1. Denis Parganlija, HADRONS@FAIR A Linear Sigma Model with Vector Mesons and Global Chiral Invariance Denis Parganlija In collaboration with Francesco Giacosa, Dirk H. Rischke (Frankfurt University) Institut für Theoretische Physik Goethe-Universität Frankfurt am Main

2. Denis Parganlija, HADRONS@FAIR Motivation Sakurai: Vector Meson Dominance - EM processes mediated by vector mesons Calculation of scattering lengths and and decay widths of Sigma, Rho(770) and (1260) from a locally symmetric Linear Sigma Model (up to vector mass terms) Local vs. Global Symmetry: Mesonic decay widths require global symmetry FAIR: in-medium properties of hadrons as a signature of chiral symmetry restoration [Source: CBM Progress Report 2007]

3. Denis Parganlija, HADRONS@FAIR Lagrangian of a Gauged Linear Sigma Model with Vector Mesons (N f =2) (Gasiorowicz and Geffen, 1969) scalars pseudoscalars vectors axialvectors

4. Denis Parganlija, HADRONS@FAIR Spontaneous Symmetry Breaking (SSB): Shift: Shift (Diagonalise): Renormalise Pseudoscalar Wave Functions: [R. Pisarski, hep-ph/9503330 (1995)] [S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)]

5. Denis Parganlija, HADRONS@FAIR Relevant Vertices for Pion-Pion Scattering Feynman Diagrams At Tree Level:

6. Denis Parganlija, HADRONS@FAIR Tree-Level Scattering Amplitude s-channel isospin I components of the scattering amplitude: scattering lengths (on the threshold): partial wave amplitude

7. Denis Parganlija, HADRONS@FAIR Results I

8. Denis Parganlija, HADRONS@FAIR Results I: as function of Experiment: = 0.233 0.023 R. Wanke, arXiv:0712.0544 [hep-ex] (NA 48/2 Ke4)

9. Denis Parganlija, HADRONS@FAIR Results I: as function of E865 NA48/2 Ke4

10. Denis Parganlija, HADRONS@FAIR Results II: Decay Widths Sigma Decay 100 MeV Width at 800 MeV Mass

11. Denis Parganlija, HADRONS@FAIR Results II: Decay Widths Neutral Rho(770) Decay (1260) Decay

12. Denis Parganlija, HADRONS@FAIR Results II: Decay Widths Decay Widths For Sigma And Rho(770) Do Not Match Experiments How To Improve Decay Widths? All Parameters Fixed Via Tree Level Masses and No Free Parameters Need At Least One Additional Parameter To Try Adjusting Rho Width (149.4 1.0)MeV

13. Denis Parganlija, HADRONS@FAIR Improvements of the Lagrangian Strategy 1: Higher-dimension terms (local invariance) Strategy 2: Non-vanishing meson masses becomes global QCD chiral symmetry: global LSM chiral symmetry global [S. Gasiorowicz and D. A. Geffen (1969), P. Ko and S. Rudaz (1994), U. G. Meissner (1988)] [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)] [D. Parganlija, F. Giacosa and D. Rischke, arXiv:0804.3949 [hep-ph] ]

14. Denis Parganlija, HADRONS@FAIR Globally Invariant Model

15. Denis Parganlija, HADRONS@FAIR Parameter Determination Masses: Decays: Scattering Lengths:

16. Denis Parganlija, HADRONS@FAIR Results III: Rho Decay Width

17. Denis Parganlija, HADRONS@FAIR Ongoing Work: Nature of Scalar Mesons Decay Widths Scattering Lengths states under 1 GeV (600) (980) states above 1 GeV (extra scalar states below 1 GeV needed: tetraquarks?) (1370) (1450) Origin of rho mass: quark condensate vs. CL mass

18. Denis Parganlija, HADRONS@FAIR Summary LSM With Local Symmetry: Scattering Lengths Favour But: Poor Results On Decay Widths (Rho) Globally Invariant LSM Lagrangian: Rho Width Fixed Exactly Insight into Assignment of Scalars ( states above 1GeV?)

19. Denis Parganlija, HADRONS@FAIR Outlook Parameters and Consequences of Global Invariance up to 4 th Order Low Energy Constants of QCD p, d Wave Scattering Lengths Chiral Models With Three Flavours Include Tensor, Pseudotensor Mesons, Baryons (Nucleons) Extension to Non-Zero Temperature: Study Chiral Symmetry Restoration