1 / 51

Thermal Dileptons + Photons: Baseline Approach

This paper discusses the electromagnetic spectral function and the fate of resonances in heavy-ion reactions. It explores the medium modifications of resonances and their correlation with the QCD phase structure in high-energy collisions.

chandar
Download Presentation

Thermal Dileptons + Photons: Baseline Approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Thermal Dileptons + Photons: Baseline Approach Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA RIKEN/BNL Workshop on “Thermal Radiation” in Heavy-Ion Reactions BNL (Upton, NY), 05.-07.12.12

  2. 1.) Intro: EM Spectral Function + Fate of Resonances Im Pem(M) in Vacuum Im Πem(M,q;mB,T) • Electromagnetic spectral function • -√s < 2 GeV: non-perturbative • -√s > 2 GeV: perturbative (“dual”) • Vector resonances “prototypes” • - representative for bulk hadrons: • neither Goldstone nor heavy flavor • Medium modifications of resonances • - QCD phase structure • - HICs: correlate (mN,T) ↔ spectral shape e+e-→ hadrons √s = M

  3. 1.2 Chiral Restoration in Lattice QCD Tpcc~155MeV [Fodor et al ’10] • compatible with hadron resonance gas (also for thermodynamics!) • chiral restoration in “hadronic phase”? (low-mass dileptons!) • cross-over ↔ smooth EM emission rates across Tpc - - ≈ qq / qq0

  4. Outline 2.) Spectral Function in Medium  Effective Hadronic Theory in Medium  QGP Emission and Lattice QCD  Chiral Restoration 3.) Dilepton Spectra in Heavy-Ion Collisions  Nature of Emission Source from SPS to RHIC  Spectral Shapes and Temperatures  Radial and Elliptic Collectivity 4.) Conclusions

  5. 2.1 Baseline I: r Meson in Hadronic Matter > rB /r0 0 0.1 0.7 2.6 > [Pisarski, Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Steele et al, Post et al, Eletsky et al, Harada et al …] Dr (M,q;mB ,T) = [M 2 - mr2 -Srpp -SrB -SrM ] -1 r-Propagator: B*,a1,K1... r Sp r SrB,rM= Selfenergies: Srpp= N,p,K… Sp Constraints:decays:B,M→ rN, rp, ... ;scattering:pN→rN, gA, … SPS RHIC / LHC

  6. 2.2 Chiral Condensate + r-Meson Broadening -ImPV / s > Sp effective hadronic theory > - Sp • h = mq h|qq|h > 0 contains quark core + pion cloud • = Shcore + Shcloud ~ + • matches spectral medium effects: resonances + pion cloud • resonances + “chiral mixing” drive r-SF toward chiral restoration - - qq / qq0

  7. 2.3 Baseline II: Perturbative + Lattice QGP Rates dRee /dM2 ~ ∫d3q f B(q0;T) ImPem dRee/d4q 1.4Tc (quenched) q=0 • rates smoothly match around Tpc: • - compatible with cross-over • - 3-fold “degeneracy” - [qq→ee] [HTL] [Braaten et al ‘91] [Ding et al ’10] [RR,Wambach et al ’99]

  8. 2.4 Vector Correlator in Thermal Lattice QCD • Euclidean Correlation fct. Lattice (quenched) [Ding et al ‘10] Hadronic Many-Body [RR ‘02] • “Parton-Hadron Duality” of finite-T lattice + in-medium hadronic?

  9. 2.5 Criteria for Chiral Restoration • Vector (r) – Axialvector (a1) degenerate [Weinberg ’67, Das et al ’67, Kapusta+ Shuryak ‘94] pQCD • QCD sum rules: • medium modifications ↔ vanishing of condensates • Degeneracy with thermal lattice-QCD • Approach to perturbative rate (QGP) → Talk by Hohler

  10. Outline 2.) Spectral Function in Medium  Effective Hadronic Theory in Medium  QGP Emission and Lattice QCD  Chiral Restoration 3.) Dilepton Spectra in Heavy-Ion Collisions  Nature of Emission Source from SPS to RHIC  Spectral Shapes and Temperatures  Radial and Elliptic Collectivity 4.) Conclusions

  11. e+ e- γ 3.1 Thermal Dilepton + Photon Emission Rates Im Πem(M,q;mB,T) Im Πem(q0=q;mB,T) • determined by the same spectral function • finite photon rate ↔ divergent dilepton rate for M → 0 • low mass: r-meson dominated ImPem~ [ImDr + ImDw /10 + ImDf /5]

  12. 3.2 SPS I: Dielectrons with CERES/NA45 • Evolve rates over fireball expansion: Excess Spectra Pb-Au(17.3GeV) Pb-Au(8.8GeV) • established large enhancement • consistent with a “r-melting” around Tpc • large effects at lower beam energy: baryons! • M→0: photon point!

  13. 3.3 SPS II: Precision with m+m- at NA60 Acc.-correctedExcess Spectra In-In(17.3GeV) [NA60 ‘09] vs. Theoretical Input Rates r cont. Mmm [GeV] [van Hees+RR ’08] • broadened r spectral function quantitatively confirmed • invariant-mass spectrum directly reflects thermal emission rate! • mass slope reveals emission temperature around Tpcc ~ 150 MeV

  14. 3.4 Low-Mass e+e- Excitation Function at RHIC PHENIX STAR QM12 • tension between PHENIX and STAR (central Au-Au) • non-central Au-Au consistent with “universal” source around Tpc • partition hadronic/QGP depends on EoS → Talks by Wang, Vujanovic, Linnyk

  15. 3.4.2 Hadronic vs. QGP Emission at RHIC (Tc=180MeV) (Tpc=170MeV) • smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield • corroborates prevalent emission source around Tpc

  16. 3.5 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220±25) MeV “moderate” • ~  T √(1+b)/(1-b)  suggests T < 200 MeV • large v2also suggests “later” emission (aka ~Tpc)

  17. 3.5.2 Thermal Photon Spectra + v2 thermal + prim. g (Tc=180MeV) [van Hees,Gale+RR ’11] • M → 0 limit of dilepton rates (continuous across Tc!) • flow blue-shift, e.g. b=0.3: T ~ 220MeV / 1.35 ~ 160 MeV • confirms bulk emission around Tpc • compatible with hydro evolution if bulk-v2 saturates at Tpc [He at al in prep.] → Talks by Skokov, Tuchin, Dusling

  18. 3.6 Elliptic Flow of Dileptons at RHIC • maximum structure due to • late r decays [He et al in prep.] [Chatterjee et al ‘07, Zhuang et al ‘09]

  19. 4.) Conclusions • Low-mass dileptons at SPS+RHIC point at universal source, • avg. emission temperatures T~150MeV ~ Tpcc(slopes, v2) • r-meson smoothly melts into QGP continuum radiation • Mechanisms underlying r-melting (p cloud + resonances) find • counterparts in hadronic S-terms, restoring chiral symmetry • Quantitative studies relating r-SF to chiral order parameters with • QCD and Weinberg-type sum rules ongoing • Need conditions under which medium effects turn off • Future precise characterization of EM emission source at • RHIC, LHC + CBM/NICA/SIS holds rich info on QCD phase • structure (spectral shape + disp. rel., source collectivity + lifetime)

  20. 4.1 How to Turn off Medium Effects • pp collisions: cocktail - seems to work (but: no medium effect) • Peripheral collisions - challenging: dense hadronic phase persists • d-A collisions: forward vs. backward y (formation time effects?) • High(er) pT • - seems to work: NA60 m+m- • Elementary projectiles on cold nuclei • - seems to work: CLASgA → e+e- X • (Gr≈ 220 MeV) full calculation fix density 0.4r0 Fe - Ti

  21. 2.3.2 NA60 Mass Spectra: pt Dependence Mmm [GeV] • rather involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

  22. 3.4.3 Hadronic vs. QGP Photons at RHIC (Tc=180MeV) (Tpc=170MeV) • smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield • corroborates prevalent emission source around Tpc

  23. 3.6 QGP Barometer: Blue Shift vs. Temperature SPS RHIC • QGP-flow driven increase of Teff ~ T + M (bflow)2 at RHIC • high pt: high T wins over high-flow r’s → minimum (opposite to SPS!) • saturates at “true” early temperature T0 (no flow)

  24. 4.1.2 Sensitivity to Spectral Function In-Medium r-Meson Width • avg. Gr(T~150MeV)~370MeVGr (T~Tc) ≈ 600 MeV → mr • driven by (anti-) baryons Mmm [GeV]

  25. 4.1.3 Mass Spectra as Thermometer Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Thermometer [NA60, CERN Courier Nov. 2009] • Overall slope T~150-200MeV (true T, no blue shift!)

  26. 3.2 Spectral Functions + Weinberg Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a1) spectral splitting [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘93] t→(2n+1)p t→(2n)p [ALEPH ’98,OPAL ‘99] rA/s rV/s pQCD pQCD • Updated “fit”: [Hohler+RR ‘12] • r+a1 resonance, excited states (r’+a1’), universal continuum (pQCD!)

  27. 3.2.2 Evaluation of Chiral Sum Rules in Vacuum • pion decay • constants • chiral quark • condensates • vector-axialvector splitting quantitative observable of • spontaneous chiral symmetry breaking • promising starting point to analyze chiral restoration

  28. 2.3 QCD Sum Rules: r and a1 in Vacuum • dispersion relation: [Shifman,Vainshtein+Zakharov ’79] • lhs:hadronic spectral fct. • rhs:operator product expansion • 4-quark + gluon condensate dominant vector axialvector

  29. 3.3 QCD Sum Rules at Finite Temperature [Hatsuda+Lee’91, Asakawa+Ko ’93, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05] rV/s T [GeV] Percentage Deviation • r and r’ melting • compatible with • chiral restoration [Hohler +RR ‘12]

  30. 2.4 Dilepton Thermometer: Slope Parameters Invariant Rate vs. M-Spectra Transverse-Momentum Spectra cont. Tc=160MeV Tc=190MeV r • Low mass: radiation from around T ~ Tpcc ~ 150MeV • Intermediate mass: T ~ 170 MeV and above • Consistent with pT slopes incl. flow: Teff ~ T + M (bflow)2

  31. 4.3.2 Revisit Ingredients Emission Rates Fireball Evolution • multi-strange hadrons at “Tc” • v2bulkfully built up at hadronization • chemical potentials for p, K, … • Hadron - QGP continuity! • conservative estimates… [Turbide et al ’04] [van Hees et al ’11]

  32. 5.1 Thermal Dileptons at LHC • charm comparable, accurate (in-medium) measurement critical • low-mass spectral shape in chiral restoration window

  33. 5.2 Chiral Restoration Window at LHC • low-mass spectral shape in chiral restoration window: • ~60% of thermal low-mass yield in “chiral transition region” • (T=125-180MeV) • enrich with (low-) pt cuts

  34. 4.3 Dimuon pt-Spectra and Slopes: Barometer Effective Slopes Teff • theo. slopes originally too soft • increase fireball acceleration, • e.g. a┴ = 0.085/fm → 0.1/fm • insensitive to Tc=160-190MeV

  35. 3.4.2 Back to Spectral Function • suggests approach to chiral restoration + deconfinement

  36. 4.2 Improved Low-Mass QGP Emission • LO pQCD spectral function: rV(q0,q) = 6∕9 3M2/2p [1+QHTL(q0)] • augment lat-QCD rate with • finite 3-momentum (g rate)

  37. 4.2 Low-Mass e+e- at RHIC: PHENIX vs. STAR • large enhancement not accounted • for by theory • cannot be filled by QGP radiation… • (very) low-mass region • overpredicted… (SPS?!)

  38. 4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: • tFB≈ (6±1) fm/c

  39. p Sp Sp Sp r Sr Sr Sr 3.2 Axialvector in Nucl. Matter: Dynamical a1(1260) p a1 resonance + + . . . = Vacuum: r In Medium: + + . . . [Cabrera,Jido, Roca+RR ’09] • in-medium p + r propagators • broadening of p-r scatt. Amplitude • pion decay constant in medium:

  40. 3.6 Strategies to Test For Chiral Restoration eff. theory for VC + AV spectral functs. Lat-QCD Euclidean correlators vac. data + elem. reacts. (gA→eeX, …) constrain Lagrangian (low T, rN) constrainVC + AV : QCD SR Lat-QCD condensates + c ord. par. EM data in heavy-ion coll. test VC - AV: chiral SRs global analysis of M, pt, v2 Realistic bulk evol. (hydro,…) Agreement with data? Chiral restoration?

  41. 4.1 Quantitative Bulk-Medium Evolution • initial conditions (compact, initial flow?) • EoS: lattice (QGP, Tc~170MeV) + chemically frozen hadronic phase • spectra + elliptic flow: multistrange at Tch ~ 160MeV • p, K, p, L, … at Tfo ~ 110MeV • v2 saturates at Tch, good light-/strange-hadron phenomenology [He et al ’11]

  42. qR qL > > > > - - qL qR 2.1 Chiral Symmetry + QCD Vacuum : flavor + “chiral” (left/right) invariant • “Higgs” Mechanism in Strong Interactions: • qqattraction  condensate fills QCD vacuum! • Spontaneous Chiral Symmetry Breaking - • Profound Consequences: • effective quark mass: • ↔ mass generation! • near-massless Goldstone bosons p0,± • “chiral partners” split: DM ≈ 0.5GeV JP=0±1± 1/2±

  43. 4.4.3 Origin of the Low-Mass Excess in PHENIX? • QGP radiation insufficient: • space-time , lattice QGP rate + • resum. pert. rates too small • must be of long-lived hadronic origin • Disoriented Chiral Condensate (DCC)? • Lumps of self-bound pion liquid? • Challenge: consistency with hadronic data, NA60 spectra! [Bjorken et al ’93, Rajagopal+Wilczek ’93] - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - ptherm + pDCC → e+ e- ↔ M~0.3GeV, small pt [Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]

  44. 2.2 EM Probes at SPS • all calculated with the same e.m. spectral function! • thermal source: Ti≈210MeV, HG-dominated, r-meson melting!

  45. 5.2 Intermediate-Mass Dileptons: Thermometer • use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T ! Thermometer • independent of partition HG vs QGP (dilepton rate continuous/dual) • initial temperature Ti ~ 190-220 MeV at CERN-SPS

  46. 4.7.2 Light Vector Mesons at RHIC + LHC • baryon effects important even at rB,tot= 0 : • sensitive to rBtot= rB + rB (r-N and r-N interactions identical) • w also melts, f more robust ↔ OZI - -

  47. = = 5.3 Intermediate Mass Emission: “Chiral Mixing” [Dey, Eletsky +Ioffe ’90] • low-energy pion interactions fixed by chiral symmetry 0 0 0 0 • mixing parameter • degeneracy with perturbative • spectral fct. down to M~1GeV • physical processes at M≥ 1GeV: • pa1→ e+e- etc. (“4p annihilation”)

  48. 3.2 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=160MeV a┴ =0.1/fm pions: Tch=175MeV a┴ =0.085/fm • modify fireball evolution: • e.g. a┴ = 0.085/fm → 0.1/fm • both large and small Tccompatible • with excess dilepton slopes

  49. 2.3.3 Spectrometer III: Before Acceptance Correction emp. ampl. + “hard” fireball hadr. many-body + fireball schem. broad./drop. + HSD transport chiral virial + hydro • Discrimination power much reduced • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

  50. 4.1 Nuclear Photoproduction: rMeson in Cold Matter g + A → e+e- X • extracted • “in-med” r-width • Gr≈ 220 MeV e+ e- Eg≈1.5-3 GeV g r [CLAS ‘08] • Microscopic Approach: + in-med. r spectral fct. production amplitude full calculation fix density 0.4r0 Fe-Ti r g N [Riek et al ’08, ‘10] M[GeV] • r-broadening reduced at high 3-momentum; need low momentum cut!

More Related