. Cramer 350 Total Pion Entropy dSp/dy 2500 Dashed line indicates systematic error in extracting Vp from HBT. 2000 dS dy 1500 P&P Why is dSp/dy linear with Np?? Solid line is a linear fit through (0,0) with slope = 6.58 entropy units per participant Dot-dash line indicates dS/dy from BSBEx fits to interpolated <f>. 1000 P&P 500 Snuc Entropy content of nucleons + antinucleons 50 STAR 100 150 200 250 300 Np November 19, 2003 40 John G. Cramer 350 Initial Entropy Density: ~(dSp/dy)/Overlap Area 45 dS dy Np2 3 40 35 30 Initial collision overlap area is roughly 2/3 proportional to Np Initial collision entropy is roughly proportional to freeze-out dSp/dy. Therefore, (dSp/dy)/Np2/3 should be proportional to initial entropy density, a QGP signal. Solid envelope = Systematic errors in Np Data indicates that the initial entropy density does grow with centrality, but not very rapidly. Our QGP “smoking gun” seems to be inhaling the smoke! 25 20 0 STAR 50 100 November 19, 2003 150 200 Np participants 41 250 300 John G. Cramer 350 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 Snn=17 GeV. 2. The pion entropy per particle Sp/Np is very low, implying a significant pion chemical potential (mp~44 MeV) at freeze out. 3. 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?) 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 quarkgluon plasma. STAR 42 John G. Cramer November 19, 2003 Overall Conclusions 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! STAR November 19, 2003 43 John G. Cramer The End STAR November 19, 2003 44 John G. Cramer