Dilepton Production from Coarse-grained Transport Dynamics Stephan Endres (in collab. with M. Bleicher, H. van Hees, J. Weil) Frankfurt Institute for Advanced Studies ITP Uni Frankfurt ECT* Trento Workshop Electromagnetic Probes May 3rd, 013 1 / 8
Overview 1 Introduction Transport Calculations and their Difficulties 3 New Approach: Coarse Grained Transport 4 First Results 5 Outlook / 8
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 / 8
The Transport Status Quo Transport models can describe dilepton production at low energies rather good nowadays There has been a lot of improvement, especially concerning the exact comparison and adjustment of the many parameters, cross-sections, branching ratios ( Janus Weil s talk) However, this is a hard job and one has to be careful Still the models show differences, and for some parameters we just have no constraints and we can just make dσ/dm ee [µb/gev] 1 0-1 - 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 assumptions. -3 0 0. 0.4 0.6 0.8 1 dilepton mass m ee [GeV] 4 / 8
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 150 ) No explicit in-medium modifications! 5 / 8
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)? 6 / 8
Room for improvements We see an excess in heavy-ion collisions (e.g. Ar+KCl @ 1.76 AGeV) not yet described by the model Recent HADES measurements indicate that our ρ 0 crosssection is too high at the threshold )] )dn/dm [1/(GeV/c π 0 (1/N - -3-4 Ar+KCl @ 1.76 AGeV HADES Acceptance > 9, 0.1 < p < 1.1 GeV/c θ ee e π 0 η ρ 0 ω Dalitz ω direct Sum σ [mb] 1-1 UrQMD 0 p+p ρ +X 0 p+p ρ +p+p Data 0 p+p ρ +X 0 p+p ρ +p+p - -8 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M [GeV/c ] -3 1 s [GeV] 7 / 8
Challenges Cross-section 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 At high energies the resonance models get into trouble anyhow How can we avoid these problems? 8 / 8
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 (00)] A Chiral EoS is used for the NA60 calculation (including chiral symmetry restoration and phase transition) [J. Steinheimer et al., J. Phys. G38 (011)] 9 / 8
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 (000)] d 8 N ρ ll d 4 xd 4 q = m 4 α ρ L(M ) π 3 gρ M f B (q 0 ; 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 0/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)] / 8
Eletsky Spectral Function In-medium self energies of the ρ Σ ρ = Σ 0 + Σ ρπ + Σ ρn were calculated using empirical scattering amplitudes from resonance dominance [V. L. Eletsky et al., Phys. Rev. C64, 035303 (001)] For ρn scattering N and resonances from Manley and Saleski Additional inclusion of the 13 and the N 150 subthreshold resonances Important, as they significantly contribute! 11 / 8
Rapp Spectral Function Includes finite temperature propagators of ω, ρ and φ meson [R. Rapp, J. Wambach, Eur.Phys.J. A6, 415-40 (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 + 0.5(ρ B + B ) 1 / 8
Densities, Temperature and Chemical Potential and ε/ε 0 ρ/ρ 0 16 14 1 Au+Au @ 3.5 AGeV energy and baryon density at x=y=z=0 ρ/ρ 0 ε/ε 0 [MeV] T and µ 100 00 B 800 Au+Au @ 3.5 AGeV T and µ at x=y=z=0 B µ T B 8 600 6 400 4 00 0 4 6 8 1 14 16 18 0 t [fm] 0 4 6 8 1 14 16 18 0 t [fm] For a central cell in an Au+Au collision @ 3.5 AGeV we get up to 15 times ɛ 0 and times ρ 0 Temperature T 140 MeV and baryon chemical potential µ B 800 MeV 13 / 8
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 > 50 Mev vacuum ρ in-medium ρ UrQMD π η 0 ρ 0 ω Dalitz ω direct 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 M [GeV/c 0.9 ] 1 14 / 8
Ar + KCl @ 1.76 AGeV )] )dn/dm [1/(GeV/c - -3-4 Ar+KCl @ 1.76 GeV compared to HADES data in-medium ρ Sum UrQMD π 0 η ω Dalitz ω direct )] )dn/dm [1/(GeV/c - -3-4 Ar+KCl @ 1.76 GeV HADES filter in-medium ρ UrQMD π 0 (1/N π 0 (1/N -8 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M [GeV/c ] -8 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 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 15 / 8
Au + Au @ 1.5 AGeV )] dn/dm [1/(GeV/c -1-3 Au+Au @ 1.5 GeV UrQMD + Eletsky in-medium ρ from cells with T > 50 Mev π 0 η ω Dal ω dir φ 0 IM ρ Sum )] dn/dm [1/(GeV/c -1-3 Au+Au @ 1.5 GeV 0 /η + Rapp Coarse-graining ρ UrQMD π from cells with T > 50 Mev Hadron Gas EoS 0 /ω/φ π 0 η ρ 0 ω φ Sum 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 M [GeV/c 0.9 ] 1 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 M [GeV/c 0.9 ] 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 16 / 8
Looking at NA60 - Eletsky Spectral Function ] -1 /dy) [0 MeV ch /dmdy)/(dn µµ (dn -8-9 - In+In @ 158 AGeV In-medium ρ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T 0 0. 0.4 0.6 0.8 1 1. 1.4 M [GeV] In-medium ρ contribution (orange) to dimuon excess was calculated with the Eletsky spectral function for a chiral EoS 4π (blue) 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 17 / 8
Rapp Spectral Function for NA60 ] -1 /dy) [0 MeV ch /dmdy)/(dn In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T χ-eos ρ ω φ QGP 4-Pion Sum (dn µµ -8-9 - 0 0. 0.4 0.6 0.8 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 18 / 8
Comparison of EoS ] -1 /dy) [0 MeV ch /dmdy)/(dn In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T χ-eos ρ ω φ QGP 4-Pion Sum ] -1 /dy) [0 MeV ch /dmdy)/(dn In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T HG-EoS ρ ω φ 4-Pion Sum µµ (dn -8 µµ (dn -8-9 -9-0 0. 0.4 0.6 0.8 1 1. 1.4 M [GeV] - 0 0. 0.4 0.6 0.8 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 19 / 8
Dependence on Baryon Density ] -1 /dy) [0 MeV ch /dmdy)/(dn In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T χ-eos ρ eff =ρ B +ρ B ρ ω φ QGP 4-Pion Sum ] -1 /dy) [0 MeV ch /dmdy)/(dn In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T HG-EoS ρ eff =ρ B +ρ B ρ ω φ 4-Pion Sum µµ (dn -8 µµ (dn -8-9 -9-0 0. 0.4 0.6 0.8 1 1. 1.4 M [GeV] - 0 0. 0.4 0.6 0.8 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 0 / 8
] Time evolution (t<.5fm) -1 /dy) [0 MeV /dmdy)/(dn ch µµ In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T χ-eos t=0-.5fm ρ ω φ QGP 4-Pion Sum (dn -8-9 - 0 0. 0.4 0.6 0.8 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 1 / 8
] Time evolution (t<5fm) -1 /dy) [0 MeV /dmdy)/(dn ch µµ In+In @ 158 AGeV In-medium ρ/ ω/ φ + QGP + 4π <dn ch /dy>=10, p > 0 GeV T χ-eos t=0fm ρ ω φ QGP 4-Pion Sum (dn -8-9 - 0 0. 0.4 0.6 0.8 1 1. 1.4 M [GeV] Later the ρ dominates, shape of the spectrum is flatter, peak at pole mass evolves / 8
Outlook Careful adjustment of dilepton production in UrQMD, especially via the ρ channel (necessary for hybrid calculations) Coarse-graining to be done at other energies and compared to further NA60, 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) 3 / 8
Summary 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 Waiting for HADES Au+Au data and for the pion beam! Further work in progress...! 4 / 8
Backup Slides 5 / 8
Dilepton sources in UrQMD Dalitz Decays π 0, η, η, ω, P γ + e + e V P +e + e Direct Decays ρ 0, 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 (VMD. Assumption: Resonance can continuously emit dileptons over its whole lifetime (Time Integration Method / Shining ) 6 / 8
(13) Resonance in UrQMD In UrQMD mass dependent widths are used, but the lifetime is massindependent τ=1/γ(m pole ) to avoid unphysically high lifetimes for low masses Now: We use mass-dependent (partial) width: Γ i,j (M) = Γ i,j M pole pole M Still differences between transport models (parametrizations, cross-sections, form factors... 7 / 8
t t t t Example: p t Spectra for p + p @ 3.5 GeV [mb/(gev/c)] dσ/dp -1 - -3-4 p+p @ 3.5 GeV M ee < 0.15 GeV/c HADES Acceptance > 9, 0.08 < p <.0 GeV/c θ ee e π 0 η ρ 0 ω Dalitz ω direct Sum [mb/(gev/c)] dσ/dp - -3-4 0.15 < M ee < 0.47 GeV/c 0 0. 0.4 0.6 0.8 1 p [GeV/c] t 0 0. 0.4 0.6 0.8 1 p [GeV/c] t [mb/(gev/c)] -4 0.47 < M ee < 0.70 GeV/c [mb/(gev/c)] 4 1 -Contribution for p+p @ 3.5 GeV mass-dependent lifetime (for M > pole mass) mass-independent lifetime M ee < 0.15 GeV/c² 4 (x ) 0.15 < M ee < 0.47 GeV/c² (x ) 0.47 < M ee < 0.70 GeV/c² dσ/dp dσ/dp - -4 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 p [GeV/c] t -8 0 0. 0.4 0.6 0.8 1 p [GeV/c] t Transverse momentum spectra at 3.5 GeV are described well with new (and were completely overshooting before) 8 / 8