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In-Medium Studies of Omega, Nucleon and Open Charm with QCD Sum Rules

In-Medium Studies of Omega, Nucleon and Open Charm with QCD Sum Rules. Ronny Thomas. Forschungszentrum Dresden-Rossendorf / TU Dresden. Dresden, September 2007. In-Medium Modification of Hadrons:  , N, D QCD Sum Rules Four-Quark Condensates.

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In-Medium Studies of Omega, Nucleon and Open Charm with QCD Sum Rules

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  1. In-Medium Studies of Omega, Nucleon and Open Charm with QCD Sum Rules Ronny Thomas Forschungszentrum Dresden-Rossendorf / TU Dresden Dresden, September 2007 • In-Medium Modification of Hadrons: , N, D • QCD Sum Rules • Four-Quark Condensates work with T. Hilger, S. Zschocke and B. Kämpfer supported by BMBF, GSI, EU, Helmholtz

  2. Universal CONDENSATES , … ? |  temperature > 0 density > 0 QCD Sum Rules QCD vacuum In-Medium Modifications Analogy: Stark & Zeemann effects

  3. Chiral condensate Gluon condensate Zschocke et al (2002) (PCAC) Trace anomaly Mixed quark-gluon condensate Catalog of four-quark condensates …

  4. „in-medium“ Nb (A=93)       0 0   LH2 (A=1)    in medium CB-TAPS  + A→ A‘ +  (→ 0 +  ) Trnka, Metag et al, PRL (2005) First moment: First moment • implies strong density dependence of specific four-quark condensate combinations RT, Zschocke, Kämpfer, PRL (2005) • change of QCD vacuum … Brown-Rho scaling ( In-medium shift  HADES)

  5. QCD Sum Rules Shifman, Vainshtein, Zakharov (1979)  meson: Current-current correlator Dispersion Relation Operator Product Expansion (OPE) Hadronic side Next talk: T. Hilger Aspects of the OPE

  6. Twice subtracted, Borel transformed dispersion relation Operator product expansion Wilson coefficients x CONDENSATES Ci small larger FOUR-QUARK CONDENSATES

  7. Catalog of Four-Quark Condensates time, parity reversal invariance, … One flavor: FIERZ Vacuum: 5 Medium: 5+5 no inverse:  nucleon Two flavors: but implies relations: Vacuum: 2•5 +10 = 20 Medium: 2•10+24 = 44 → flavor symmetry: 10 (20)

  8. med 1 0 2 4 n / n0 1 Four-Quark Condensates Factorization and beyond: Chiral Symmetry: invariant → order parameter not V-A not invariant  invariant N (vacuum) invariant

  9. Nucleon in medium RT, Hilger, Kämpfer, NPA (2007) condensates Weighted dispersion relation condensates moments: Parametrization of hadronic side: →Sum rules in pole ansatz: Furnstahl, Griegel, Cohen, PRC (1992)

  10. Analysis: Nucleon in medium four-quark condensates 3 coupled sum rule equations: * Drukarev et al, PRD (2003) ** Plohl, Fuchs, PRC (2006)

  11. Scalar self-energy Numerical impact of density dependence of combined four-quark condensates: Vector self-energy

  12. N Vector, scalar self-energies Analytical estimates: Example for fine-tuned set opposite effects In-medium Ioffe approximation:

  13. Comparison:  in medium Zschocke, Pavlenko, Kämpfer, PLB (2003)

  14. Morath, Weise (2001) Hayashigaki (2000) ~ - ( 0 … 50 ) MeV ~ 30 … 50 MeV at saturation density ? Zschocke (2005) Open Charm: D CBM and PANDA @ FAIR D+ similar to K- - 80 MeV at saturation density Scheinast et al (KaoS), PRL (2006) D-,K+dc, us D meson in medium: D+,K-dc, us

  15. Example of Operator Product Expansion for D-meson: amplifier mixing of QCD condensates under renormalization (Diploma thesis T. Hilger)

  16. Conclusion • catalog of four-quark condensates • combinations of in-medium four-quark condensates:  → strong density dependence N → some density dependence • different sum rules → no factorization of combined four-quark condensates → combinations like e.g. may serve as further order parameters of chiral symmetry breaking • further hadrons probe other condensates: D → CBM, PANDA Modified QCD vacuum

  17. : Nucleon • interpolating field not unique • inclusion of derivatives Braun, Schäfer et al, PLB (1993) t = -1 Ioffe interpolating field: ci: (for vacuum)

  18. Nucleon in vacuum Chiral condensate full QSR

  19. QCD Sum Rules: 3 equations

  20. ← small impact 3 coupled sum rule equations weak density dependence of specific four-quark condensate combinations Gross-Boelting, Fuchs, Fäßler, NPA (1999) Drukarev, Fäßler et al, PRC (2004): • nucleon matrix elements of four-quark • operators for the nucleon structures • → weak density dependence Lattice: Göckeler, Schäfer et al, NPB (2002)

  21. Analysis: Nucleon in medium Threshold dependence

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