1. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 1 B. Kampfer I Institute of Radiation Physics I www.hzdr.de Propagation of Spectral Functions and Dilepton Production (Imprints of Chiral Restoration on Dielectron Spectra) B. Kämpfer Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden Changes of hadron properties in medium carry signals of the way in which the vacuum changes in a nuclear environment W. Weise, NPA 574 (1994) 347c - the hydro picture: local equilibrium - kinetic approach: BRoBUU - rho meson: VOC - AdS/QCD: emissivities and spectral fncts - theory: making particles, e.g. e+ e-

2. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 2 The Hydro Picture - ignore pre-equilibrium - sum contributions over space + time till f.o.*) - add free decays after f.o. (hadronic cocktail) *) only local equilibrium emissivities are needed Wightman fnct ret. Green fnct schematic hydro: T(t), n(t)

3. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 3 Old Dream GMOR or a la BR or Joffe fireball evolution for SIS18 Eur.Phys.J. A17 (2003) 83-87 caveat: riding on a steep bckg  disappearence of the signal f.o.

4. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 4 Kinetic Approaches: Transport Models - evolve distribution functions in space + time - species are coupled via coll. terms + decays (problems: detailed balance, cross sections) - mean field(s) included - propagate spectral functions many realizations are at our disposal (Frankfurt, Giessen, Tubingen,...) here: BRoBUU = derivate of Giessen evolved by Barz, Wolf, Zetenyi, Schade „much room for improvements“

5. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 5 BUU Transport Code propagation of broad resonances Kadanoff-Baym  Cassing-Juchem, Leupold (2000) test particles ansatz

6. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 6 The Open Nuclear & Particle Physics Journal 3 (2010) 1, arXiv 0910.1541, nucl-th/0605036, Barz et al.0910.1541nucl-th/0605036 Spectral Functions: extreme mass shifts

7. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 7 Mass Evolution toward Freeze Out red: time instant of disappearence

8. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 8

9. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 9 tiny in-medium effects (even with extreme paramerters)

10. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 10

11. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 11 Prediction: Au + Au postdictions: C+C (1.04 AGeV - DLS, 1 AGeV – HADES)

12. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 12 QCD Sum Rules: Predictions of Medium Modifications? (i)as solution of integral eq. (Fredholm 1): too scarce information on OBE side (ii) MEM: (iii) moments: mean (= center of gravity) – OK variance (= width) skewness (= deformation) kurtosis (= up/down shot) too large gap in powers of M (iv) insert hadronic model (v) pole + continuum ansatz truncate: i < 6 (8, 12) Titov, BK, PRC (2007) Kwon, Weise, PRC (2010): another hierarchy+chiral gap Gubler, Morita, Oka, PRL (2011)

13. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 13 QCD sum rules: hadron spectral moments  QCD condensates (n,T), Landau Kwon, Procura, Weise PRC (2008): num. irrelevant Hatsuda, Lee PRC (1992): center of gravity maximum flatness in Borel window

14. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 14 chiral transformations VOC: keep even conds., but set odd conds. to zero Bordes, Dominguez, Pennarrocha, Schilcher JHEP (2006): reconstruct from QCD sum rule Hilger, Thomas, BK, Leupold PLB (2012)

15. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 15 rho Meson and a Schematic VOC Scenario (vanishing of chirally odd condenstates: VOCOC = V(OC)  VOC) chiral restoration:  0 (large density/temperature) vac VOC 2 spectral moment

16. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 16 vacuum: parameterize the spectral function  consistent QCD sum rule result data: ALEPH (2005),

17. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 17 VOC vac keep width keep peak improvement of Leupold, Peters, Mosel NPA (1998)

18. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 18 VOC: minimum scenario of chiral restoration  broadening as signal of chiral restoration disclaimer: at chiral restoration more can happen VOC much less influence of VOC NA60

19. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 19 Chiral Partners chiral transf. with open charm Hilger, BK, Leupold PRC (2011) chiral QCD sum rules splitting of spectral densities between chiral partners must be driven by order parameters of spontaneous chiral symmetry breaking only Wigner‘s nondegeneracy HohlerHohler, Rapp, Nucl.Phys. A892 (2012) 58 Rapp

20. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 20 the case of V-A in contrast to Weinberg‘s sum rules: no Goldstone properties on r.h.s. (qQ currents are not conserved) heavy quark symmetry: degeneracy of V – P, A - S vacuum: Hayashigaki, Terasaki 0411285 Reinders, Rubinstein, Yazaki PR (1985) r.h.s.: „order parameters“ of chiral symm. breaking Hilger, Buchheim, BK, Leupold PPNP(2012):

21. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 21 AdS/QCD 5D Riemann: x,z 4D Minkowski: x semi-class. gravity strongly coupled gauge theo. X(x, z) gauge-inv. Operators (x) asymp. AdS black brane: T (Hawking) s (Bekenstein) semi-class. functional correlation functions breaking conf. sym. by mass scale, e.g. dilation + potential

22. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 22 Example 1: only dilaton  medium bottom-up approach: EoS (lattice QCD)  dilaton potential ansatz: Gubser type pot. + polynom. distortions

23. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 23 lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184

24. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 24 benefit: w/o further input  spectral functions  transport coefficients not universal (as, e.g. sheary viscosity/entropy) but sensitive dependence on pot. parameters

25. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 25 AdS/QCD, soft-wall model, Cui. Takeuchi, Wu, 1112.5923 (T in GeV) JHEP 1204 (2012) 144 Example 2: meson in vector channel Abelian field strength of V soft-wall model: mass shift

26. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 26 AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076 Schwarzschild BH  Reissner-Nordstrom BH: chem. pot. vision: beyond soft-wall ansatz  dilaton consistent with EoS problem: missing unique QCD results with quarks mass shift + broadening

27. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 27 e+ e- Production: Theory coupling to an external field/environment  particle production - gravitation: cosmic expansion (Basler, BK 1990) - homog. E(t) field: dyn. Schwinger effect - E = const field: Schwinger effect - m(t) due to chiral restoration (Greiner et al. 1995, 1996, 2012) mimicks E(t), looks like dyn. Schwinger effect, non-Markovian process problem: what are particles, quasi-particles, out-states?

28. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 28 q qbar production by chiral mass shift m(t) Michler et al., arXiv:1208.6565arXiv:1208.6565

29. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 29 BlaschkeBlaschke, BK, Schmidt, Panferov, Prozorkevich,SchmidtPanferovProzorkevich Smolyansky Smolyansky. arXiv:1301.1640arXiv:1301.1640 E(t) = E0 sin (νt) exp (−t^2/tG^2 ) tG = 10 Dynamical Schwinger Effect

30. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 30 Summary Medium changes of condensates (should) drive medium modifications of hadrons difficult to identify rho, omega mass shifts (if there are any) in AA via inv. e+e- mass spectra (BRoBUU) QCD sum rules: no direct link to shape of hadron spect. fncts. Landau term vs. density effects in condensates omega: significant density dependence of 4q conds. needed to balance Landau damping term Thomas, Hilger, BK PRL 2005 chiral sum rules most favorable dream: AdS/CFT correspondence  AdS/QCD: EoS, transport coeff. + hadrons

31. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 31 BUU Width of Strangeonium p proposed by Hernandez, Oset, ZPA (1992) PLB (2011)

32. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 32 in Valencia – Paryev models: analog in omega and phi photo-production CLAS, PRL (2011) CLAS PRL (2010) CBELSA-TAPS PRL (2008) prediction of broadening: Klingl, Wass, Weise, PLB (1998) Spring-8: Ishikawa et al., PLB (2005) V e+ e- Oset, Cabrera,...

33. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 33 ANKE data: Phys.Rev. C85 (2012) 035206 BRoBUU: H. Schade

34. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 34 ANKE PRC (2012) BUU: H. Schade mystery: phi phase space stopping power of nuclear matter p A cms(pN) y

35. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 35 Hot/Dense Medium in AdS/CFT 1998: Maldacena, Gubser, Klebanov, Polyakov Witten class. gravity in 5D asymptotically AdS + black brane  thermo field theory: hQCD 5D gravity setting: Riemann-Hilbert + scalar field gravitondilaton decoupled in strong-coupling limit

36. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 36 condensate = vacuum + density dep. part q density sigma term QCD trace anomaly GOR lattice charmonium scalar twist-2DIS pdf GLS SR fac. hyp. twist-3 pdf fac. hyp. > Narison if real condensate: couples to gravity

37. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 37 OBE sides: medium effects  significant medium effects Kapusta, Shuryak PRD (1994) elaboration of hadronic sides for light-light mesons vac med. vac med. HohlerHohler, Rapp, Nucl.Phys. A892 (2012) 58 Rapp

38. B. Kampfer I Institute of Radiation Physics I www.hzdr.de Member of the Helmholtz Association page 38 AdS/CFT Emissivities BaierBaier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) 081901, JHEP 1207 (2012) 094StrickerTaanilaVuorinen at T > 200 MeV, one obtains the thermalization time scale ~ 0.1 fm/c, which one might compare with the typical production time of dileptons with mass/energy larger than 5 GeV, tau_p < 0.04 fm/c. It appears that dilepton pairs produced early on have a reasonable chance to escape the system while it is still out of thermal equilibrium.  problem of particle production in dynamical systems