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Propagation of Spectral Functions and Dilepton Production

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

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Propagation of Spectral Functions and Dilepton Production

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  1. 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. The Hydro Picture • ignore pre-equilibrium • - sum contributions over space + time till f.o.*) • - add free decays after f.o. (hadronic cocktail) Wightman fnct ret. Green fnct *) only local equilibrium emissivities are needed schematic hydro: T(t), n(t)

  3. GMOR or a la BR or Joffe Old Dream fireball evolution for SIS18 Eur.Phys.J. A17 (2003) 83-87 • caveat: • riding on a • steep bckg • disappearence of the signal f.o.

  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. BUU Transport Code propagation of broad resonances test particles Kadanoff-Baym  Cassing-Juchem, Leupold (2000) ansatz

  6. The Open Nuclear & Particle Physics Journal 3 (2010) 1, arXiv 0910.1541, nucl-th/0605036, Barz et al. Spectral Functions: extreme mass shifts

  7. Mass Evolution toward Freeze Out red: time instant of disappearence

  8. tiny in-medium effects (even with extreme paramerters)

  9. Prediction: Au + Au postdictions: C+C (1.04 AGeV - DLS, 1 AGeV – HADES)

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

  11. Kwon, Procura, Weise PRC (2008): QCD sum rules: hadron spectral moments  QCD condensates (n,T), Landau center of gravity maximum flatness in Borel window num. irrelevant Hatsuda, Lee PRC (1992):

  12. 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)

  13. rho Meson and a Schematic VOC Scenario 2 (vanishing of chirally odd condenstates: VOCOC = V(OC)  VOC) chiral restoration: <q q>  0 (large density/temperature) vac spectral moment VOC

  14. vacuum: parameterize the spectral function data: ALEPH (2005),  consistent QCD sum rule result

  15. VOC vac keep width keep peak improvement of Leupold, Peters, Mosel NPA (1998)

  16. NA60 VOC VOC: minimum scenario of chiral restoration  broadening as signal of chiral restoration disclaimer: at chiral restoration more can happen much less influence of VOC

  17. Chiral Partners Hohler, Rapp, Nucl.Phys. A892 (2012) 58 chiral transf. with open charm chiral QCD sum rules Hilger, BK, Leupold PRC (2011) Wigner‘s nondegeneracy splitting of spectral densities between chiral partners must be driven by order parameters of spontaneous chiral symmetry breaking only

  18. the case of V-A r.h.s.: „order parameters“ of chiral symm. breaking Hayashigaki, Terasaki 0411285 Reinders, Rubinstein, Yazaki PR (1985) vacuum: 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 Hilger, Buchheim, BK, Leupold PPNP(2012):

  19. 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

  20. Example 1: only dilaton  medium bottom-up approach: EoS (lattice QCD)  dilaton potential ansatz: Gubser type pot. + polynom. distortions

  21. lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184

  22. benefit: w/o further input  spectral functions  transport coefficients not universal (as, e.g. sheary viscosity/entropy) but sensitive dependence on pot. parameters

  23. Example 2: meson in vector channel Abelian field strength of V soft-wall model: AdS/QCD, soft-wall model, Cui. Takeuchi, Wu, 1112.5923 (T in GeV) mass shift JHEP 1204 (2012) 144

  24. Schwarzschild BH  Reissner-Nordstrom BH: chem. pot. AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076 mass shift + broadening vision: beyond soft-wall ansatz  dilaton consistent with EoS problem: missing unique QCD results with quarks

  25. 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?

  26. q qbar production by chiral mass shift m(t) Michler et al., arXiv:1208.6565

  27. Dynamical Schwinger Effect tG = 10 Blaschke, BK, Schmidt, Panferov, Prozorkevich, Smolyansky. arXiv:1301.1640 E(t) = E0 sin (νt) exp (−t^2/tG^2 )

  28. 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

  29. p Width of Strangeonium proposed by Hernandez, Oset, ZPA (1992) BUU PLB (2011)

  30. e+ e- V in Valencia – Paryev models: Oset, Cabrera,... prediction of broadening: Klingl, Wass, Weise, PLB (1998) analog in omega and phi photo-production CLAS, PRL (2011) CBELSA-TAPS PRL (2008) Spring-8: Ishikawa et al., PLB (2005) CLAS PRL (2010)

  31. ANKE data: Phys.Rev. C85 (2012) 035206 BRoBUU: H. Schade

  32. ANKE PRC (2012) BUU: H. Schade mystery: phi phase space p cms(pN) A y stopping power of nuclear matter

  33. Hot/Dense Medium in AdS/CFT 1998: Maldacena, Gubser, Klebanov, Polyakov Witten class. gravity in 5D decoupled in strong-coupling limit asymptotically AdS + black brane  thermo field theory: hQCD 5D gravity setting: Riemann-Hilbert + scalar field graviton dilaton

  34. condensate = vacuum + density dep. part GOR lattice sigma term > QCD trace anomaly scalar charmonium Narison fac. hyp. fac. hyp. q density twist-2 DIS pdf DIS pdf twist-3 pdf DIS pdf GLS SR if real condensate: couples to gravity

  35. OBE sides: medium effects vac med.  significant medium effects vac elaboration of hadronic sides for light-light mesons med. Kapusta, Shuryak PRD (1994) Hohler, Rapp, Nucl.Phys. A892 (2012) 58

  36. AdS/CFT Emissivities Baier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) 081901, JHEP 1207 (2012) 094 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

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