Phenomenology of Dilepton Production in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Compressed Baryonic Matter Workshop 2006 ECT* Trento,

T=1.4T c [Tokyo] Spectral Functions Thermalization  study the phase diagram: (highest) temperature of the matter chiral symmetry restoration (mass generation!) in-medium spectral properties below + above T c Introduction: EM-Probes -- Basic Questions Inevitable consequences of QGP, link to lattice QCD 1.0 T/T c mm ‹qq› - [Bielefeld] Chiral Condensate QCD Phase Diagram

2.) Electromagnetic Emission and Chiral Symmetry  EM Thermal Rates  Axial-/Vector Correlators and Chiral Sum Rules 3.) Medium Effects and Thermal Dileptons  Vector Mesons in Medium: Hadronic Many-Body Theory  Experimental and Theoretical Constraints 4.) Dileptons at SPS  CERES and NA60 Data  Interpretation + Open Issues 5.) Conclusions Outline

2.) EM Emission Rates and Chiral Symmetry E.M. Correlation Function: e + e - γ Im Π em (M,q;  B,T) Im Π em (q 0 =q;  B,T) Radiation Sources: Relevance: Quark-Gluon Plasma: high mass + temp. qq → e + e , … M > 1.5GeV, T >T c Hot + Dense Hadron Gas: M ≤ 1 GeV     → e + e , … T ≤ T c - qqqq _ e+ee+e  e+e-e+e- 

2.2 Chiral Symmetry Breaking and Restoration Splitting of “chiral partners”  - a 1 (1260)  Chiral Symmetry Breaking Axial-/Vector in Vacuum pQCD cont. at T c : Chiral Restoration Im  em ~ [ImD  +ImD  /10+ImD  /5] Low-Mass Dilepton Rate:  -meson dominated! Axialvector Channel:  ±  invariant mass-spectra ~ Im D a1 (M) ?!

2.3 Chiral Sum Rules Energy-weighted moments of difference vector – axialvector: [Weinberg ’67] [Das etal ’67] explicit link: V  A spectral fcts. (models) ↔ order parameters (lattice QCD) extended to finite temperature [Kapusta+ Shuryak ‘93]

> >    B *,a 1,K 1... N, ,K … 3.1 Medium Effects I: Hadronic Many-Body Theory D  (M,q;  B,T) = [M 2 - m  2 –   –   B -   M ] -1  -Propagator: [Chanfray etal, Herrmann etal, RR etal, Weise etal, Post etal, Eletsky etal, Oset etal, …] Constraints: - vacuum decays: B,M→  N,  - scattering data:  N,  A,  N→  N NANA  -ex Nuclei  N =0.8  0 [Urban et al. ’98]   =   =  -Selfenergies: 

3.1.2  (770) Spectral Function in Nuclear Matter In-med  -cloud +   -N → B* resonances Relativist.   -N → B* (low-density approx) In-med  -cloud +  -N → N(1520) Constraints:  N,  A  N →  N PWA constraints from elementary reactions → model agreement! consistent with QCD sum rules N=0N=0 N=0N=0  N =0.5  0 [Urban etal ’98] [Post etal ’02] [Cabrera etal ’02]

[RR+Gale ’99]  -Meson Spectral Functions at SPS  -meson “melts” in hot and dense matter baryon density  B more important than temperature reasonable agreement between models  B /  Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [Eletsky etal ’01] Model Comparison [RR+Wambach ’99]

4.) Dilepton Spectra in Heavy-Ion Collisions entropy (+baryon-number) conservation volume expansion: V FB (  )= (z 0 +v z  )  (R ┴ + 0.5a ┴  2 ) 2  N [GeV]  [fm/c] Pb-Pb Collisions: Trajectories in the Phase Diagram Thermal Emission:

4.1 Pb-Au Collisions at SPS: CERES/NA45 QGP contribution small medium effects on  -meson! in-med spec-fct drop mass q-qbar dual [Kämpfer] Central Pb(158AGeV)+Au

4.2 In-In at SPS: Dimuons from NA60 excellent mass resolution and statistics for the first time, dilepton excess spectra could be extracted! quantitative theory? [Damjanovic et al. PRL ’06]

4.2.2 In-In at SPS: Theory vs. NA60 predictions:  -spectral function of [RR+Wambach ’99] uncertainty in fireball lifetime (±25% norm.); or: infer  FB ≈ 7fm/c ! relative strength of thermal sources fix  melting confirmed, incl. p t dependence;  and  ?! [van Hees +RR ‘06]

“4  “ states dominate in the vacuum e.m. correlator above M ≈ 1.1GeV lower estimate: use vacuum 4  correlator upper estimate: O (T 2 ) medium effect → “chiral V-A mixing”: with Intermediate-Mass Region [Eletsky+Ioffe ‘90] [van Hees+RR ‘06] 44 22

4.2.4 NA60 Data: Other  -Spectral Functions switch off medium modifications bare parameters: dropping mass free spectral function ruled out meson gas insufficient either dropping mass as used for CERES disfavored (free  decays?) vector dominance? [Brown+Rho ’91,Hatsuda+Lee ’92,…]

4.3 Pb-Au Excess Radiation: CERES/NA45 very-low-mass enhancement, required for photon production addt’l meson-Bremsstrahlung  →   K→  K  [Liu+RR’06] WA98 “Low-q t Anomaly”

4.4 (Some) Open Issues Heavy-Ion Collisions [NA60] - centrality dependence, free  ’s (surface vs. volume) - sensitivity to dynamical evolution (hydro, transport) - quantitative  and  - thermal radiation at intermediate mass (M=1.5-3 GeV) - chiral restoration: ▪ “duality” (hadron liquid → sQGP) ▪ chiral sum rules ▪ chiral mixing in the M=1-1.5GeV region Cold Nuclei [CB/TAPS, KEK-E325] - dropping  -mass + broadening - dropping  -mass without broadening ?!

5.) Conclusions Strong medium effects in l + l  spectra new level of precision in NA60  -melting at T c, no apparent mass shift alternative models? (quality control) In-medium V-meson spectroscopy has begun … Chiral Restoration: - direct (exp.): measure axialvector - indirect (theo.): (1) effective model (constraints) (2) chiral sum rules (V-A moments) vs. lQCD (3) compatibility with dilepton/photon data HADES, RHIC, LHC, SPS-09, CBM, …, elementary reactions

4.2.4 NA60 Data: Chiral Virial Approach also compare fireball vs. hydrodynamics lack of broadening good agreement hydro - fireball [ van Hees+RR ‘06] [Dusling,Teaney+Zahed ‘06]

4.2.4 NA60 Data: Cocktail vs. in-Medium  [Damjanovic ‘05] cocktail concentrated at high p t !

3.2 Dilepton Emission Rate: Hadron Gas vs. QGP Hard-Thermal-Loop QGP rate enhanced over Born rate “matching” of HG and QGP in vicinity of T c “Quark-Hadron Duality” ?! [Braaten,Pisarski+Yuan ’90] [qq→ee] [qq + HTL] ----

[Leupold ’98, Ruppert etal ’05] 0.2% 1% QCD Sum Rules +  (770) in Nuclear Matter dispersion relation for correlator: lhs: OPE (spacelike Q 2 ): rhs: hadronic model (s>0): [Shifman,Vainshtein +Zakharov ’79] 4-quark condensate!

density dependence: QCD sum rules: C ≈ 0.15 temperature dependence:  quark condensate from chiral perturbation theory: vector dominance coupling: (gauge invariance!) 3.3 Medium Effects II: Dropping Mass [Brown+Rho ’91, ‘02] Scale Invariance of L QCD → bare parameters change!? [Hatsuda+ Lee ‘92] [Pelaez ‘03]

3.1 Lattice QCD (QGP) T=1.5T c lQCD << pQCD at low mass (finite volume?) currently no thermal photons from lQCD vanishing electric conductivity!? but: [Gavai ’04] Dilepton Rate ~ Im  ( ,q=0)/  2 EM Correlator Im  ( ,q)/  2 [Bielefeld Group ’02, ‘05] 3.) Medium Effects and Thermal Dileptons

3.4 In-Medium IV: Vector Manifestation of Chiral Symmetry Hidden Local Symmetry:  -meson introduced as gauge boson, “Higgs” mechanism generates  -mass O Vacuum:  L ↔ , good phenomenology (loop exp. O (p/  , m  /  , g)) In-Medium: T-dep. m  (0), g  matched to OPE (spacelike),  match <  , Renormalization Group running → on-shell  - dropping  -mass → 0 (RG fixed point at T c ), - violation of vector dominance: a = 2 → 1 [Harada, Yamawaki etal, ‘01] e.m. spectral function? matching HG-QGP: massless mesons? ~(a-2) ~a   

drop. mass (norm.) [RR+Wambach ’99; RR’03] 4.2 Recent Advances at SPS: Power of Precision drop. mass (norm.) NA60 Data vs. Model Predictions  -meson “melting” supported (baryons!) dropping mass (as used to explain CERES data) ruled out open issues: (1) M > 0.9GeV (4  →     !?) (2) normalization: 0.6 (p t 1GeV) (3) other models (vector manifestation, chiral virial approach, …)

4.2.2 Modified Fireball and Absolute Normalization  -spectral function unchanged since [RR+Wambach ’99] expanding fireball, fixed S (↔N ch ): V FB (  )=(z 0 +v z  )  (R ┴ a ┴  2 ) 2 Increase a ┴  reduced lifetime (  =9→6fm/c), increased v ┴ =0.4→0.5c reasonable agreement with absolute normalization, but … too little yield at high p t ; “free  ”?  ? check central … [van Hees+ RR in prep.] [courtesy S.Damjanovic]

Revival Attempts for Dropping  -Mass E.g., [Skokov+Toneev ‘05] Bjorken regime:  FB =0.5 fm/c?!  >1GeVfm -3 ≈  c for  =8 fm/c?! Not compatible with gauge invariance (no m  * in VDM) acceptance? Fireball Evolution

4.2.5 Chiral Virial Approach vs. NA60 (central) [Steele,Yamagishi +Zahed ’99] [implementation van Hees+RR ’05]

5.) Electromagnetic Probes Thermal Photons I : SPS Expanding Fireball + pQCD pQCD+Cronin at q t >1.6GeV  T 0 =205MeV suff., HG dom. addt’l meson-Bremsstrahlung  →   K→  K  substantial at low q t [Liu+ RR’05] WA98 “Low-q t Anomaly” [Turbide,RR+Gale’04]

thermal radiation q t <3GeV ?! QGP window 1.5<q t <3GeV ?! Thermal Photons II: RHIC also:   -radiation off jets shrinks QGP window q t <2GeV ?! [Gale,Fries,Turbide,Srivastava ’04]

Hadronic Many-Body Theory RHIC: Vector Mesons in Medium baryon effects important even at  B,net =0 : sensitive to  B,tot =   +  B, most pronounced at low M  more robust ↔ OZI - Dilepton Emission Rates Quark-Hadron Duality ?! in-med HG ≈ in-med QGP ! [qq→ee] [qq+O(  s )] ----

5.3.2 Dileptons II: RHIC low mass: thermal! (mostly in-medium  ) connection to Chiral Restoration: a 1 (1260)→ , 3  int. mass: QGP (resonances?) vs. cc → e + e - X (softening?) - [RR ’01] [R. Averbeck, PHENIX] QGP