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V. Workshop on Particle Correlations and Femtoscopy

V. Workshop on Particle Correlations and Femtoscopy. η ’. η ’. *. Significant in-medium reduction of the mass of η ’ mesons in √s NN = 200 GeV Au+Au collisions Róbert Vértesi 1 , Tam ás Csörgő 1,2 , János Sziklai 1 1 MTA KFKI RMKI , Budapest Hungary

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V. Workshop on Particle Correlations and Femtoscopy

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  1. V. Workshop on Particle Correlations and Femtoscopy η’ η’ * Significant in-medium reduction of the mass of η’ mesons in √sNN= 200 GeV Au+Au collisions Róbert Vértesi1, Tamás Csörgő1,2, János Sziklai1 1MTA KFKI RMKI, Budapest Hungary 2Department of Physics, Harvard University, Cambridge USA arXiv:0905.2803 [nucl-th] CERN, 10/14/2009 R. Vértesi

  2. Outline • Three-quark model, Chiral symmetry breaking • Restoration of symmetry in a hot, dense medium • Role of the η' mass • Dilepton spectra in Heavy Ion Collisions • η' mass through π± Bose-Einstein correlations • Possible experimental signatures • BEC measurements at RHIC • Dilepton excess found by PHENIX • BEC-calculations for different models • Spectra, λ*(mT),systematics… R. Vértesi

  3. ChiralSymmetryBreaking K0 K+ η π0 π− π+ η’ K− K0 • The three-quarkmodel • SU(3) flavour-symmetry • Spontaneouslybroken => 9 Goldstone bosons • Correspondingtolightmesons • Thereareonly 8! (Meson-octet) • UA(1) chiralsymmetryexplicitlybroken • Distincttopologicalvacuum-states • Tunneling b/w them– quasiparticles (instantons)‏ • 9thboson gainsmass−η' (958 MeV)‏ R. Vértesi

  4. Restoration of theSymmetryin a Hot, DenseMedium K0 K+ π− η π0 π+ K− K0 η’ * • Highenergydensities • Asymptoticfreedomαs → 0 • Nontrivialtopologyvanishes • U(1) no more broken • SU(3) restored Remark: From SSB, Oneexpectsmasslessmesons.However, theflavoursymmetry is inexact. • Massreduction Lowerbound(Gell-Mann – Okubo): Upperbound(S,NS isosinglet eigenstates): Δm is theextra massfrominstantonsina not-so-densemedium R. Vértesi

  5. Signature: ParticleAbundancy • Hagedorn-model • Production of light mesons: TH~160 MeV Hagedorn-temperature • In case of a possible mass drop: • Number of η'swould be small: • With a strongly reduced η' mass: • An enhancement of a factor of 50 at maximum • Increased weight of strange states, rather 3 to 16 • Consequence of the reduced mass:An increased abundancy of η' mesons R. Vértesi

  6. The η' throughPhaseTransition • Hadronization • Reduced-mass η' mesons produced with a decreased mass with an increased abundancy • Decoupling from non-Goldstonic matter • Mean free path for annihilation is large • Long lived • ”Condensate” in the medium • Low-pTη' mesons are unable to get on-shell in the vacuum • Medium acts as a trap for low- pT η's • As medium dissolves, the η's regain their original mass The Return of the prodigal Goldstone boson. J. I. Kapusta, D. Kharzeev, L. D. McLerran Phys.Rev.D53:5028-5033,1996. Hep-ph/9507343 R. Vértesi

  7. Channels of Observation • Leptonic decay • Increased η'/πproportion in the low-pT range • Excess in theℓ+ℓ−spectrum under the ρ mass • η meson (BR=63%)‏ • Enhancement of η production • BEC of charged pions • Sensitive to the sources of the pions • Direct measurement? • Would be convincing, however, poor S/B ratio (π0→γγ) R. Vértesi

  8. source S(x,k)‏ x2 x1 1,2 k1 k2 detector HBT effect (BEC) • Discovered and still used in Astrophysics • Consider two plain vawes: • Bosons: symmetrization needed • Spectra: • Correlation: • Simplified picture: plain wave, no multiparticle-interactions, thermalization etc. R. Vértesi

  9. π±Correlationsand theCore-Halo picture Core: π±, K±, Λ, Σ, … Halo: η’, η, ω, KS • Pions from QM freezeout • Primordial (from phase transition) • Fast decaying resonances • Long-life resonances (ω,η,η',KS0) • Correlation • Intercept • Correlation measurent ↔λ*(mT) ↔ core−halo ratio Core Halo R. Vértesi

  10. SimulatingtheCondensate • Resonance ratios from different models ALCOR, FRITIOF, Kanetaet al., Letessieret. al., Stachelet al., UrQMD. • η' excess: • Restored η' mass: • If , the η'can’t get onshell; a M-B distribution is assumed: • Parameters • From measurementsTFO= 177 MeV, <uT> = 0.48 • Conservative assumption TFOη' =TFOTcond=TFO • Hydrodynamicalmodels α (related to the dimension of expansion) • Looked for: in-medium mass mη'*inverse slope B-1 • Spectra from decays using JETSET R. Vértesi

  11. SPS data and simulation: No signal • Data:NA44 200 GeVS+Pb • Resonances:FRITIOF • Earlier, less refinedmodelling of condensate • No sign of mass reduction NA44S+Pb data mT (GeV) Signal of partial U(A)(1) symmetry restoration from two pion Bose-Einstein correlations T. Csörgő, D. Kharzeev,, S.E. Vance. e-Print: hep-ph/9910436 R. Vértesi

  12. RHIC data • Properties • CentralAu+Au sNN1/2 = 200 GeV • Mid-rapidity|η|<0.1 • π+π+ correlation measurements • λ*(mT)/λ*max(different methods) • Data used in the analysis • PHENIX Sinyukov 50% • STAR Edgeworth expansion(6th order, only even) • Shown for comparison purposes • PHENIX preliminary • STAR Gauss R. Vértesi

  13. Finding the most likely mass • Simulations all over the (B-1, m*) plain • Here: Resonance ratios ofKaneta & Xu, arXiv:nucl-th/0405068 • Mapping the confidence level • Choose best λ*(mT)/λ*maxfit • By this model:mη'*=530 MeV R. Vértesi

  14. Calculations vs. Prediction α = 0 α = -1/2 • Theoretical region:Kapusta et al. arXiv:nucl-th/9507343 • Sigma-contours from model calculations: either in accordance with theory, or slightly below • Different α expansion exponents: systematic uncertainity R. Vértesi

  15. Systematics and Results • Largest uncertainity: models for resonance ratios • Modifying parameters in the widest reasonable range • −1/2≤α≤ +1/2 (1) • 140 MeV ≤ Tcond≤ 220 MeV • 100 MeV ≤TFO≤177 MeV (altogether 17 x 1248 x 1000000 events simulated) • An upper boundary can be determined for the η’ mass: Each and every setup fails when m*η’ > 750 MeV (failure means CL<0.1%) R. Vértesi

  16. Systematics – a Visual Summary Letessieret al. α=0 Tcond=177 MeV TFO=177 MeV Tcond=220 MeV α=-1/2 α=+1/2 Tcond=140 MeV TFO=100 MeV R. Vértesi

  17. Dilepton Excess in CERES • Measurement • Model calculations • Excess in the range b/w theπand ρ mass Invariant e+ e- pair yield measurements compared to hadronic modelyealds e+ e- pair production in Pb - Au collisions at 158-GeV per nucleon. CERES cn. (G. Agakichiev et al.). Jun 2005. 39pp. Eur.Phys.J.C41:475-513,2005. e-Print: nucl-ex/0506002 R. Vértesi

  18. Au+Au invariant e+ e- pair yield Significant excess in PHENIX 200 GeV Au+Au measurements Not present in p+p data – in accordance with hadronic models Excess must be an effect of the hot, dense medium Dilepton Excess in PHENIX • A. Adareet al. (PHENIX cn.)Phys.Lett.B670:313-320,2009. • S. Afanasiev et al.(PHENIX cn.) e-Print: arXiv:0706.3034 R. Vértesi

  19. The η’ Spectrum mT-m [GeV] • Resonance ratios from Kaneta – XuarXiv:nucl-th/0405068 • An enhancement factor of ~24, mostly at low-pT • Breaks mT–scaling at low-pT • Possible explanation of the dilepton excess  needs check! R. Vértesi

  20. Conclusion K0 K+ η π0 π+ K− K0 η’ * π− • Cross-check with dilepton spectrum needed • More λ* data at low pT is needed to reduce systematics • Revitalize interest in chiral symmetry restoration m*η’mη’ < - 200 MeV at the 99.9% confidence levelfrom PHENIX+STAR π+π+correlation data + 6 models R. Vértesi

  21. The End Thank You for your attention backup slides follow… R. Vértesi

  22. mT-scaling central periph. pp E. Shuryak, Prog.Part.Nucl.Phys.53:273-303,2004.  R. Vértesi

  23. η' mass: Fitted values R. Vértesi

  24. η' mass: Acceptability boundaries R. Vértesi

  25. Dilepton excess in details Fig.26: Invariant mass spectrum of e+e- pairs compared to expectations from the model of hadron decays for p+p and for different Au+Au centrality classes. Fig.29: e+e- pair invariant mass distributions in p + p (left) and minimum bias Au+Au collisions (right). The pT ranges are shown in the legend. R. Vértesi

  26. Resonances: Kaneta-Xu vs. RHIC • Statistical chemical freezeout model • Central mid-η 200 GeV Au+Au • Describes PHENIX hadron spektrum well Kaneta & Xu, arXiv:nucl-th/0405068 R. Vértesi

  27. Resonances:Letessier-Rafelski vs. RHIC • Statistical chemical freezeout model • Central mid-η 200 GeV Au+Au J.Letessier J.Rafelski, arXiv:nucl-th/0504028 R. Vértesi

  28. Resonances:ALCOR vs. RHIC • Coalescence-model • η’/ η ratio has to be fixed from other models (Kaneta, here) P. Levai, T.S. Biro, T. Csorgo, J. Zimanyi, hep-ph/0007247 R. Vértesi

  29. Resonances:FRITIOF vs. RHIC • 200 GeV mid-rapidity Au+Au simulation • Note:Does not describe STAR data, neither the unified PHENIX+STAR dataset. For PHENIX data only, it is consistent with mη’=958MeV. B. Anderson et al., Nucl. Phys. B 281 (1987) 289. R. Vértesi

  30. Resonances:Stachel et al. vs. RHIC • Statistical chemical freezeout model • Central mid-η 200 GeV Au+Au J.Stachel et al., arXiv:nucl-th/9907090 R. Vértesi

  31. Resonances:UrQMD vs. RHIC • 200 GeV midrapidity • Au+Au, RHIC √sNN=200 GeV J. P. Sullivan et al., Phys. Rev. Lett. 70 (1993) 3000 R. Vértesi

  32. Rafelski vs. PHENIX R. Vértesi

  33. Rafelski vs. PHENIX & STAR R. Vértesi

  34. Rafelski vs. STAR R. Vértesi

  35. Systematics: Rafelskiα=−1/2 R. Vértesi

  36. Systematics: Rafelskiα=0 R. Vértesi

  37. Systematics: Rafelskiα=+1/2 R. Vértesi

  38. Systematics: Rafelski T’=140 MeV R. Vértesi

  39. Systematics: Rafelski T’=177 MeV R. Vértesi

  40. Systematics: Rafelski T’=220 MeV R. Vértesi

  41. Systematics: Rafelski TFO=100 MeV R. Vértesi

  42. Systematics: Rafelski TFO=177 MeV R. Vértesi

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