HADES versus DLS: no puzzle anymore ! Elena Bratkovskaya , Workshop ‚Bremsstrahlung in dilepton production‘ GSI, Darmstadt

10 years of DLS puzzle DLS-puzzle (since 1997): new (1997) DLS data for C+C and Ca+Ca at 1.04 A GeV are higher than the old (1995) DLS data by ~ a factor of 5-7 at 0.15<M<0.5 GeV new (1997) DLS data for C+C and Ca+Ca at 1.04 A GeV are higher than the old (1995) DLS data by ~ a factor of 5-7 at 0.15<M<0.5 GeV Transport models: Transport models:  good description of p+p and p+d data from 1 to 5 GeV  missing yield at 0.15 < M < 0.5 GeV for C+C and Ca+Ca at 1.04 A GeV ( similar results obtained by HSD ‘97, UrQMD’98 and Tübingen QMD‘03) 10 years of waiting for HADES …

A decade of search for the solution of the DLS puzzle Constraints on ,  by TAPS data: Constraints on ,  by TAPS data: HSD: good description of TAPS data on ,  multiplicities and m T -spectra => ,  dynamics under control ! Other channels:   accounting for in-medium effects (collisional broadening of vector meson spectral functions, dropping vector meson masses) does not provide enough enhancement at intermediate M  contribution from N(1520) (E.B.&C.M. Ko, PLB 445 (1999) 265) and higher baryonic resonances are small (cf. Gy. Wolf et al., PRC67 (2003) ) Also:  accounting for anisotropies in e+e- emission gives only a small effect HSD‘98

DLS versus HADES Experiment: No contradiction between DLS and HADES ! What about theory ?

Dileptons from transport models HSD HSD UrQMD 1.3 (1998) UrQMD 1.3 (1998) UrQMD 2.2 (2007) (Frankfurt) UrQMD 2.2 (2007) (Frankfurt) RQMD (Tübingen) RQMD (Tübingen) IQMD (Nantes) IQMD (Nantes) BRoBUU (Rossendorf) BRoBUU (Rossendorf)

HSD – Hadron-String-Dynamics transport approach HSD – Hadron-String-Dynamics transport approach for each particle species i (i = N, R, Y, , , K, …) the phase-space density f i follows the transport equations for each particle species i (i = N, R, Y, , , K, …) the phase-space density f i follows the transport equations with collision terms I coll describing: with collision terms I coll describing:  elastic and inelastic hadronic reactions: baryon-baryon, meson-baryon, meson-meson baryon-baryon, meson-baryon, meson-meson  formation and decay of baryonic and mesonic resonances  string formation and decay ( for inclusive particle production: BB  X, mB  X, X =many particles) BB  X, mB  X, X =many particles) implementation of detailed balance on the level of 1  2 implementation of detailed balance on the level of 1  2 and 2  2 reactions (+ 2  n multi-particle reactions in HSD) and 2  2 reactions (+ 2  n multi-particle reactions in HSD) off-shell dynamics for short-lived states off-shell dynamics for short-lived states Basic concept of HSD BB  B´B´, BB  B´B´m mB  m´B´, mB  B´ Baryons: B=(p, n, , N(1440), N(1535),...) Mesons: m=( , , 

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

Time integration method for dileptons   t0t0t0t0 t abs time FFFF  F – final time of computation in the code t 0 – production time t abs – absorption (or hadronic decay) time  e-e-e-e- e+  e-e-e-e- e+ ‚Reality‘: ‚Virtual‘ – time integ. method: only ONE e+e- pair with probability ~ Br(  ->e+e-)= Calculate probability P(t) to emit an e+e- pair at each time t and integrate P(t) over time!  : t 0 < t < t abs  : t 0 <t < infinity

The time integration method for dileptons in HSD  e-e-e-e- e+ Dilepton emission rate: FFFF Dilepton invariant mass spectra: 0 < t <  F time t 0 =0  F < t < infinity

NN bremsstrahlung - SPA Soft-Photon-Approximation (SPA): N N -> N N e + e -   - >e + e - Phase-space corrected soft-photon cross section: SPA implementation in HSD: e + e - production in elastic NN collision with probability: elasticNN ‚quasi- elastic‘ N N -> N N ‚off-shell‘ correction factor

NN bremsstrahlung: OBE-model OBE-model: N N -> N N e + e - ‚pre‘‚post‘ ‚post‘‚pre‘ + gauge terms charged meson exchange contact terms (from formfactors) The strategy to restore gauge invariance is model dependent! Kaptari&Kämpfer, NPA 764 (2006) 338

Bremsstrahlung – a new view on an ‚old‘ story 2007 (era of HADES): The DLS puzzle is solved by accounting for a larger pn bremsstrahlung !!! New OBE-model (Kaptari&Kämpfer, NPA 764 (2006) 338): pn bremstrahlung is larger by a factor of 4 than it has been pn bremstrahlung is larger by a factor of 4 than it has been calculated before (and used in transport calculations)! calculated before (and used in transport calculations)! pp bremstrahlung is smaller than pn, however, not zero; consistent with the 1996 calculations from de Jong in a T-matrix approach pp bremstrahlung is smaller than pn, however, not zero; consistent with the 1996 calculations from de Jong in a T-matrix approach

HSD: Dileptons from p+p and p+d - DLS bremsstrahlung is the dominant contribution in p+d for 0.15 < M < 0.55 GeV at ~1-1.5 A GeV bremsstrahlung is the dominant contribution in p+d for 0.15 < M < 0.55 GeV at ~1-1.5 A GeV

HSD: Dileptons from A+A at 1 A GeV - DLS bremsstrahlung and  -Dalitz are the dominant contributions in A+A for 0.15 < M < 0.55 GeV at 1 A GeV ! bremsstrahlung and  -Dalitz are the dominant contributions in A+A for 0.15 < M < 0.55 GeV at 1 A GeV !

Preliminary HADES data HSD: Dileptons from C+C at 1 and 2 A GeV - HADES HADES data show exponentially decreasing mass spectra HADES data show exponentially decreasing mass spectra Data are better described by in-medium scenarios with collisional broadening Data are better described by in-medium scenarios with collisional broadening In-medium effects are more pronounced for heavy systems such as Au+Au In-medium effects are more pronounced for heavy systems such as Au+Au

HSD: Dilepton p T and y spectra from C+C at 1 A GeV - HADES HSD predictions for p T and y spectra are in good agreement HSD predictions for p T and y spectra are in good agreement with the HADES data for all M-bins! with the HADES data for all M-bins! Preliminary HADES data

HSD: Dilepton p T and y spectra from C+C at 2 A GeV - HADES HSD predictions for p T and y spectra are in good agreement HSD predictions for p T and y spectra are in good agreement with the HADES data for all M-bins! with the HADES data for all M-bins! M<0.15 GeV/c 2 M>0.55 GeV/c <M<0.55 GeV/c 2 Preliminary HADES data

Bremsstrahlung in UrQMD 1.3 (1998) Ernst et al, PRC58 (1998) 447 Bremsstrahlung-UrQMD’98 smaller than bremsstrahlung-Kaptari’06 by a factor of 3-6 SPA: SPA implementation in UrQMD (1998): e + e - production in elastic NN collisions (similar to HSD)

Dileptons from pp and pd - UrQMD 1.3 Ernst et al, PRC58 (1998) 447 „old“ bremsstrahlung: missing yield for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV „old“ bremsstrahlung: missing yield for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV

Dileptons from A+A - UrQMD 1.3 Ernst et al, PRC58 (1998) 447 „old“ bremsstrahlung: missing yield for A+A at 0.15 < M < 0.55 GeV at 1 A GeV „old“ bremsstrahlung: missing yield for A+A at 0.15 < M < 0.55 GeV at 1 A GeV (consistent with HSD with „old SPA“)

Dileptons from A+A - UrQMD 2.2 (2007) D. Schumacher, S. Vogel, M. Bleicher, Acta Phys.Hung. A27 (2006) 451 NO bremsstrahlung in UrQMD 2.2

Dileptons from pp and pd - RQMD (Tübingen) C. Fuchs et al., Phys. Rev. C (2003) NO bremsstrahlung: missing yield for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV NO bremsstrahlung: missing yield for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV

Dileptons from A+A - RQMD (Tübingen) C. Fuchs et al., Phys. Rev. C (2003) NO bremsstrahlung in RQMD NO bremsstrahlung in RQMD too strong  Dalitz contribution (since no time integration?) too strong  Dalitz contribution (since no time integration?) HADES - RQMD‘07 DLS - RQMD‘03 1 A GeV

Bremsstrahlung in IQMD (Nantes) M. Thomere, C. Hartnack, G. Wolf, J. Aichelin, PRC75 (2007) SPA implementation in IQMD (?): e + e - production in each NN collision (i.e. elastic and inelastic) !? - differs from HSD and UrQMD’98 (only elastic NN collisions are counted!) HADES: C+C, 2 A GeV

Bremsstrahlung in BRoBUU (Rossendorf) H.W. Barz, B. Kämpfer, Gy. Wolf, M. Zetenyi, nucl-th/ SPA implementation in BRoBUU (?): e + e - production in each NN collision (i.e. elastic and inelastic) ! - similar to IQMD (Nantes)

Test in HSD: bremsstrahlung production in NN collisions (only elastic vs. all) In HSD assume: e + e - production from „old“ SPA bremsstrahlung in each NN collision (i.e. elastic and inelastic reactions) => can reproduce the results by Gy. Wolf et al., i.e. IQMD (Nantes) and BRoBUU (Rossendorf) !

Summary: Bremsstrahlung in transport models Transport models give similar results ONLY with the same initial input ! => REQUESTS: „unification“ of the treatment of dilepton production in transport models: Similar cross sections for elementary channels Similar cross sections for elementary channels Time-integration method for dilepton production Time-integration method for dilepton production Off-shell treatment of broad resonances Off-shell treatment of broad resonances+ Consistent microscopic calculations for e + e - bremsstrahlung from NN and mN collisions! We need: clear separation of the individual contributions in a form applicable in transport codes, e.g. many-dimensional matrix (or parametrization) for d  /dMdydp T (s,M,y,p T )

Summary HADES succeeded: the DLS puzzle is solved ! Outlook: need new pp and pd data from HADES for a final check!