Electromagnetic probes of the Electromagnetic probes of the QGP QGP Elena E lena Bratkovskaya Bratkovskaya Institut fü ür Theoretische Physik r Theoretische Physik & FIAS, & FIAS, Institut f Uni. Frankfurt Uni. Frankfurt BLTP, 3 September, 2014 BLTP, 3 September, 2014
Electromagnetic probes: photons and dileptons Electromagnetic probes: photons and dileptons � Advantages: � Feinberg (76), Shuryak (78) � Disadvantages: � Advantages: Disadvantages: � low emission rate � low emission rate � dileptons and real photons are � dileptons and real photons are � production from hadronic corona � production from hadronic corona emitted from different stages of the emitted from different stages of the reaction and not effected by final- - reaction and not effected by final � many production sources which � many production sources which state interactions state interactions cannot be individually cannot be individually disentangled by experimental data disentangled by experimental data � provide undistorted information � provide undistorted information about their production channels about their production channels � promising signal of QGP � promising signal of QGP – – ‚thermal ‚ thermal‘ ‘ photons and dileptons photons and dileptons � Requires � � � � � � � Requires theoretical models theoretical models which describe the dynamics dynamics which describe the of heavy- -ion collisions during ion collisions during of heavy the whole time evolution! the whole time evolution! Elena Bratkovskaya (Uni. Frankfurt) JINR (Dubna), 3 September 2014 2
Dynamical models for HIC Dynamical models for HIC Macroscopic Macroscopic Microscopic Microscopic Non- Non -equilibrium microscopic transport models equilibrium microscopic transport models – – based on many- -body theory body theory based on many hydro- -models: models: hydro � description of QGP and hadronic phase � description of QGP and hadronic phase Hadron- -string string Partonic cascades Hadron Partonic cascades by hydrodynamical equations for the fluid by hydrodynamical equations for the fluid models models pQCD based pQCD based � � assumption of local equilibrium assumption of local equilibrium (UrQMD, IQMD, HSD, (Duke, BAMPS, … …) ) (UrQMD, IQMD, HSD, (Duke, BAMPS, � EoS with phase transition from QGP to HG � EoS with phase transition from QGP to HG QGSM, GiBUU, … …) ) QGSM, GiBUU, � initial conditions (e � initial conditions (e- -b b- -e, fluctuating) e, fluctuating) Parton- -hadron models: hadron models: Parton � QGP: � QGP: pQCD pQCD based cascade based cascade ideal viscous ideal viscous � massless q, g � massless q, g � hadronization: coalescence � (Jyv (Jyvä äskyl skylä ä,SHASTA, ,SHASTA, (Romatschke, (2+1)D VISH2+1, (Romatschke, (2+1)D VISH2+1, hadronization: coalescence TAMU, … …) ) (3+1)D MUSIC,… …) ) TAMU, (3+1)D MUSIC, (AMPT, HIJING HIJING) ) (AMPT, � QGP: � QGP: lQCD EoS lQCD EoS � massive quasi � massive quasi- -particles particles ‚Hybrid Hybrid‘ ‘ (Macro+Micro) ‚ (Macro+Micro) fireball models: fireball models: (q and g with spectral functions) (q and g with spectral functions) � QGP phase: � QGP phase: hydro hydro with QGP EoS with QGP EoS � no explicit dynamics: � in self- in self -generated mean generated mean- -field field no explicit dynamics: � hadronic freeze � hadronic freeze- -out: after burner out: after burner - - � dynamical hadronization � dynamical hadronization parametrized time parametrized time hadron- hadron -string transport model string transport model � HG: off � HG: off- -shell dynamics shell dynamics evolution (TAMU) evolution (TAMU) (‚ ( ‚hybrid hybrid‘ ‘- -UrQMD, EPOS, UrQMD, EPOS, … …) ) ! applicable for strongly applicable for strongly ! interacting systems ! interacting systems ! Elena Bratkovskaya (Uni. Frankfurt) JINR (Dubna), 3 September 2014 3
Modeling of photon/dilepton emission Modeling of photon/dilepton emission Feinberg (76), (76), McLerran McLerran, , Toimela Toimela (85) (85), , Feinberg I. Emission rate I. Emission rate from from thermal field theory thermal field theory: : Weldon (90), Gale, Weldon (90), Gale, Kapusta Kapusta (91) (91) � Bose distribution: � � Photons: � 3 Bose distribution: g � d R �ν Photons: �ν Π q = = = = − − − − Im (q = = = = | q | ) f(q ,T) 1 0 π ) 0 0 3 3 = = = = f(q ,T) d q ( 2 0 q / T − − e − − 1 0 � Dileptons: � 3 2 � d R 2 e 1 �ν Dileptons: Π E E = = = = L Im (q , q ) f(q ,T) + + + + − − − − µ ν µ ν µ ν µ ν π ) 0 0 3 3 6 4 d p d p ( 2 q + + + + − − − − � L � L µν is the electromagnetic leptonic tensor µν is the electromagnetic leptonic tensor µν µν µν µν µν µν ∫ ∫ ∫ ∫ � Π � 4 ipx Π Π Π Π < < < < > > > > Π Π Π Π µν Π µν is the is the retarded photon self energy retarded photon self energy at finite T : at finite T : ~ i d x e [ J ( x ), J ( 0 )] Π Π µν µν µν µν µν µν µ ν µ ν µ ν µ ν µ µ µ µ ν ν ν ν T ρ in � Hadron phase: � mD ρ ρ ρ ρ ρ ρ ρ Hadron phase: using using VDM VDM: : Ι Ι m Ι Ι Ι m Π Π Π Π Π ~> ~> Ι Ι Ι mD Ι Ι in- -medium medium ρ ρ ρ ρ ρ - -meson spectral function meson spectral function Ι Ι Ι Π Π Π Ι Ι Ι ρ ρ ρ from many- -body approach body approach ( cf. from many ( cf. Rapp, Chanfrey, Wambach, NPA 617 Rapp, Chanfrey, Wambach, NPA 617 ( (1997) 472 ) 1997) 472 ) � s � � � � � � � study of the tudy of the in in- -medium properties of hadrons medium properties of hadrons at high baryon density and T at high baryon density and T PRL 110 (2013) 182301 PRL 110 (2013) 182301 � restoration � restoration of chiral symmetry ( of chiral symmetry ( ρ ρ ρ ρ ρ - -a a 1 ): ρ ρ ρ 1 ): ρ ~> chiral condensate (by mD ρ ρ ρ ρ ρ Ι Ι mD ρ ρ ~> chiral condensate (by Weinberg sum Weinberg sum rules) rules) Ι Ι Ι Ι Ι Ι (cf. Hohler, Rapp, arXiv:1311.2921 (cf. Hohler, Rapp, arXiv: 1311.2921) ) � Rates at q � 0 are related to electric � � � � 0 � � � � Rates at q 0 0 are related to electric conductivity conductivity σ σ σ σ σ σ 0 σ σ 0 � � � � Probe of � � � � Probe of electric properties of the QGP electric properties of the QGP dR T σ = = q = = PHSD plot from Cassing et al., PRL 110 (2013) 182301; PHSD plot from Cassing et al., PRL 110 (2013) 182301; 0 0 4 3 π 3 d x d q 4 cf. also NJL: Marty et al., PRC87 (2013) cf. also NJL: Marty et al., PRC87 (2013) 3, 034912 3, 034912; ; q → → → → 0 0 poster by R.Marty QM poster by R.Marty QM‘ ‘14 14 Elena Bratkovskaya (Uni. Frankfurt) JINR (Dubna), 3 September 2014 4
Modeling of photon/dilepton emission Modeling of photon/dilepton emission Applicable also for Applicable also for II. Emission rate Emission rate from from relativistic kinetic theory relativistic kinetic theory: : II. non- -equilibrium equilibrium non � � � γ+3) � (e.g. for 1+2 � � � � γ+3) γ+3) γ+3) γ+3) (e.g. for 1+2 γ+3) γ+3) γ+3) system ! system ! 3 = ∫ 3 3 3 d R d p d p d p ∫ ∫ ∫ 4 4 1 2 3 = = = π π π π δ δ δ δ + + + + − − − − − − − − q ( 2 ) ( p p p q ) 0 1 2 3 3 3 3 3 π π π π π π π π π π π π d q 2 ( 2 ) E 2 ( 2 ) E 2 ( 2 ) E 1 2 3 f ( E ) f ( E )[ 1 ± ± ± ± f ( E )] � f(E) � f(E) - - distribution function distribution function 2 1 2 3 × × × × | M | 3 π π π π 2 ( 2 ) � Μ � Μ – Μ Μ Μ Μ Μ Μ – invariant invariant scattering matrix element scattering matrix element from microscopic models from microscopic models � Modeling of hadronic elementary reactions � Modeling of hadronic elementary reactions: : Chiral models, OBE models,… … (Born (Born- -type diagrams) type diagrams) Chiral models, OBE models, � Problems: � Problems: � very � very limited experimental information limited experimental information on mm, mB elementary reactions on mm, mB elementary reactions � Hadrons change their properties in the hot and dense medium: � Hadrons change their properties in the hot and dense medium: � from vacuum cross sections to � � � � � � � from vacuum cross sections to in in- -medium medium, i.e. , i.e. from ‚ from ‚T T- -matrix matrix‘ ‘ to to ‚ ‚G G- -matrix matrix‘ ‘ approaches (many approaches (many- -body theory) body theory) E.g. : ρ ρ - ρ -meson collisional broadening meson collisional broadening – – important for dilepton studies! important for dilepton studies! E.g. : ρ ρ ρ ρ ρ Elena Bratkovskaya (Uni. Frankfurt) JINR (Dubna), 3 September 2014 5
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