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Density Dependence of Condensates (Medium Modifications of Hadrons). B. Kämpfer. Research Center Dresden-Rossendorf Technical University Dresden. * in preparation. with R. Thomas, Th. Hilger. Hadrons = Excitations of QCD Ground State. QCD ground state (vacuum). n,T .
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Density Dependence of Condensates (Medium Modifications of Hadrons) B. Kämpfer Research Center Dresden-Rossendorf Technical University Dresden * in preparation with R. Thomas, Th. Hilger
Hadrons = Excitations of QCD Ground State QCD ground state (vacuum) n,T
UniversalMaterial Constants of Vacuum? dil. symm. break. symm. break. (spont.), o.p. Condensates, Monopoles, Instantons, Vortices, ... vacuum =
Medium in Dilute Gas Approx.
Expansion not à la Taylor but Wilson: OPE Wilson coeff. quark& gluon operators Observables:
QCD Sum Rules à la Borel condensates Landau damp. pert. term Borel 4-quark condensates (factorization fails)
CB-TAPS: Trnka et al. ´05
Zschocke, Pavlenko, BK PLB ´03 also dim-8 contributions norm. moment Thomas/Zschocke/BK PRL ´05 strong density dependence of combined 4-quark conds.: chirally invariant otherwise: Landau damping term would push up the mass
Book Keeping of 4-Quark Condensates a la Klingl & Weise 1. flavor-pure NPA 2007 by Fierz:
w/o color (1 ... 10) w/ color nucleon: no inverse pure flavor conds.: (1‘ ... 10‘) componets not indep. relations exist between 4-q conds. (not accurately fulfilled in models) Tuebingen chiral quark model : approx. fulfilled
2. flavor mix NPA 2007 all together: vacuum: 2•5 +10 = 20 medium: 2•10+24 = 44 flavor symmetry: 10 (20)
4-q conds. for nucleon 4-q conds. for V interpolating current: Fierz Joffe: t = -1
4-q cond. = order parameter of chiral symmetry? example: nucleon in vacuum chirally invariant: chirally non-invariant: vacuum: Jido ´96
Ansatz: l.h.s=
3 indep. sets of combinations of 4-q conds. enter
phenomenological point of view
Scheinast et al. PRL 2006 magnifier 2000 2001 D in medium: Weise/Morath, Hayashigaki expected pattern: hadron scenario Lutz, Korpa 2005: w/o inel. w/ inel.
basic features (Weise,Morath 2001): Pole + Continuum Ansatz w/o change of continuum
Weise/Morath ... ´99: tiny in-medium effects Generalis/Broadhurst ´84: medium resistent OPE: operator mixing
CB-TAPS & Borel QSR: 1. Conclusions strong in-medium change of 4q cond. 4q cond. = new order parameter? 2. N: 4q conds. vs. phenomenlogy 3. D: Sensors for QCD vaccum Quantify change of QCD vacuum: nB, T dependence of material constants hadron masses condensates
Limitations of usual QCDSR even/odd parts: isolating lowest states neg. energy
Tlab = 25 AGeV Chem. Freeze-Out Cleymans-Redlich-Wheaton param. Fuchs et al.: T > 100 MeV meson effects Leupold: 4-q cond. vs. nB, T
Spec. Function [GeV^-2] E [GeV] 1.6 2.0 = center of gravity of pole ansatz is not appropriate: D+ Lutz, Korpa pole + continuum ansatz
How to Measure Med.-Mod. of D Mesons? K- FAIR: CBM PANDA D0 pi+ lesson from K: measure multiplicity of D Tsushima, Sibirtsev, Friman, Lee,...
3. ss sector: ? strangeness in nucleon? OZI rule
Case of Strangeness: K 2.5 GeV Au (1 AGeV) + Au BUU Uhlig et al. (KaoS) PRL 2005 Scheinast at al. (KaoS) PRL 2006
Case of Di-Electrons A QCD sum rules CB-TAPS Rossendorf BUU model
e+ e- Understanding Hadron Masses Stark Zeeman nuclear matter = external field Brown & Rho (1991): search by HADES ... sensors for QCD vacuum?
e+ e- Nucleus as Laboratory HADES KEK CLAS no FSI: direct probes V. Metag & U. Mosel CB-TAPS @ ELSA FSI