Dilepton production and off- -shell shell Dilepton production and - PowerPoint PPT Presentation

Dilepton production and off- -shell shell Dilepton production and off transport dynamics at SIS energies transport dynamics at SIS energies Elena lena Bratkovskaya Bratkovskaya E Institut für Theoretische Physik, Uni. Frankfurt , Uni. Frankfurt Institut für Theoretische Physik 12 August 2009, EMMI Workshop on ‘Virtual Bremsstrahlung 12 August 2009, EMMI Workshop on ‘Virtual Bremsstrahlung and HADES‘ and HADES‘ Uni. Frankfurt Uni. Frankfurt

Applicability of transport approaches and viscous hydro ransport approaches and viscous hydro Applicability of t η /s The ratio of shear viscosity to entropy density η /s defines the defines the applicability of applicability of The ratio of shear viscosity to entropy density many- -body approaches ! body approaches ! many ideal hydro: η η /s = 0 ! Recall: ideal hydro: /s = 0 ! Recall: Validity of transport approaches (in 2PI approximation): Validity of transport approaches (in 2PI approximation): λ > d λ a) classically: > d a) classically: 1/3 of - 1/3 free path λ λ must be larger than the average distance d = must be larger than the average distance d = ρ ρ - mean- -free path of mean the `degrees of freedom` (hadrons or partons) the `degrees of freedom` (hadrons or partons) 1/3 = 2/3 /(16 1/3 T) : λ λ > d = > d = ρ ρ - = π π 2/3 -1/3 for gluons (e.g. C. Greiner et al.) (e.g. C. Greiner et al.) : /(16 1/3 T) for gluons using η η /s = 4/15 T /s = 4/15 T λ λ � � � � � � η /s > 0.22 η � � /s > 0.22 using � < E/2 � b) quantum mechanics: < E/2 b) quantum mechanics: particles � � must be less than about half the quasi width of quasi- -particles must be less than about half the quasi- - width of quasi 2 +M 2 ) 1/2 particle energy E = (p 2 +M 2 ) 1/2 particle energy E = (p 2 +(3T) 2 ) 1/2 (Juchem, Cassing, Greiner 2003) : average energy <E> = (M : average energy <E> = (M 2 +(3T) 2 ) 1/2 (Juchem, Cassing, Greiner 2003) � for M=0: η η /s > 0.18 η /s � ( η /s > 0.18 /s is even is even lower lower for M >2T as in PHSD!) for M >2T as in PHSD!) for M=0: ( PHSD:W. Cassing, E. B., PRC 78 (2008) 034919; arXiv:0907.5331 [nucl nucl- -th] th] PHSD:W. Cassing, E. B., PRC 78 (2008) 034919; arXiv:0907.5331 [

η /s What do we know about η /s? ? What do we know about N. Demir, S.A. Bass : PRL 102 (09) 172302 D. Teaney: nucl- -th / 0905.2433 th / 0905.2433 N. Demir, S.A. Bass : PRL 102 (09) 172302 D. Teaney: nucl pQCD pQCD UrQMD UrQMD hadron gas − partons partons hadron gas η /s > 0.5 In hadronic phase: η /s > 0.5 In hadronic phase: D. Teaney: dissipative dissipative D. Teaney: � � transport is valid! � � � � � � transport is valid! (viscous) hydro works for (viscous) hydro works for η /s < 0.3 n partonic phase: η η /s < 0.3 ! in partonic phase: /s < 0.3 η i /s < 0.3 ! … What the experiment tells us about η η /s at RHIC? /s at RHIC? … What the experiment tells us about

Experimental situation in Au+Au at RHIC Experimental situation in Au+Au at RHIC PHENIX η/ η/ η/ η/ s=0.48 viscous hydro viscous hydro η/ η/ s=0.32 η/ η/ η/ η/ η/ η/ s=0.16 parton transport parton transport η/ s=1/4 π η/ η/ η/ π π π ideal hydro ideal hydro � � The off The off- -shell transport shell transport - - with parton with parton- -hadron degrees of freedom hadron degrees of freedom – – is is valid at least up to RHIC energies ! at least up to RHIC energies ! valid Data from R. Lacey: CBM Workshop, March 2009 Data from R. Lacey: CBM Workshop, March 2009

‚History‘ of dilepton cocktails of dilepton cocktails ‚History‘ Gy. Wolf et al., Gy. Wolf et al., Nucl Nucl. . Phys. Phys. A A517 (1990) 615 517 (1990) 615 [Similar to : C.M. Ko et al., NPA 512 (1990) 772] [Similar to : C.M. Ko et al., NPA 512 (1990) 772] BUU: BUU: • first calculation of dilepton production in • first calculation of dilepton production in heavy- -ion collisions within a transport model ion collisions within a transport model heavy • implementation of the basic dilepton channels • implementation of the basic dilepton channels • time integration (‚shining‘) method • time integration (‚shining‘) method • discussion of in • discussion of in- -medium effects medium effects E.B., W. Cassing, E.B., W. Cassing, Nucl Nucl. . Phys. Phys. A A807 (2008) 214 807 (2008) 214 HSD : HSD : • … + • … + • off • off- -shell transport dynamics shell transport dynamics • dynamical treatment of resonances with broad • dynamical treatment of resonances with broad spectral functions spectral functions • in • in- -medium effects (dropping mass, collisional medium effects (dropping mass, collisional broadening) broadening)

Dilepton cocktail in HSD Dilepton cocktail in HSD • All particles decaying to dileptons are • All particles decaying to dileptons are electromagnetic decays electromagnetic decays first produced in BB, mB or mm collisions first produced in BB, mB or mm collisions • ‚Factorization‘ of diagrams • ‚Factorization‘ of diagrams in the in the transport approach: transport approach: e + e - e + γ * γ γ γ e - N N R γ * γ γ γ N R R = N N N N N • The dilepton spectra are calculated • The dilepton spectra are calculated perturbatively perturbatively with the with the time integration method time integration method. .

Zoom: Dilepton channels Zoom: Dilepton channels � under control! � � � electromagnetic decays � � � � under control! electromagnetic decays π,η,∆,ω,ρ,φ,... production production – – π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... π,η,∆,ω,ρ,φ,... can be controlled by N+N and can be controlled by N+N and π π π π +N exp. data +N exp. data π π π π not for HADES not for HADES NN, π N bremsstrahlung = ‚background‘ radiation = ‚background‘ radiation - - hard to control by hard to control by NN, π π N bremsstrahlung π π π π π exp. data! exp. data! � reliable theoretical model for NN and � � � � � � � reliable theoretical model for NN and π N bremsstrahlung is needed! π N bremsstrahlung is needed! π π π π π π

NN and π N bremsstrahlung - - SPA SPA NN and π π π π N bremsstrahlung π π π Phase- -space corrected space corrected Phase Soft- -Photon Photon- -Approximation Approximation (SPA): (SPA): Soft - ) soft- -photon cross section: photon cross section: - (or soft e - + e + e N N − > N N e N N e + e - (or π π N N − >π N e N e + ) N N −> − − − − > > > > π π π π − −>π − − − >π >π >π >π − − > > π π − − >π >π ∗ ∗ - + e - γ ∗ ∗ ∗ ∗ ∗ ∗ ->e >e + e - γ γ γ γ γ γ γ (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) (π) ‚quasi- - elastic‘ elastic‘ ‚quasi N N - -> N N > N N N N π N N - -> > π π N N π π π π π π π π π π π π π elastic elastic NN ( π NN ( π π π N) π N) π π π ‚off ‚off- -shell‘ correction factor shell‘ correction factor SPA implementation in HSD: SPA implementation in HSD: - production in + e � � e + e - production in elastic NN ( elastic NN ( π N) e π π N) π π π π π ( ( ( ( ) ) ) ) d σ dP(s, M, q ) s, M, q 1 collisions with probability: with probability: collisions � = = = = � ⋅ ⋅ ⋅ ⋅ σ elast dMd q dMd q NN( π π π π N) (as in Gy. Wolf et al., (as in Gy. Wolf et al., NPA NPA517 (1990) 615) 517 (1990) 615)

Bremsstrahlung – – a new view on an ‚old‘ story a new view on an ‚old‘ story Bremsstrahlung 1 1 10 10 Bremsstrahlung Schäfer et al.'94 de Jong&Mosel'96 p+n, 1.04 GeV 0 0 10 10 Shyam&Mosel'03 2 )] 2 )] µ b/(GeV/c µ b/(GeV/c Kaptari&Kämpfer'06 -1 -1 10 10 µ µ σ /dM [ µ µ µ σ /dM [ µ -2 -2 10 10 SPA, in HSD'97 d σ d σ σ σ Schäfer et al.'94 σ σ -3 -3 10 10 Shyam&Mosel'03 p+p, 1.04 GeV Kaptari&Kämpfer'06 -4 -4 10 10 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 2 ] M [GeV/c New OBE- -model model (Kaptari&Kämpfer, NPA 764 (2006) 338): (Kaptari&Kämpfer, NPA 764 (2006) 338): New OBE • pn • pn bremstrahlung is bremstrahlung is larger larger by a factor of by a factor of 4 4 than it has been than it has been calculated before (and used in transport calculations before)! )! calculated before (and used in transport calculations before • pp • pp bremstrahlung is smaller than pn, however, bremstrahlung is smaller than pn, however, not zero not zero; consistent ; consistent with the 1996 calculations from F. F. de Jong in a T de Jong in a T- -matrix approach matrix approach with the 1996 calculations from 2007 ‚DLS puzzle‘ : Experimentally: HADES = DLS ! Experimentally: HADES = DLS ! 2007 ‚DLS puzzle‘ : Theory: the DLS puzzle is solved by accounting for a larger pn the DLS puzzle is solved by accounting for a larger pn Theory: bremsstrahlung ! bremsstrahlung !