Femtoscopy in relativistic heavy-ion collisions by PHENIX

Femtoscopy in relativistic heavy-ion collisions by PHENIX Physics seminar at Ohio State University October 11, 2007 Akitomo Enokizono

Outline • Physics motivations • Introduction of femtoscopy (HBT) analysis • Hadron PID by PHENIX detector • Result-1) Centrality dependence of 3-D HBT radii • Sanity check for femtoscopic analysis scheme • Comparison between different collision energy, species • Result-2) Momentum dependence of 3-D HBT radii • Comparison between different collision energy, species • Comparison between different particles • Result-3) Detailed source structures by imaging analysis • What can we learn from imaged source functions? • Comparison between STAR and PHENIX results • Summary • Future plans of femtoscopic analysis

Physics interest of relativistic heavy-ion collisions From "Future Science at the Relativistic Heavy Ion Collider" @ RHIC II Science Workshops • RHIC experiments and following many theoretical efforts (e.g hydrodynamics model) have been very successful in investigating and describing the QGP state (hard observables) quantitatively: • how hot and dense the matter is • how opaque the matter is against jets • how strongly the matter is coupled • and the matter is considered to be almost perfect fluid (/s<<1). C. Loizides, hep-ph/0608133v2 How fast the extremely hot and dense matter thermalizes and freezes-out, how much the system size grows, what is the nature of the phase transition that occurs at RHIC? Is it different from AGS, SPS energies?

EXCLUDED Kinetic freeze-out  Hadron phase Chemical freeze-out  Mixed Phase (?) v2 scaling for pi/k/p/phi/deuteron (?) order phase transition  Partonic phase Perfect liquid thermalized quark state 1st order? 2nd order? cross-over? PHENIX Au+Au 200GeV PRL 99, 052301 (2007) pre-equilibrium Pre-collision Physics interest of HBT: Space-time of evolution ? Time ? ? ? Space These parameters can be accessed by systematic measurements of HBT for different collision energies/species, particle species.

HBT: Interferometry of two identical particles Quantum statistical (Bose-Einstein) correlation • RobertHanbury Brown & Richard Q. Twiss • Angular diameter of stars from two photon correlation (1950s) • Goldhaber, Goldhaber, Lee, Pais • A radius of nucleon-nucleon collisions (1960s) • Symmetric property of boson wave-function or asymmetric property of fermion wave-function) R.Hanbury Brown (1914-2002) G. Goldhaber (1924-) S. Goldhaber (1923-1965) p1 r1 x1 ΔR r2 x2 p2 where q = p1 - p2

If there is a finite emission duration of particles 3-D HBT (“side-out-long”) parameterization Rside observer Beam axis Rout Rlong Rout Rside Au Au Beam axis Detector FC : Coulomb correction function (iteratively estimated) Rlong= Longitudinal HBT radius Rside= Transverse HBT radius Rout = Transverse HBT radius + particles emission duration  = source chaoticity : coherence, resonance, mis-identification

Systematic study of the system size dependence of HBT radii is a sanity check for the femtoscopic analysis technique. Outward size is also affected by opacity - Need to study HBT size for different particles. A caveat: HBT radii  Geometrical source radii HBT size is the “length of homogeneity” (space-momentum correlation) HBT size decreases as the transverse mass momentum (mT) or collective flow of source increases. Detector ηf=0 B. Tomasik, U. Heinz, nucl-th/9805016 Rside ηf=0.5 kT=400MeV/c opacity ω=0 ω=5 ω=10 Rout

Good pi/K separation p~1.2 GeV/c Hadron PID by PHENIX detector • Charged hadron for PHENIX HBT analyses have been identified by west central arm. • ||<0.35, =/2 • p/p = 0.7% + 1.0%p • t(PbSc) = 500 ps Year Species sNN int.Ldt Ntot 2000 Au+Au 130 1 mb-1 10M 2001/2002 Au+Au 200 24 mb-1 170M 2002/2003 d+Au 200 2.74 nb-1 5.5G 2003/2004 Au+Au 200 241 mb-1 1.5G Au+Au 62 9 mb-1 58M 2004/2005 Cu+Cu 200 3 nb-1 8.6G Cu+Cu 62 0.19 nb-1 0.4G Cu+Cu 22.5 2.7 mb-1 9M FCAL South FCAL North

Momentum dependence Centrality dependence PHENIX Preliminary PHENIX Preliminary Run4 Au+Au 200 GeV (KK) PHENIX Preliminary PHENIX Preliminary PHENIX Preliminary PHENIX Preliminary Run4 Au+Au 200 GeV (KK) PHENIX Preliminary PHENIX Preliminary Measured 3-D correlation functions Run2 Au+Au 200 GeV () PHENIX Au+Au 130GeV Phys. Rev. Lett. 88, 192302 (2002) Run4 Au+Au 62 GeV () Run5 Cu+Cu 62 GeV () Run5 Cu+Cu 200 GeV ()

Centrality (Npart) dependence of HBT radii • All HBT radii show linear increase as the cub-root of the number of participants (Npart1/3). • Spherically symmetric source Rside ~ Rout ~ Rlong. • Rside and Rlong show systematic deviations between 200 GeV and 62.4 GeV data sets, while Rout are almost consistent over the energy range. PHENIX Preliminary 0.2<kT<2.0 GeV/c

Multiplicity dependence of HBT radii • All HBT radii show linear increase as the cube-root of track multiplicity (N1/3). • HBT radii extracted from Au+Au/Cu+Cu collisions at 62-200 GeV are consistent with each other at the same track multiplicity. • Multiplicity is a parameter which determines HBT radii. PHENIX Preliminary 0.2<kT<2.0 GeV/c

Rout is not scaled with dN/dy but Npart for AGS-RHIC energy? Or emission duration is significantly changed from AGS to SPS? Rside and Rlong seem to scale with dN/dy rather than Npart. Energy scan of multiplicity scaling of HBT radii M.A. Lisa, S. Pratt, R. Soltz, U. Wiedemann nucl-ex/0505014 Need detailed study of HBT radii as a function of dNch/dy between AGS-SPS energy region Interesting to see this scaling holds at LHC.

HBT puzzle: Rout/Rside ~ 1 << theoretical prediction Au+Au 62 GeV Cu+Cu 200GeV Au+Au 200 GeV 3D Hydro (PCE) Hirano&Nara, NPA743('04)305 PHENIX Preliminary 0.2<kT<2.0 GeV/c • Rout/Rside ~ 1 from peripheral to central collisions (Instantaneous freeze-out?) • Hydrodynamic models qualitatively predict Rout/Rside differences for different collision systems but fail to predict the absolute value.

mT dependence of HBT radii for all data sets • HBT radii are systematically different between 62 and 200 GeV --> Difference of dNch/dy for different collision energies. • All HBT radii decrease as mT increase --> The transverse and longitudinal expansions. • mT dependence of Rside looks weaker for Cu+Cu than Au+Au --> Npart dependence of transverse flow. PHENIX Preliminary 0-30% centrality

62GeV? 200GeV? mT dependence of Rout/Rside ratio 0-30% centrality PHENIX Preliminary Rout/Rside ratio decreases as a function of mT at 200 GeV but not at 62 GeV? Need further investigations for higher mT region.

Au+Au at 200 GeV (0-30% centrality) K+K+ + K-K- (Run4) Sys.Err. ++ -- (Run2) Sys.Err. Hydro+UrQMD – kaon Hydro+UrQMD – pion (S. Soff, nucl-th/0202240, Tc=160MeV) Result of charged kaon HBT radii PHENIX Preliminary • No significant differences of HBT radii between pion and kaons as a function mT. • Hydrodynamic comparisons hint at small final hadron rescattering effect in Au+Au 200 GeV ? Or perhaps HBT radii are insensitive to the effect.

halo Core Strong FSI (2) FSI (Coulomb repulsion for like-charged particles, strong interaction for protons) significantly disturb measured Bose-Einstein correlations, making it difficult to extract the actual source shape. Imaging analysis can accommodate any type of correlation with known FSI. Detector BEC Coulomb Why source imaging? (1) Traditional HBT analysis is restricted by the assumption of Gaussian source. But, there is no reason to expect the emission source to be Gaussian. It might be more natural to expect the source is a non-Gaussian shape in relativistic heavy-ion collisions due to long-lived resonances, rescattering effects. The Gaussian assumption is not natural. “Core-Halo” model

Restore Image Need to optimize imaging parameters for each C(q) data rmax : Maximum r to be imaged. qscale = /2Δr Imaging analysis scheme D.A. Brown and P. Danielewicz Phys. Rev. C. 64, 014902 (2001) is kernel which can be calculated from BEC and known final state interactions of pairs. is source function which represents the emission probability of pairs at r in the pair CM frame.

1-D charged pion S(r) in Au+Au at 200 GeV PHENIX Au+Au 200GeV Phys. Rev. Lett. 98, 132301 (2007) • The imaged source function deviates from the Gaussian source function at > 15-20 fm. • Where is the non-Gaussian component coming from? • Resonance (->+-0, c~20 fm) effect, life time effect, or hadron re-scattering effect?

Optimization of imaging for STAR and PHENIX PHENIX Au+Au 200GeV Phys. Rev. Lett. 98, 132301 (2007) STAR Au+Au 200GeV Preliminary Michal Bystersky (WPCF2007)

Comparison between STAR and PHENIX results • Optimized STAR and PHENIX results are very similar, but STAR data is close to Gaussian shape? • Need to investigate the discrepancy of C(q) at low-q region.

1-D charged kaon S(r) in Au+Au at 200 GeV PHENIX preliminary PHENIX preliminary Au+Au 200 GeV, 0.3<kT<2.0 GeV/c 0-30% centrality Au+Au 200 GeV, 0.3<kT<2.0 GeV/c 0-30% centrality • The result hints at non-Gaussian structure in kaon emission function. • Systematic errors are still big and we need further investigations by MC.

3-D source imaging results and comparisons with models also give more detailed insights into the non-Gaussian structure. What is the cause of the non-Gaussian structure? M. Csanád, T. Csörgő and M. Nagy, hep-hp/0702032 • The time dependent mean free path naturally creates non-Gaussian tails (Levy type exponential distribution).

Summary • Centrality dependence of 3-D HBT radii • HBT radii linearly increases as a function of (Npart)1/3 or or (multiplicity)1/3 • HBT radii are found to scale well with multiplicity rather than Npart. • A short emission duration (Rout/Rside~1) excludes a naïve assumption of 1st order phase transition, and inconsistent with hydrodynamics results. • Momentum dependence of 3-D HBT radii • Rout/Rside(mT) behaves differently between 62 and 200 GeV. • HBT radii are insensitive to hadron rescattering effect. • Detailed source structure by HBT-imaging analysis • Charged pi/K show non-Gaussian structure at large r region. • Some important information will be investigated at large r (out of usual HBT radii) region. To understand the whole picture of relativistic heavy-ion collisions, we need to fully understand HBT observables!

Future plan of HBT analysis • HBT analyses at PHENIX • 3-D HBT-imaging analysis. • The first result for pions will be published by PEHNIX soon. • Direct photon/pi0 HBT analyses • Space-time information of QGP state • No Coulomb effect • HBT radii with lower energy scan • How does the space-time evolution change around critical point? • HBT analyses at LHC experiments • Charged hadron HBT radii in Pb+Pb at sNN = 5.5 TeV • Does the multiplicity scaling still work at LHC energy? • How does the kT dependence look like? • HBT-imaging analysis as jet tomography • Space-time information of jet fragments in the extreme hot and dense matter. • Heavy flavor HBT • Space-time information of very early stage of relativistic heavy-ion collisions. • But very small HBT- due to the S/N, and decayed particles still carry HBT info?

Thanks!

Extra Slides

Each component (e.g. life time, omega, kinetics. etc) seems to have different magnitude of contribution in the 3-D space. It is hard to figure out the origin of non-Gaussian structure just by looking at 1-D space. 3-D emission source function (Prediction) D.A. Brown, R. Soltz, J. Newby, A. Kisiel nucl-th/07051337

3D Hydro (Hirano) 3D Hydro (Hirano) Scaled to Npart=281 Hydro + URQMD (Soff) Momentum dependence of 3-D HBT radii PHENIX 200GeV (pi+pi+) S. S. Adler et al., Phys. Rev. Lett. 93, 152302 (2004) PHENIX 200GeV (pi-pi-) STAR 200 GeV (pi-pi) Still there is a big difference between data and full hydrodynamics calculations RHIC HBT puzzle! • Dynamical x-p correlation is hard to predict, and a problem is “indirect” and “inconsistent” comparison of fitted HBT radii: • Do ad hoc corrections for FSI (e.g. Coulomb effect). • Fit to correlation in a assumption of Gaussian shape. • Even comparisons between experimental results are done with different Coulomb corrections, Gaussian assumptions, rapidity acceptances…

Hydrodynamics prediction of 1D source function T. Csörgő, R. Vértesi,M. Csanád and M. Nagy The tail by HRC reproduce the experimental non-Gaussian structure very well - Lavy type distribution. The tail strongly depends on PID (particle type) in theMC simulation in which largest for kaons - that have the smallest cross sections.

HBT radii well scale with cubir root of Npart Assuming cylindrical source Vfinal~ Const.×Rside2×Rlong  Npart Source volume at the hadron freeze-out stage is proportional to its initial source volume for entire centrality Collision centrality dependence of HBT radii Fit wit Ri(Npart) = 0.5 fm + a×Npartb a [fm]b χ2/dof Rside : 0.61  0.11 0.32  0.03 3.1/7 Rout : 0.61  0.11 0.33  0.03 5.7/7 Rlong : 0.58  0.11 0.34  0.03 5.8/7

Energy dependence of source size and life time • Transverse source radius at freeze-out stage (Rgeom) is twice more larger than the initial size (= Au R.M.S radius ~ 3.07 fm), • Rgeom and the life time of the source slightly increase with the collision energy, about 2~3 fm from AGS energy and about 1 fm from SPS energy.

Azimuthal HBT analysis J. Newby DNP/JPS fall 2005

BudaLund Fit M. Csanad, T. Csorgo, B. Lorstad and A. Ster, J. Phys. G 30, S1079 (2004)

Hydrodynamics predictions of HBT radii M.A. Lisa, S. Pratt, R. Soltz, U. Wiedemann nucl-ex/0505014

Optimization of imaging for STAR result Optimize imaging for STAR data Remove first 3 bins

Comparison between STAR and PHENIX result

3-D HBT angle-averaged source function In side-out-long parameterization: Rout (PCMS)  γRout (rest frame) γ: Averaged γ boost factor of pair Angle averaged Gaussian S(rinv) for high kT region is enhanced by S(rout) at large r region.

Femtoscopy in relativistic heavy-ion collisions by PHENIX