A Theoretical View on Dilepton Production Transport Calculations vs. Coarse-grained Dynamics Stephan Endres (in collab. with M. Bleicher, H. van Hees, J. Weil) Frankfurt Institute for Advanced Studies ITP Uni Frankfurt Transport Meeting WS 13/14 November 6th, 13 1 / 3
Overview 1 Introduction Transport Calculations and their Difficulties 3 Coarse Grained Transport Aproach 4 First Results 5 Outlook / 3
Why Dileptons...? Dileptons represent a clean and penetrating probe of hot and dense nuclear matter Reflect the whole dynamics of a collision Once produced they do not interact with the surrounding matter (no strong interactions) Aim of studies In-medium modification of vector meson properties Chiral symmetry restoration 3 / 3
Ultra-relativistic Quantum Molecular Dynamics Hadronic non-equilibrium transport approach Includes all baryons and mesons with masses up to. GeV Two processes for resonance production in UrQMD (at low energies) Collisions (e.g. ππ ρ) Higher resonance decays (e.g. N N + ρ) Resonances either decay after a certain time or are absorbed in another collision (e.g. ρ + N N 15 ) No explicit in-medium modifications! 4 / 3
Dilepton sources in UrQMD Dalitz Decays π, η, η, ω, P γ + e + e V P +e + e Direct Decays ρ, ω, φ Dalitz decays are decomposed into the corresponding decays into a virtual photon and the subsequent decay of the photon via electromagnetic conversion Form factors for the Dalitz decays are obtained from the vector-meson dominance model Assumption: Resonance can continuously emit dileptons over its whole lifetime (Time Integration Method / Shining ) 5 / 3
The Resonance Mess Which resonances do I have to include? Which resonance is produced with which probability? What is the actual branching ratio (e.g. to the ρ)? Many parameters one can play with, as they are not fixed... 6 / 3
N*/ * Nρ Branching Ratios 7 / 3
Example: Exclusive Resonance Cross-Sections σ [mb].5 1.5 1.5 p+p p+p*(144) UrQMD Data.5 3 3.5 4 4.5 5 5.5 6 6.5 7 s [GeV] σ [mb] 1.8 1.6 1.4 1. 1.8.6.4. p+p p+p*(15) UrQMD Data.5 3 3.5 4 4.5 5 5.5 6 6.5 7 s [GeV] σ [mb] 1. 1.8.6.4. p+p p+p*(168) UrQMD Data.5 3 3.5 4 4.5 5 5.5 6 6.5 7 s [GeV] σ [mb] 4 ++ p+p + 3.5 UrQMD Data 3.5 1.5 1.5.5 3 3.5 4 4.5 5 5.5 6 6.5 7 s [GeV] 8 / 3
Transport Results p+p Results look quite nice after adjusting resonance production and branching ratio )] dσ/dm [mb/(gev/c -1 - -3-4 p+p @ 3.5 GeV HADES Acceptance > 9,.8 < p <. GeV/c θ ee e π η ρ ω Dalitz ω direct )] dσ/dm [µb/(gev/c 1-1 - p+p @. GeV HADES Acceptance θ ee > 9,.1 < p < 1.3 GeV/c e π η ρ ω Dalitz ω direct -3-4 -7.1..3.4.5.6.7.8.9 1 M [GeV/c ].1..3.4.5.6.7.8.9 1 M [GeV/c ] 9 / 3
Transport Results We see an excess in heavy-ion collisions (e.g. Ar+KCl @ 1.76 AGeV) not yet described by the model )] )dn/dm [1/(GeV/c (1/N π - -3-4 Ar+KCl @ 1.756 GeV HADES Acceptance θ ee > 9,.1 < p < 1.1 GeV/c e π η ρ ω Dalitz ω direct )] )dn/dm [1/(GeV/c (1/N - -3 π -4 C+C @ AGeV HADES Acceptance > 9,. < p <. GeV/c θ ee e π η ρ ω Dalitz ω direct -7-7 -8.1..3.4.5.6.7.8.9 1 M [GeV/c ] -8.1..3.4.5.6.7.8.9 1 M [GeV/c ] / 3
Transport Results At low energies around E kin = 1 GeV, a pure transport description becomes difficult as well Processes like NN and πn bremsstrahlung become dominant, especially for p+n interactions (How avoid double counting?) form factor? Which / how to dertermine? )] dσ/dm [µb/(gev/c 1 p+p @ 1.5 GeV HADES Acceptance θ ee > 9,.5 < p < 1.8 GeV/c e π η ρ ω Dalitz ω direct )] )dn/dm [1/(GeV/c - -3-4 C+C @ 1 AGeV HADES Acceptance > 9,. < p <. GeV/c θ ee e π η ρ ω Dalitz ω direct π -1 (1/N - -3-7 -4.1..3.4.5.6.7.8.9 1 M [GeV/c ] -8.1..3.4.5.6.7.8.9 1 M [GeV/c ] 11 / 3
The Transport Status Quo There has been a lot of improvement, especially concerning the exact comparison and adjustment of the many parameters, cross-sections, branching ratios (compare GiBUU results by Janus) However, this is a hard job and one has to be careful Still the models show big differences in some details dσ/dm ee [µb/gev] 1-1 - p + p at 3.5 GeV data total Moniz,Ernst Moniz,Wolf Moniz,Krivo Manley,Ernst Manley,Wolf Manley,Krivo Bass,Ernst Bass,Wolf Bass,Krivo -3..4.6.8 1 dilepton mass m ee [GeV] 1 / 3
Challenges Cross-sections not implemented explicitly but intermediate baryonic resonances are used Some cross-sections are even unmeasured or unmeasurable (especially for ρ and lack of data) General difficulties of the transport approach at high density: Off-shell effects Multi-particle collisions How can we avoid these problems? 13 / 3
Coarse Graining We take an ensemble of UrQMD events and span a grid of small space time cells. For those cells we determine baryon and energy density and use Eckart s definition to determine the rest frame properties use EoS to calculate T and µ B For the Rapp Spectral function, we also extract pion and kaon chemical potential via simple Boltzmann approximation At SIS, an equation of state for a free hadron gas without any phase transition is used [D. Zschiesche et al., Phys. Lett. B547, 7 ()] A Chiral EoS is used for the NA6 calculation (including chiral symmetry restoration and phase transition) [J. Steinheimer et al., J. Phys. G38 (11)] 14 / 3
Dilepton Rates Lepton pair emission is calculated for each cell of 4-dim. grid, using thermal equilibrium rates per four-volume and four-momentum from a bath at T and µ B. The ρ dilepton emission (similar for ω, φ) of each cell is accordingly calculated using the expression [R. Rapp, J. Wambach, Adv. Nucl. Phys. 5, 1 ()] d 8 N ρ ll d 4 xd 4 q = m 4 α ρ L(M ) π 3 gρ M f B (q ; T)ImD ρ (M, q; T, µ B ) The 4π lepton pair production can be determined from the electromagnetic spectral function extracted in e + e annihilation [Z. Huang, Phys. Lett. B361, 131 (1995)] d 8 N 4π ll d 4 xd 4 q = 4α (π) e q /T M 16π 3 α σ(e+ e 4π) QGP contribution is evaluated according to Cleymans et al. [J. Cleymans et al., Phys. Rev. D35, 153 (1987)] 15 / 3
Eletsky Spectral Function In-medium self energies of the ρ Σ ρ = Σ + Σ ρπ + Σ ρn were calculated using empirical scattering amplitudes from resonance dominance [V. L. Eletsky et al., Phys. Rev. C64, 3533 (1)] For ρn scattering N and resonances from Manley and Saleski Additional inclusion of the 13 and the N 15 subthreshold resonances Important, as they significantly contribute! 16 / 3
Rapp Spectral Function Includes finite temperature propagators of ω, ρ and φ meson [R. Rapp, J. Wambach, Eur.Phys.J. A6, 415-4 (1999)] Medium modifications of the ρ propegator D ρ 1 M m ρ Σ ρππ Σ ρm Σ ρb include interactions with pion cloud with hadrons (Σ ρππ ) and direct scatterings off mesons and baryons (Σ ρm, Σ ρb ) Pion cloud modification approximated by using effective nucleon density ρ eff = ρ N + ρ N +.5(ρ B + B ) 17 / 3
Previous Calculations Previous calculations were done with a fireball model [H. van Hees, R. Rapp, Nucl. Phys. A86, 339 (8)] The zone of hot and dense matter is described by an isentropic expanding cylindrical volume V FB (t) = π (r, + 1 ) a t (z + v z, t + 1 ) a zt Problem: How to choose parameters? Is it a plausible description or a too simple picture? Make calculations with better constrained input... 18 / 3
UrQMD Energy and Baryon Density as Input... ] and ρ/ρ Energy and baryon density [ε/ε ε/ε 1 Transversal density profile at T=1fm ρ/ρ 8 6 4 - -8-4 - 4 6 8 x-axis [fm] ] and ρ/ρ Energy and baryon density [ε/ε 1 Longitudinal density profile at T=5fm Central In+In @ 158 AGeV ε/ε ρ/ρ 8 6 4-8 -4-4 6 8 z-axis [fm] The UrQMD input we use gives a more and realistic and nuanced picture of the collision evolution Energy and baryon density are by no means homogeneous in the whole fireball Different expansion dynamics might lead to significantly differing dilepton spectra 19 / 3
Temperature and Chemical Potential from Coarse Graining Baryon Chemical Potential µ [MeV] B 1 8 6 4 In+In @ 158 AGeV (χ-eos) Au+Au @ 1.5 AGeV (HG-EoS) Temperature T [MeV] 5 15 5 In+In @ 158 AGeV (χ-eos) Au+Au @ 1.5 AGeV (HG-EoS) 4 6 8 1 14 16 18 Time t [fm] 4 6 8 1 14 16 18 Time t [fm] For a central cell in an Au+Au collision @ 1.5 AGeV we get very high µ B up to MeV and a maximum temperature of MeV For In+In at NA6 energy, the baryon density decreases very fast after the start of the collision, the temperature reaches a maximum of 3 MeV / 3
Au+Au @ 3.5 AGeV The UrQMD ρ contribution as well as the coarse-graining results for the vacuum and in-medium spectral functions are shown In-medium ρ melts away at the pole mass while it becomes dominant at lower masses )] dn/dm [1/(GeV/c 1-1 - -3-4 Au+Au @ 3.5 GeV UrQMD + in-medium / vacuum ρ from cells with T > 5 Mev vacuum ρ in-medium ρ UrQMD π η ρ ω Dalitz ω direct.1..3.4.5.6.7.8 M [GeV/c.9 ] 1 1 / 3
Ar + KCl @ 1.76 AGeV )] )dn/dm [1/(GeV/c - -3-4 Ar+KCl @ 1.76 GeV compared to HADES data in-medium ρ UrQMD π η ω Dalitz ω direct )] )dn/dm [1/(GeV/c - -3-4 Ar+KCl @ 1.76 GeV HADES filter in-medium ρ UrQMD π (1/N π (1/N -7-7 -8.1..3.4.5.6.7.8.9 1 M [GeV/c ] -8.1..3.4.5.6.7.8.9 1 M [GeV/c ] Comparison of Eletsky spectral funktion to existing HADES data shows that the in-medium ρ is dominated by the 13 contribution Still below the data for intermediate mass region / 3
Au + Au @ 1.5 AGeV )] dn/dm [1/(GeV/c Au+Au @ 1.5 GeV 1-1 - -3 UrQMD + Eletsky in-medium ρ In-med. ρ Vacuum ρ π η ω Dal ω dir φ Vacuum sum (incl. ) )] dn/dm [1/(GeV/c -1-3 Au+Au @ 1.5 GeV /η + Rapp Coarse-graining ρ UrQMD π from cells with T > 5 Mev Hadron Gas EoS /ω/φ π η ρ ω φ -4.1..3.4.5.6.7.8.9 1 + - e e Invariant Mass M [GeV/c ] -7.1..3.4.5.6.7.8 M [GeV/c.9 ] 1 Eletsky and Rapp spectral function agree quite well here The Dalitz-ω from the Rapp spectral function lies on the UrQMD result, while we don t see a significant (direct-)ω peak in the coarse-grained result 3 / 3
Looking at NA6 - Eletsky Spectral Function ] -1 /dy) [ MeV ch /dmdy)/(dn µµ (dn -7-8 -9 In+In @ 158 AGeV <dn ch /dy>=1, p > GeV T In-medium ρ QGP 4 pion Vacuum ρ (for comparison)..4.6.8 1 1. 1.4 Invariant Mass M [GeV/c ] In-medium ρ contribution (blue) to dimuon excess was calculated with the Eletsky spectral function for a chiral EoS 4π (orange) and QGP (green) contribution are included as well, they are negligible mostly at low masses, but dominate above 1 GeV Eletsky spectral function gives a good overall agreement, but can not describe the low-mass tail of the excess dimuons completely 4 / 3
Rapp Spectral Function for NA6 ] -1 /dy) [ MeV ch /dmdy)/(dn -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T χ-eos ρ ω φ QGP 4-Pion (dn µµ -8-9 -..4.6.8 1 1. 1.4 M [GeV] Calcuation for Rapp spectral function (with ρ, ω and φ included) and additional QGP and 4π contribution Fits the data quite well at the ρ pole mass, but is too low in the low mass tail 5 / 3
Comparison of EoS ] -1 /dy) [ MeV ch /dmdy)/(dn -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T χ-eos ρ ω φ QGP 4-Pion ] -1 /dy) [ MeV ch /dmdy)/(dn -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T HG-EoS ρ ω φ 4-Pion µµ (dn -8 µµ (dn -8-9 -9 -..4.6.8 1 1. 1.4 M [GeV] -..4.6.8 1 1. 1.4 M [GeV] With the Hadron Gas EoS we get a better agreement at low masses The lack of QGP lowers the result at high masses 6 / 3
Dependence on Baryon Density ] -1 /dy) [ MeV ch /dmdy)/(dn -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T χ-eos ρ eff =ρ B +ρ B ρ ω φ QGP 4-Pion ] -1 /dy) [ MeV ch /dmdy)/(dn -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T HG-EoS ρ eff =ρ B +ρ B ρ ω φ 4-Pion µµ (dn -8 µµ (dn -8-9 -9 -..4.6.8 1 1. 1.4 M [GeV] -..4.6.8 1 1. 1.4 M [GeV] An increase in baryon density (take ρ eff = ρ B + ρ B ) leads to a better description Baryons crucial for description of low mass tail 7 / 3
] Time evolution (t<.5fm) -1 /dy) [ MeV /dmdy)/(dn ch µµ -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T χ-eos t=-.5fm ρ ω φ QGP 4-Pion (dn -8-9 -..4.6.8 1 1. 1.4 M [GeV] The broadening is large at the beginning of the evolution, no peak at the ρ pole mass Same order of magnitude for QGP and in-medium ρ 8 / 3
] Time evolution (t<5fm) -1 /dy) [ MeV /dmdy)/(dn ch µµ -7 In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=1, p > GeV T χ-eos t=fm ρ ω φ QGP 4-Pion (dn -8-9 -..4.6.8 1 1. 1.4 M [GeV] Later the ρ dominates, shape of the spectrum is flatter, peak at pole mass evolves 9 / 3
Dileptons at RHIC dn/(dmdy) [c²/gev] 1-1 Au+Au @ GeV MinBias STAR Acceptance 4 pion QGP π η η' ρ ω Dalitz ω direct φ dn/(dmdy) [c²/gev] 1-1 Au+Au @ GeV MinBias STAR Acceptance Eletsky spectral function 4 pion QGP π η η' ρ ω Dalitz ω direct φ - - -3-3 -4-4..4.6.8 1 1. M [GeV]..4.6.8 1 1. M [GeV] Comparison between pure transport and transport + in-medium ρ from coarse-graining 3 / 3
Outlook Coarse-graining to be done at other energies and compared to further NA6, CERES, RHIC, LHC data [Rapp, Hees] [CERES Collab.] [STAR Collab.] Investigation of diffent equations of state Further dilepton calculations with hybrid model (transport + hydro) Using different input from transport (e.g. from GiBUU) 31 / 3
mary New approach to combine realistic transport caluclations with in-medium modified spectral functions for vector mesons Non-equilibrium treatment highly non-trivial Use equilibrium rates for a coarse-grained transport dynamics First calculations show that we get a good description of the invariant mass spectrum, the coarse-graining is applicable for all energy regimes Explanation of dilepton measurements is still a challenge for theory Need for more experimental input! Waiting for HADES Au+Au data and for the pion beam! Further work in progress...! 3 / 3