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1 Quark matter probed by dileptons Olena Linnyk July 02, 2010

2 Information from photons and dileptons ε/t Lattice QCD: µ B =0 µ B =530 MeV T/T c But what are the properties of this phase?! Z. Fodor et al., PLB 568 (2003) 73

3 HSD transport model - basic concepts HSD Hadron-String-Dynamics transport approach Based on: Generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for Greens functions G < h(x,p) in phase-space space representation (in the first order gradient expansion, beyond the quasiparticle approximation). Numerical solution: Monte Carlo simulations with a large number of test-particles Degrees of freedom in HSD: hadrons - baryons and mesons including excited states (resonances) strings excited color singlet states (qq-q) q) or (q-qbar) leading quarks (q, qbar) & diquarks (q-q, q, qbar-qbar qbar) Au+Au (central) HSD a microscopic model for heavy-ion reactions: very good description of particle production in pp, pa reactions unique description of nuclear dynamics from low (~100 MeV) to ultrarelativistic (~20 TeV) energies Multiplicity π + η K + K φ D(c) D(c) HSD ' 99 J/Ψ AGS SPS RHIC Energy [A GeV]

4 Dilepton signal of the QGP at SPS dn/dm per 20 MeV Peripheral HSD: free s. f. coll. broad. dropp. mass + coll. broad. In+In, 160 A GeV, all p T 2500 NA Semi-Peripheral dn/dm per 20 MeV Semi-Central Central High mass tail not reproduced in HSD. Non-hadronic origin? NA60 data at low M are well described by an in-medium scenario with collisional broadening E. Bratkovskaya, W. Cassing, O. Linnyk, PLB 670 (2009) 428

5 Dilepton excess seen also at RHIC 1/N evt dn/dm [1/(GeV/c 2 )] p+p, s 1/2 =200 GeV PHENIX sum HSD: π 0 η η' ρ ω φ c+ c > e + +e (PYTHIA) HSD provides a good description of pp data. But standard in-medium effects of vector mesons (compatible with the NA60 and CERES data at SPS) do not explain the large enhancement observed by PHENIX in the invariant mass from 0.2 to 0.5 GeV in Au+Au collisions at s 1/2 =200 GeV relative to pp collisions! E. Bratkovskaya, W. Cassing, O. Linnyk, PLB 670 (2009) 428 1/N evt dn/dm [1/(GeV/c 2 )] 1/N evt dn/dm [1/(GeV/c 2 )] HSD (free spectral functions): PHENIX sum π 0 η η' ρ ω φ c + c > e + +e (PYTHIA) min. bias Au+Au, s 1/2 =200 GeV min. bias Au+Au, s 1/2 =200 GeV PHENIX HSD: free spectral functions collisional broadening dropp. mass + coll. broad

6 From hadrons to partons In order to study of the phase transition from hadronic to partonic matter, i.e. the sqgp, we need a consistent transport model with explicit interactions of quarks and gluons outside strings (!) phase transition from hadronic to partonic degrees of freedom lqcd EoS for the partonic phase => phase transition is always a cross-over over Transport theory: off-shell Kadanoff-Baym equations for the Green s functions G < h(x,p) in phase-space space representation with partonic and hadronic phases Parton-Hadron-String-Dynamics (PHSD) QGP phase described by input from the Dynamical QuasiParticle article Model (DQPM) W. Cassing, E. Bratkovskaya, PRC 78 (2008) W. Cassing, EPJ ST 168 (2009) 3 A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

7 PHSD step by step 1) Initial A+A collisions HSD: string formation and decay to pre-hadrons 2) Fragmentation of pre-hadrons into quarks: using the quark spectral functions from the DQPM DQPM: Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 3) Partonic phase: quarks and gluons (= dynamical quasiparticles ) with off-shell spectral functions (width, mass) defined by the DQPM elastic and inelastic parton-parton interactions with the effective cross sections from the DQPM q + qbar (flavor neutral) <=> gluon (colored) gluon + gluon <=> gluon (possible due to large spectral width) q + qbar (color neutral) <=> hadron resonances 4) Hadronization: based on DQPM - massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell mesons and baryons: gluons q + qbar; q + qbar meson (or string); q + q +q baryon (or string) (strings act as doorway states for hadrons) 5) Hadronic phase: hadron-string interactions off-shell HSD Cassing, Bratkovskaya, PRC 78 (2008)

8 Dynamical QuasiParticle Model (DQPM) α S (T) T/T C N τ =8 DQPM fit to lqcd Interacting quarks and gluons : massive with large spectral width T = T c Gluon ρ(ω): ε/t T = 1.35 T c QCD EoS lqcd DQPM AB-Bag SB limit T/T c T = 3 T c A. Peshier, PRD 70(2004)034016; A. Peshier, W. Cassing, PRL 94(2005)172301; Cassing, NPA 791(2007)365, NPA(2007)793 Fodor et al, PLB 568 (2003) 73

9 Dilepton emission from parton interactions q γ * l + quark gluon gluon quark gluon γ* q l - anti-quark γ* quark γ* quark quark LO NLO pqcd applicability Small α S perturbative ordering Asymptotic plane waves massless spinors On-shell (free) quarks and gluons no width The challenge: full off-shell treatment of massive partons with large widths

10 Running α S is large α S vs energy density non-perturbative α S energy densities achieved in HIC Importance of higher orders in α S α S Partons are off-shell ε c ε [GeV/fm 3 ] Modification of cross sections by the masses and widths of partons 8 6 dn ds m quark 0.4 kinematically not allowed g+q > q+γ* m gluon dn ds m quark q+q > γ* q+q > g+γ* m anti-quark

11 Off-shell LO q+qbar q γ * e + q e - Note: In the limit of parton masses 0, the perturbative QCD result is recovered O. Linnyk, S. Leupold, U. Mosel, PRD 75 (2007)

12 Off-shell LO q+qbar q q γ * e + e - σ(s) σ [mb] Drell-Yan mechanism q+qbar >µ + µ on-shell vs off-shell m 1 =0.3 GeV, m 2 =0.15 GeV m 1 =0.3 GeV, m 2 =0.3 GeV m 1 =0.3 GeV, m 2 =0.6 GeV m 1 =0.6 GeV, m 2 =0.6 GeV Onshell (m 1 =m 2 =0) Q [GeV] / σ(s) on-shell σ(s) off-shell Drell-Yan mechanism q+qbar >µ + µ on-shell vs off-shell m =0.3 GeV, m =0.15 GeV 1 2 m 1 =0.3 GeV, m 2 =0.3 GeV m 1 =0.3 GeV, m 2 =0.6 GeV m 1 =0.6 GeV, m 2 =0.6 GeV Q-Q 0 [GeV] As large Q, the perturbative QCD result is recovered O. Linnyk, arxiv:

13 Off-shell NLO q+qbar quark γ* anti-quark gluon etc. See details in O. Linnyk, arxiv:

14 Off-shell NLO q+qbar quark γ* dσ(s)/dq 2 [mb/gev 2 ] Gluon Bremsstrahlung q+qbar > >g+µ + µ 10-3 on-shell vs off-shell On-shell Off-shell, µ=0.8 GeV, m q =0 Off-shell, µ=0.8 GeV, m q =0.6 GeV Q [GeV] dσ(s)/dq 2 [off-shell] : [on n-shell] anti-quark Gluon Bremsstrahlung q+qbar > >g+µ + µ on-shell vs off-shell µ=0.8 GeV, m q =0.6 GeV µ µ=0.8 GeV, m q = Q [GeV] gluon Note: In the limit of parton masses 0, the perturbative QCD result is recovered O. Linnyk, arxiv:

15 Sub-leading diagrams Virtual quark decay Gluon Compton Scattering Virtual gluon decay O. Linnyk, arxiv:

16 From cross sections to rates Factorization: Convolution of the elementary cross sections with parton spectral functions (DQPM parametrization) and with phenomenological distributions of quark (gluon) collisions in QGP yields observable dilepton rates. O. Linnyk, arxiv:

17 Dilepton rates with on-shell (pqcd) cross sections dn/dq [a.u.] 10-4 q+qbar >µ + µ Dilepton rates on-shell, running α S q+qbar > >g+µ + µ q+g > >q+µ + µ LO q+qbar = DY term = Born term NLO q+qbar gluon Compton 10-8 m q =0 m g = Q [GeV] Note: LO and NLO q+qbar are comparable due to large α S O. Linnyk, arxiv:

18 Dilepton rates from massive quarks and gluons dn/dq [a.u.] 10-4 q+qbar >µ + µ q+qbar > >g+µ + µ q+g > >q+µ + µ 10-8 m q =0 m g =0 Dilepton rates on-shell, running α S Q [GeV] dn/dq [a.u.] 10-4 q+qbar >µ + µ 10-8 m q =0.3 GeV m g =0.8 GeV Dilepton rates massive partons q+qbar > >g+µ + µ q+g > >q+µ + µ Q [GeV] Note: Threshold in the Born contribution due to finite masses of incoming particles. O. Linnyk, arxiv:

19 Dileptons from massive and broad quarks, gluons dn/dq [a.u.] dn/dq [a.u.] 10-4 q+qbar >µ + µ q+qbar > >g+µ + µ q+g > >q+µ + µ 10-8 m q =0 m g =0 Dilepton rates on-shell, running α S Q [GeV] Dilepton rates massive partons 10-4 q+qbar >µ + µ q+qbar > >g+µ + µ q+g > >q+µ + µ m q =0.3 GeV Q [GeV] dn/dq [a.u.] 10-3 q+qbar >µ + µ Dilepton rates Massive and broad partons q+qbar > >g+µ + µ q+g > >q+µ + µ m g =0.8 GeV Q [GeV] O. Linnyk, arxiv: Broad spectral functions of partons have a pronounced effect on observables. The threshold of the Born term is smeared, the contributions of the 2->2 processes increase

20 NA60: sqgp shines already at SPS dn/dm per 20 MeV Peripheral In+In, 160 A GeV, all p T PHSD Semi-Peripheral dn/dm per 20 MeV Semi-Central Central NA DDbar ρ coctail ρ, free s.f. ρ, in-med. s.f. (col. broad.) dileptons from QGP sum=ρ+qgp+ddbar Implementation of the derived cross sections into the PHSD transport approach > the comparison to the data.

21 PHENIX data peripheral 1/N 2 evt dn/dm [1/(GeV/c )] Au+Au, s 1/2 =200 GeV, 20-40% central PHENIX HSD PHSD π 0 η η' ρ ω φ a 1 D q+qbar->γ * q+qbar->γ * +g q+g->γ * +q Peripheral data are explained quite well in the whole range of M. We observe no excess over the predicted hadronic yield at low masses. There is a small contribution from the partonic phase seen at M>1 GeV. 10-8

22 PHENIX data semi-central 10-1 evt dn/dm [1/(GeV/c 2 )] 1/N evt Au+Au, s 1/2 =200 GeV, 10-20% central π 0 η η' PHENIX ρ ω φ HSD a 1 D PHSD q+qbar->γ * q+qbar->γ * +g q+g->γ * +q The contibution of the QGP to the dilepton radiation in semi-central collisions is increased compared to the peripheral ones. Partonic channels dominate the observed yield at M>2 GeV (apart from the charmonium peaks). The data are explained in a wide range of M. There is a discrepancy between the data and the PHSD results at M= GeV. 10-8

23 PHENIX data central 10-1 t dn/dm [1/(GeV/c 2 )] 1/N evt Au+Au, s 1/2 =200 GeV, 0-10% central π 0 η η' PHENIX ρ ω φ HSD a 1 D PHSD q+qbar->γ * q+qbar->γ * +g q+g->γ * +q The contribution of the QGP to the dilepton radiation clearly increases with centrality. Partonic channels dominate the observed yield at high masses. There is a large discrepancy between the data and PHSD at M= GeV. While the data are explained satisfactory both at smaller masses and at M>0.6 GeV. 10-8

24 PHENIX data vs PHSD 1/N evt dn/dm [1/(GeV/c 2 )] min. bias Au+Au, s 1/2 =200 GeV 10-1 PHENIX PHSD (free spectral functions:) sum 10-2 π 0 η η' ρ ω φ c + c > e + +e QQbar HSD 1/N evt dn/dm [1/(GeV/c 2 )] min. bias Au+Au, s 1/2 =200 GeV 10-1 PHSD (free spectral functions:) PHENIX sum π 0 η η' ρ ω φ c + c > e + +e (Jaakko) QQbar HSD Radiation from hadrons in HSD and PHSD is essentially the same. The excess over the considered mesonic sources at M= GeV is not explained by the QGP radiation as incorporated presently in PHSD. The partonic channels fill out the discrepancy between the hadronic contributions and the data at M>1 GeV.

25 Conclusions Parton-Hadron-String-Dynamics (PHSD) theory provides a consistent description of the phase transition to QGP in heavy ion collisions. The dilepton data from NA60 and CERES at SPS energies at masses below 1 GeV are rather well described within off-shell HSD including a collisional broadening of vector mesons Yield of dilepton pairs at masses above 1 GeV indicates the presence of the strongly interacting QGP and is described by the interaction of dynamical quasiparticles. Neither the incorporated hadronic no partonic sources account for the enhancement observed by PHENIX in the invariant mass from 0.2 to 0.5 GeV in Au+Au collisions at s 1/ 2 =200 GeV (relative to pp collisions).

26

27 PHSD: Transverse mass spectra at top SPS Central Pb + Pb at top SPS energies 1/m T dy [(GeV) -2 T dn/dm ] Pb+Pb, 80 A GeV, 7%, mid-rapidity 10 4 NA π HSD PHSD K + K * m T -m 0 [GeV] 1/m T dy [(GeV) -2 T dn/dm ] 10 4 Pb+Pb, 160 A GeV, 5%, mid-rapidity 10 3 π NA49 HSD PHSD K K * m T -m 0 [GeV] PHSD gives harder spectra and works better than HSD at top SPS energies

28 Acceptance corrected NA60 data Mass region above 1 GeV is dominated by partonic radiation

29 PHSD: Hadronization details Local off-shell transition rate: (meson formation) using W m - Gaussian in phase space Cassing, E.B., PRC 78 (2008) Cassing, EPJ ST 168 (2009) 3

30 NA60: m T spectra 10-4 In+In, 158 GeV PHSD NA 60 PHSD NA 60 Inverse slope parameter T eff for dilepton spectra vs NA60 data 350 In+In, 158 A GeV, dn ch /dη>30 /dηdm T ) / (dn ch /dη) µµ /d 1/m T (dn µµ [(GeV/c 2 ) -2 ] 10-8 M= GeV M= GeV PHSD NA 60 M= GeV M= GeV PHSD, a.u. NA 60 T eff , LMR,, IMR NA60 data PHSD PHSD Evolution of the inverse m T - m T - slope parameter T eff with Conjecture: mass is reproduced! spectrum from sqgp is softer than from hadronic phase since quark-antiquark annihilation occurs dominantly before the collective radial flow has developed!