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Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450)

Institut für Theoretische Physik Goethe-Universität Frankfurt am Main. Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450). Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke.

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Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450)

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  1. Institut für Theoretische Physik Goethe-Universität Frankfurt am Main Structure of Scalar Mesons f0(600), a0(980), f0(1370) and a0(1450) Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke [Based on arXiv: 1003.4934 [hep-ph]] Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  2. Motivation: Effective Theories of QCD andLinear Sigma Model • Description of low-energy hadrons (mesons) • Generalisation to T, μ≠ 0 Linear Sigma Model: • Treats chiral partners on the same footing • Vacuum calculations → calculations at T≠0 • Degeneration of chiral partners above TC Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  3. Motivation: Structure of Scalar Mesons • Spontaneous Breaking of Chiral Symmetry→ Goldstone Bosons (π) • Restoration of Chiral Invariance and Deconfinement ↔ Degeneration of Chiral Partners (π/σ) • Nature of scalar mesons • Scalar states under1 GeV →f0(600), a0(980) • Scalar states above 1 GeV → f0(1370), a0(1450) – additional scalar states under 1 GeV required (tetraquarks?) f0(600), „sigma“ f0(1370) Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  4. Scenario I: Scalars under 1 GeV • Nf = 2 Scalars→ Pseudoscalars → Vectors → Axialvectors → scalars pseudoscalars vectors axialvectors Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  5. Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf=2) 12 parameters photon Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  6. Shift: Shift (Diagonalise): Spontaneous Symmetry Breaking (SSB): [S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)] [R. Pisarski, hep-ph/9503330 (1995)] • Renormalise Pseudoscalar Wave Functions: 11 parameters Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  7. Parameter Determination • Three Independent Parameters: Z, m1, mσ Quark Condensate ~ Gluon Condensate Isospin [NA48/2 Collaboration, 2009] Angular Momentum (s wave) Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  8. Scenario I – Results • Boundaries of mσ ← scattering lengths Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  9. Scenario I – Sigma Decay • Γσ→ππ [H. Leutwyler et al.] [J. R. Peláez et al.] Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  10. Scenario I - Results • Our ResultExperimental Value [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)] [KLOE Collaboration, hep-ex/0612029v3] Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  11. Scenario II: Scalars above 1 GeV • Nf = 2 Scalars→ Pseudoscalars → Vectors → Axialvectors → scalars pseudoscalars vectors axialvectors Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  12. Decay Width f0(1370) → ππ [D. V. Bugg, arXiv: 0710.4452 [hep-ex]] Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  13. The Rho Mass Contributions Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  14. Scenario II – Scattering Lengths • Scattering lengths saturated • Additional scalars: tetraquarks, quasi-molecular states • Glueball Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  15. Summary • LSM with global U(2)Rx U(2)Linvariance: scattering lengths, low-energy meson decay widths • General phenomenology in agreement with experiment (ρ→ππ, a1→πγ, f1→aoπ, a0→ηπ decay, ππscattering lengths) • The f0(600) → ππ decay widthfails to match experiment ↔quarkonium structure of f0(600), a0(980) excluded • Quarkonium structure off0(1370), a0(1450) favoured, f0(1370) → ππ in agreement with experiment • Scalar states under 1 GeV required for correct description of pion-pion scattering lengths Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  16. Outlook • Consequences of Global Invariance up to 4th Order • Chiral Models With Three Flavours • Mixing in the Scalar Sector • Extension to Non-Zero Temperature: Study Chiral Symmetry Restoration • Low Energy Constants of QCD • p, d Wave Scattering Lengths • Include Tensor, Pseudotensor Mesons, Baryons (Nucleons) Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  17. Spare Slides Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  18. Scenario I – Sigma Decay • m1 = 0→ mρ generated from the quark condensate only; our result: m1 = 652 MeV • a1→σπ Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  19. Scenario I: a1→ ρπ Decay [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)] Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  20. Scenario II: Parameter Determination • Masses: • Pion Decay Constant • Five Parameters: Z, h1, h2, g2, mσ Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

  21. Comparison: the Model with and without Vectors and Axial-Vectors Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland

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