HBT Dan Magestro, The Ohio State University Overview of HBT interferometry Overview of HBT interferometry The SPS & RHIC HBT program The SPS & RHIC HBT program Recent “standard” HBT results Recent “standard” HBT results The RHIC HBT puzzle The RHIC HBT puzzle New directions:  dependence, pp vs. AuAu, non-Id,  HBT New directions:  dependence, pp vs. AuAu, non-Id,  HBT : A (mostly) experimental overview

Quark Matter Dan Magestro, Ohio State University q out q side q long Hanbury Brown-Twiss interferometry R side R long R out x1x1 x2x2 p1p1 p2p2 Two-particle interferometry: p-space separation  space-time separation Two-particle interferometry: p-space separation  space-time separation HBT: Quantum interference between identical particles HBT: Quantum interference between identical particles q (GeV/c) C (q) 1 2 Final-state effects (Coulomb, strong) also can cause correlations, need to be accounted for Final-state effects (Coulomb, strong) also can cause correlations, need to be accounted for Gaussian model (3-d):

Quark Matter Dan Magestro, Ohio State University The HBT program at SPS and RHIC Technique: Study interferometry as differentially as possible Technique: Study interferometry as differentially as possible RHIC: Fertile ground for correlations studies beam energy onset effects, transition phenomena transverse momentum (k T ) dynamics, collective expansion particle species differences in emission collision system origins of correlations, phase space azimuthal angle spatial anisotropies, constrain system evolution HBT in HI collisions: Explore space-time evolution of system HBT in HI collisions: Explore space-time evolution of system Geometry: spatial distribution of emission points Geometry: spatial distribution of emission points Dynamics: hot & dense early stages reflected in freeze-out pattern Dynamics: hot & dense early stages reflected in freeze-out pattern Lifetime: sensitive to nature of phase transition Lifetime: sensitive to nature of phase transition

Quark Matter Dan Magestro, Ohio State University  HBT excitation function STAR, PRL 87 (2001)

Quark Matter Dan Magestro, Ohio State University The k T (m T ) dependence x-p correlations arise mostly due to collective expansion x-p correlations arise mostly due to collective expansion Radial flow pushes higher-p T particles more at surface Radial flow pushes higher-p T particles more at surface Kolb & Heinz, QGP3 (nucl-th/ ) Analytical expressions Analytical expressions System lifetime (Sinyukov) System lifetime (Sinyukov) Transverse flow velocity, system size Transverse flow velocity, system size expansion duration transverse rapidity

Quark Matter Dan Magestro, Ohio State University Little difference from SPS to RHIC Little difference from SPS to RHIC Consistent lifetimes:  f ~ 8-10 fm/c Consistent lifetimes:  f ~ 8-10 fm/c CERES, Nucl.Phys. A 714 (2003) 124 k T (GeV/c) NA49, Phys.Lett. B 557 (2003) 157 m T scaling ~ holds up to 1 GeV at SPS m T scaling ~ holds up to 1 GeV at SPS

Quark Matter Dan Magestro, Ohio State University HBT at √s = 200 GeV PHENIX  -HBT: k T, centrality dependence at 200 GeV (nucl-ex/ ) PHENIX  -HBT: k T, centrality dependence at 200 GeV (nucl-ex/ ) New Coulomb treatment causes ~ 10-15% change in R out /R side New Coulomb treatment causes ~ 10-15% change in R out /R side STAR  -HBT: k T, centrality and  dependence at 200 GeV (later) (nucl-ex/ ) STAR  -HBT: k T, centrality and  dependence at 200 GeV (later) (nucl-ex/ ) Sufficient statistics for triple- differential analysis! Sufficient statistics for triple- differential analysis!

Quark Matter Dan Magestro, Ohio State University A highlight from this week Burt Holzman, PHOBOS

Quark Matter Dan Magestro, Ohio State University The RHIC HBT Puzzle - 1 Hydrodynamics at RHIC Hydrodynamics at RHIC  Can describe soft p T spectra and v 2 consistently, for several particle species Fast thermalization in partonic phase (~½ fm/c), lives for ~15 fm/c Fast thermalization in partonic phase (~½ fm/c), lives for ~15 fm/c  Underpredicts R side and its k T dependence  Overpredicts R out and R long by factor ~2 Kolb & Heinz, QGP3 (nucl-th/ ) Hydro doesn’t work. Why is this a puzzle? Hydro doesn’t work. Why is this a puzzle? Expanding fireball, undergoing phase transition, should at least cause R out > R side Expanding fireball, undergoing phase transition, should at least cause R out > R side R side R out STAR PHENIX hydro only hydro+hadronic rescatt Soff, Bass Dumitru Hadronic rescattering phase makes it worse

Quark Matter Dan Magestro, Ohio State University The RHIC HBT Puzzle Default initial conditions (fit p T & v 2 ) Kolb & Heinz, QGP3 (nucl-th/ ) √s = 130 GeVSTAR PHENIX k T (GeV/c) 3. Thermalize faster, or initialize Hydro with non-zero flow 2. Freeze-out directly at hadronization Conflicts with fits to particle spectra Conflicts with fits to particle spectra Can HBT puzzle be resolved in Hydro? 4. Hydro + partial chemical equilibrium Hirano and Tsuda, PRC 66 (2002) Chemical potentials maintain proper abundances through hadronic evolution Chemical potentials maintain proper abundances through hadronic evolution Smaller R long, but fails R out, R side Smaller R long, but fails R out, R side R out (fm) R side (fm) R long (fm)

Quark Matter Dan Magestro, Ohio State University The RHIC HBT Puzzle Parton cascade with opacity Molnar and Gyulassy, nucl-th/ Pion freeze-out distribution sensitive to transport opacity  Pion freeze-out distribution sensitive to transport opacity  √s = 130 GeVSTAR PHENIX k T (GeV/c) 6. Positive x o -t correlation ?! Lin, Ko and Pal, PRL 89 (2002) Alternative approaches  R out (fm) R side (fm) R long (fm)  = 7.73  = 3.01  = 0.60 Lin, Ko and Pal, PRL 89 (2002)

Quark Matter Dan Magestro, Ohio State University The RHIC HBT Puzzle - 4 Blast-wave parametrization Retiere and Lisa, nucl-th/ Blast-wave parametrization Retiere and Lisa, nucl-th/ Longitudinal boost invariance Longitudinal boost invariance Relative particle abundances not fixed Relative particle abundances not fixed Constant parameters at freeze-out Constant parameters at freeze-out √s = 130 GeVSTAR PHENIX k T (GeV/c) Buda-Lund Hydro parameterization Csorgo et al, nucl-th/ Buda-Lund Hydro parameterization Csorgo et al, nucl-th/ Not boost invariant (Hubble flow) Not boost invariant (Hubble flow) Freeze-out smeared in temperature Freeze-out smeared in temperature Hinting at the solution R out (fm) R side (fm) R long (fm) Retiere, Lisa Csorgo et al TfTfTfTf 104  3 MeV ffff 8.9  0.3 fm/c ToToToTo 214  7 MeV ffff 6.0  0.2 fm/c

Quark Matter Dan Magestro, Ohio State University Azimuthally sensitive  HBT HBT(  ): probe spatial anisotropy at freeze-out Wiedemann, PRC 57 (1998) 266 HBT(  ): probe spatial anisotropy at freeze-out Wiedemann, PRC 57 (1998) 266 Freeze-out shape probes nature & timescale of system evolution Freeze-out shape probes nature & timescale of system evolution How much (if any) initial spatial deformation survives system expansion? How much (if any) initial spatial deformation survives system expansion? Initial geometry → aniosotropies in pressure gradients   Preferential in-plane expansion → decreases spatial anisotropy  Freeze-out source shape via HBT → measure of pressure, expansion time (model-dependent) late rescatteringhydrodynamic expansion time x beam into screen R side 2 reaction plane q out q side q long   = 0°  = 90° R side (large) R side (small)

Quark Matter Dan Magestro, Ohio State University HBT(  ): Centrality & k T dependence STAR Collaboration, nucl-ex/ Au+Au, √s = 200 GeV

Quark Matter Dan Magestro, Ohio State University Fourier coefficients of HBT(  ) oscillations 0 th -order FC: centrality & k T dependence mirrors  -integrated analyses; quantitatively consistent 0 th -order FC: centrality & k T dependence mirrors  -integrated analyses; quantitatively consistent Relative amplitudes increase from central to peripheral collisions Relative amplitudes increase from central to peripheral collisions meansrelative amplitudes STAR Collaboration, nucl-ex/ Freeze-out eccentricity can be estimated from relative amplitudes Blast-wave: rel. amplitudes sensitive to spatial anisotropy, depend weakly on collective flow Retiere and Lisa, nucl-th/ Freeze-out eccentricity can be estimated from relative amplitudes Blast-wave: rel. amplitudes sensitive to spatial anisotropy, depend weakly on collective flow Retiere and Lisa, nucl-th/ no temporal component

Quark Matter Dan Magestro, Ohio State University Fourier coefficients of HBT(  ) oscillations RxRx RyRy  initial =  final STAR Collaboration, nucl-ex/ Out-of-plane sources at freeze-out Out-of-plane sources at freeze-out Pressure and/or expansion time was not sufficient to quench initial shape Pressure and/or expansion time was not sufficient to quench initial shape From v 2 we know... From v 2 we know... Strong in-plane flow → significant pressure build-up in system Strong in-plane flow → significant pressure build-up in system  Short expansion time plays dominant role in out-of-plane freeze-out source shapes Evolution of eccentricity → consistent with  ~ 9 fm from R long Sinyukov fit Evolution of eccentricity → consistent with  ~ 9 fm from R long Sinyukov fit

Quark Matter Dan Magestro, Ohio State University Universal pion freeze-out Use HBT radii to estimate freeze-out volume V f Use HBT radii to estimate freeze-out volume V f VfVf NN CERES, PRL 90 (2003) Fold  -  and  -N cross sections with experimentally-measured dN/dy’s Fold  -  and  -N cross sections with experimentally-measured dN/dy’s Mean free path can be estimated from these two relations: Mean free path can be estimated from these two relations: CERES proposed a simple ansatz to investigate if critical mean free path for pions f drives freeze-out CERES proposed a simple ansatz to investigate if critical mean free path for pions f drives freeze-out Does this work for lighter systems? Does this work for lighter systems?

Quark Matter Dan Magestro, Ohio State University HBT in p+p collisions at RHIC RHIC: HBT for 3 very different systems at same c.m. energy & with same detector RHIC: HBT for 3 very different systems at same c.m. energy & with same detector k T dependence of HBT radii presumably arises in different ways k T dependence of HBT radii presumably arises in different ways p+p Multistring fragmentation Au+Au Collective expansion transverse plane T. Gutierrez for STAR Coll, poster R out R side R long p+p

Quark Matter Dan Magestro, Ohio State University p+p → d+Au → Au+Au All three systems exhibit similar k T dependence (?!) All three systems exhibit similar k T dependence (?!) Systematic study underway to assess “Gaussian-ness” of correlation Systematic study underway to assess “Gaussian-ness” of correlation T. Gutierrez for STAR Coll, poster R out (fm) R side (fm) R long (fm) R out / R out (pp) R side / R side (pp) R long / R long (pp) preliminary

Quark Matter Dan Magestro, Ohio State University Same universal freeze-out in p+p, d+Au ? VfVf NN CERES, PRL 90 (2003) V f (fm 3 ) d+Au p+p √s=200 GeV 0 N  (fm 2 ) f ~ 1 fm seems to hold for light systems as well (!) f ~ 1 fm seems to hold for light systems as well (!) Why are p+p, d+Au and Au+Au so similar? Why are p+p, d+Au and Au+Au so similar? Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+Au Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+Au dN/dy’s taken from power-law fits to STAR p T spectra (nucl-ex/ ) dN/dy’s taken from power-law fits to STAR p T spectra (nucl-ex/ )

Quark Matter Dan Magestro, Ohio State University Non-identical particle correlations Study emission asymmetries with final-state interactions Study emission asymmetries with final-state interactions Strong radial flow induces species-dependent x-p correlations Strong radial flow induces species-dependent x-p correlations Case 1 Particle emitted closer to center is slower Case 2 Particle emitted closer to center is faster Effective interaction time larger Effective interaction time larger Stronger correlation Stronger correlation Effective interaction time shorter Effective interaction time shorter Weaker correlation Weaker correlation The two cases can be discriminated The two cases can be discriminated Two correlation functions: “lighter particle faster”, “lighter particle slower” Two correlation functions: “lighter particle faster”, “lighter particle slower” Compare correlation strength of two CF’s Compare correlation strength of two CF’s

Quark Matter Dan Magestro, Ohio State University Non-identical particle correlations “pion faster” shows stronger correlation “pion faster” shows stronger correlation  pions on average emitted nearer to source center Arises naturally in collective expansion picture Arises naturally in collective expansion picture Similar studies are underway for many particle combinations Similar studies are underway for many particle combinations Exotic correlations like  -  can yield information about nature of  flow Exotic correlations like  -  can yield information about nature of  flow C(pion faster) / C(pion slower)  K pion faster PRELIMINARY pion slower A. Kisiel for STAR Blast-wave picture pions protons low  high  Au+Au, √s = 200 GeV

Quark Matter Dan Magestro, Ohio State University HBT of direct photons Photon interferometry in heavy ion collisions Photon interferometry in heavy ion collisions Probes initial state, not final-state interactions Srivastava and Kapusta; Timmerman et al; Peressounko PRC 67 (2003) Probes initial state, not final-state interactions Srivastava and Kapusta; Timmerman et al; Peressounko PRC 67 (2003) A major challenge experimentally! A major challenge experimentally! Low relative direct photon yield Low relative direct photon yield Many sources of small-Q inv pairs: photon conversions,  0 HBT, mis-id  ’s, resonance decays, etc. Many sources of small-Q inv pairs: photon conversions,  0 HBT, mis-id  ’s, resonance decays, etc. WA98: First  -HBT in R.H.I.C. WA98: First  -HBT in R.H.I.C. R inv quantitatively similar to  HBT in same k T region R inv quantitatively similar to  HBT in same k T region → Soft photons arise in late stages of collision → Soft photons arise in late stages of collision WA98 Collaboration, nucl-ex/ < k T < 0.2 GeV/c 0.2 < k T < 0.3 GeV/c  0 peak WA98 Collaboration, nucl-ex/ Direct photon yield can be accessed with Direct photon yield can be accessed with

Quark Matter Dan Magestro, Ohio State UniversityConclusions Identical-meson HBT interferometry Identical-meson HBT interferometry HBT is the observable that doesn’t fit into dynamic picture at low p t HBT is the observable that doesn’t fit into dynamic picture at low p t p+p, d+Au and Au+Au exhibit similar k T dependence, similar freeze-out pion mean free path p+p, d+Au and Au+Au exhibit similar k T dependence, similar freeze-out pion mean free path Azumithally sensitive HBT Azumithally sensitive HBT Evidence for out-of-plane extended sources at freeze-out Evidence for out-of-plane extended sources at freeze-out Short-lived system “remembers” its initial spatial anisotropy Short-lived system “remembers” its initial spatial anisotropy Non-identical particle correlations Non-identical particle correlations Lighter particles emitted closer to center Lighter particles emitted closer to center Direct photon interferometry Direct photon interferometry Similar R inv for  - and  -HBT; access to low-p T direct photon yield Similar R inv for  - and  -HBT; access to low-p T direct photon yield

Quark Matter Dan Magestro, Ohio State University “HBT brings us from enlightenment to tragedy, and back to enlightenment, on a time scale of four years.” Reinhard Stock The HBT puzzle is three years old.  2004 is looking promising!

Quark Matter Dan Magestro, Ohio State University

Quark Matter Dan Magestro, Ohio State University BACK-UPS

Quark Matter Dan Magestro, Ohio State University Recent “standard” HBT results - SPS NA44: High m T  - and p-HBT (nucl-ex/ ) NA44: High m T  - and p-HBT (nucl-ex/ )

Quark Matter Dan Magestro, Ohio State University Recent “standard” HBT results - SPS NA49: Kaon HBT (Phys.Lett. B 557 (2003) 157) NA49: Kaon HBT (Phys.Lett. B 557 (2003) 157) Less influence from resonances & feeddown Less influence from resonances & feeddown New results shown this week New results shown this week 20, 30, 40, 80, 158 AGeV (!) 20, 30, 40, 80, 158 AGeV (!) T = 120  12 MeV →  f ~ 9.5  1 fm,  T ~ 0.55

Quark Matter Dan Magestro, Ohio State University A highlight from this week preliminary 0-30% PHENIX Preliminary Mike Heffner, PHENIXSelemon Bekele, STAR

Quark Matter Dan Magestro, Ohio State University Refined Coulomb treatment Final-state interactions (Coulomb, strong) influence correlation signal Final-state interactions (Coulomb, strong) influence correlation signal Traditionally, all pairs in CF corrected for Coulomb Traditionally, all pairs in CF corrected for Coulomb This over-corrects the CF → increases width, decreases radii This over-corrects the CF → increases width, decreases radii CERES: Apply Coulomb correction only to pairs participating in B-E (Nucl. Phys. A 714 (2003) 124) CERES: Apply Coulomb correction only to pairs participating in B-E (Nucl. Phys. A 714 (2003) 124) First proposed in: Bowler PLB 270 (1991) 69 fraction of non-participating pairs Adopted by in recent papers by STAR, PHENIX STAR Coll, nucl-ex/ ; PHENIX Coll, nucl-ex/ Adopted by in recent papers by STAR, PHENIX STAR Coll, nucl-ex/ ; PHENIX Coll, nucl-ex/ PHENIX Coll, nucl-ex/ Coulomb-corrected uncorrected

Quark Matter Dan Magestro, Ohio State University Collision timescale Evolution time (fm/c) Hydrodynamical model Blast-wave fit R long Sinyukov fit cc  eq HBT(  ) Buda-Lund

Quark Matter Dan Magestro, Ohio State University HBT(  ) predictions from hydrodynamics Hydro: Freeze-out shape sensitive to lifetime, initial conditions Hydro: Freeze-out shape sensitive to lifetime, initial conditions k T dependence probes different regions of space-time source k T dependence probes different regions of space-time source Realistic hydro parameters: Source orientation reflected in HBT(  ) oscillations Realistic hydro parameters: Source orientation reflected in HBT(  ) oscillations Heinz & Kolb, PLB 542 (2002) 216 Hydro calculations initialized with fits to RHIC spectra & v 2

Quark Matter Dan Magestro, Ohio State University HBT(  ) experimental technique 1. Construct correlation functions for discrete bins w.r.t. reaction plane angle 1. Construct correlation functions for discrete bins w.r.t. reaction plane angle 2. Apply HBT formalism to extract R ij 2 vs.  Additional out-side cross-term Additional out-side cross-term reaction plane q out q side q long  3. Oscillations of R ij 2 reflect spatial anisotropies in system Oscillations governed by geometrical symmetries Oscillations governed by geometrical symmetries R side 2 Out-of-plane In-plane  = 0°  = 90° R side (large) R side (small)

Quark Matter Dan Magestro, Ohio State University A simple estimate –  0 from  init and  final “radial flow” P. Kolb, nucl-th/ BW →  X,  F.O. (  X >  Y ) hydro: flow velocity grows ~ t From R L (m T ):  0 ~ 9 fm/c consistent picture Longer or shorter evolution times X inconsistent toy estimate:  0 ~  0 (BW)~ 9 fm/c