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Scalar and Axial-Vector Mesons in a Three- Flavour Sigma Model

Institut für Theoretische Physik Technische Universität Wien , Goethe- Universität Frankfurt. Scalar and Axial-Vector Mesons in a Three- Flavour Sigma Model. Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke (Frankfurt) György Wolf and Péter Kovács

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Scalar and Axial-Vector Mesons in a Three- Flavour Sigma Model

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  1. InstitutfürTheoretischePhysikTechnischeUniversitätWien, Goethe-Universität Frankfurt Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke (Frankfurt) György Wolf and PéterKovács (Budapest) [Based on: Phys.Rev. D82 (2010) 054024 (arXiv:1003.4934) Int.J.Mod.Phys. A26 (2011) 607-609 (arXiv:1009.2250) and PhD Thesis of D. Parganlija (2012)] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  2. Introduction:Definitions and Experimental Data • Mesons: quark-antiquarkstates • Quantum numbers: JPC • Scalar mesons: JPC = 0++[σ or f0(600), a0(980), a0(1450)…] • Pseudoscalar mesons: JPC = 0-+ [π, K, η, η´…] • Vector mesons: JPC = 1-- [ρ, K*, ω, φ(1020)…] • Axial-Vector mesons: JPC = 1++ [a1(1260), f1(1285), K1(1270), K1(1400)…] Parity Charge Conjugation Total Spin Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  3. Motivation: PDG Data on JPC = 0++ Mesons • Sixstatesupto 1.8 GeV (isoscalars) Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  4. Motivation: Reasons to Consider Mesons • Mesons: hadronic states with integer spin • More scalar mesons than predicted by quark-antiquark picture → Classification needed Look for tetraquarks, glueballs… • Walecka Model: Nucleon-nucleon interaction via σ meson • Restoration of chiral invariance and decofinement ↔ Degeneration of chiral partners π and σ→ σ has to be a quarkonium • Identify the scalar quarkonia→Need a model with scalar and other states Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  5. An Effective Approach:Linear Sigma Model • Implements features of QCD: • SU(Nf)L x SU(Nf)R Chiral Symmetry • Explicit and Spontaneous Chiral Symmetry Breaking; Chiral U(1)A Anomaly • Vacuum calculations → calculations atT≠0 • Chiral-Partners degeneration above TC→ order parameter for restoration of chiral symmetry • The model here: Nf = 3(mesons with u, d, s quarks) in scalar, pseudoscalar, vectorand axial-vectorchannels → extended Linear Sigma Model - eLSM Vacuum spectroscopy of quark-antiquark states Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  6. Resonances I • Pseudoscalars • Vectors Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  7. Resonances II • Axial-Vectors • Scalars Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  8. The Lagrangian I • Scalars and Pseudoscalars Chiral Anomaly Explicit Symmetry Breaking Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  9. The Lagrangian II • Vectors and Axial-Vectors Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  10. Sigma Model Lagrangian with Vector and Axial-Vector Mesons (Nf = 3) • More (Pseudo)scalar – (Axial-)Vector Interactions • Perform Spontaneous Symmetry Breaking (SSB):σN→ σN + ϕN, σS→ σS + ϕS • 18 parameters, 10 independent, none free → fixed via fit of masses and decay widths/amplitudes Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  11. Possible Assignments • Isospin 1 • Isospin ½ • Isospin 0 (Isoscalars) Check all possibilities Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  12. Best Fit Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  13. What We Did Not Find Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  14. Summary • Linear Sigma Model with Nf = 3 and vector and axial-vector mesons –eLSM • Predominantly scalar states above 1 GeV: • Axial-Vectors a1 and K1 seen as states Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  15. Summary: Results onJPC = 0++ Mesons [S. Janowski, D. Parganlija, F. Giacosa and D. H. Rischke, PR D 84 (2011) 054007] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  16. Outlook • Lagrangian With Three Flavours + Glueball + Tetraquarks • Mixing in the Scalar Sector: Quarkonia, Tetraquarks and Glueball • Four Flavours • Extension to Non-Zero Temperatures and Densities • Include Tensor, Pseudotensor Mesons, Baryons (Nucleons) Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  17. Spare Slides Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  18. Quantum Chromodynamics (QCD) • QCD Lagrangian • Symmetries of the QCD Lagrangian Local SU(3)c Colour Symmetry Global ChiralU(Nf)x U(Nf) Symmetry CPT Symmetry Z Symmetry Trace Symmetry Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  19. Chiral Symmetry of QCD • Left-handed and right-handed quarks: • Chirality Projection Operators • Transform quark fields • Quark part of the QCD Lagrangian: invariant Explicit Breaking of the Chiral Symmetry Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model ChiralSymmetry

  20. Chiral Currents • Noether Theorem: • Vector current Vμ = (Lμ +Rμ)/2 • Axial-vector current Aμ = (Lμ -Rμ)/2 • Vector transformation of • Axial-vector Transformation of ρ(770)-like Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model a1(1260)-like

  21. Spontaneous Breaking of Chiral Symmetry • Transform the (axial-)vector fields • Chiral Anomaly Theory: ρ and a1should degenerate Experiment: Spontaneous Breaking of the Chiral Symmetry (SSB) → Goldstone Bosons (pions, kaons…) Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  22. Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  23. Sigma Model Lagrangian with Vector and Axial-Vector Mesons (Nf = 3) • Scalars and Pseudoscalars Chiral Anomaly Explicit Symmetry Breaking Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  24. Sigma Model Lagrangian with Vector and Axial-Vector Mesons (Nf = 3) • Vectors and Axial-Vectors Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  25. Motivation: QCD Features in an Effective Model • QCD Lagrangian • Chirality Projection Operators Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  26. Motivation:QCD Features in an Effective Model • Global Unitary Transformations invariant not invariant Chiral Symmetry Explicit Symmetry Breaking Spontaneously Broken in Vacuum In addition: Chiral U(1)A Anomaly Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  27. Motivation: Structure of Scalar Mesons • Spontaneous Breaking of Chiral Symmetry→ Goldstone Bosons(Nf= 2 → 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) – not preferred by Nf= 2 results • Scalar states above 1 GeV→ f0(1370), a0(1450) – preferred by Nf= 2 results f0(600), „sigma“ f0(1370) [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: 054024, 2010; arXiv: 1003.4934] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  28. Calculating the Parameters • Shift the (axial-)vector fields: • Canonically normalise pseudoscalars and KS: • Perform a fit of all parameters except g2 (fixed via ρ → ππ) • 9 parameters,none free→fixed via masses [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: 054024, 2010; arXiv: 1003.4934] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  29. Other Results • η – η’ mixing angle θη= 43.9° ↔ KLOE Collaboration: θη= 41.4° ± 0.5° • Rho meson mass has two contributions: • K*→ Kπ Data: 48.7 MeVOur value: 44.2 MeV • φ(1020) → K+K- Data: 2.08 MeVOur value: 2.33 MeV Quark Condensates ~ Gluon Condensate Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  30. Note: Nf = 2 Limit • The f0(600) state not preferred to be quarkonium [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: 054024, 2010; arXiv: 1003.4934] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  31. Note: Nf = 2 Limit [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: 054024, 2010; arXiv: 1003.4934] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  32. Scenario II (Nf =2): Scattering Lengths • Scattering lengths saturated • Additional scalars: tetraquarks, quasi-molecular states • Glueball Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  33. Scenario II (Nf =2): Parameter Determination • Masses: • Pion Decay Constant • Five Parameters: Z, h1, h2, g2, mσ Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  34. Scenario I (Nf =2): Other Results • Our ResultExperimental Value [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)] [KLOE Collaboration, hep-ex/0612029v3]: Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  35. Scenario I (Nf =2): a1→σπDecay • m1 = 0→ mρ generated from the quark condensate only; our result: m1 = 652 MeV • a1→σπ Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  36. Comparison: the Model with and without Vectors and Axial-Vectors (Nf=2) Note: other observables (ππ scattering lengths, a0(980)→ηπ decay amplitude, phenomonology of a1, and others) are fine [Parganlija, Giacosa, Rischke, Phys. Rev. D 82: 054024, 2010] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  37. Scenario I (Nf =2): a1→ ρπ Decay [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)] Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  38. Scenario I (Nf =2) : Parameter Determination • Three Independent Parameters: Z, m1, mσ Quark Condensate ~ Gluon Condensate [S. Janowski (Frankfurt U.), Diploma Thesis, 2010] Isospin [NA48/2 Collaboration, 2009] Angular Momentum (s wave) Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  39. Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf =2) • Vectors and Axial-Vectors vectors axialvectors Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

  40. Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf =2) • Scalars and Pseudoscalars Chiral Anomaly Explicit Symmetry Breaking scalars pseudoscalars photon Denis Parganlija (TU Vienna / GU Frankfurt) Scalar and Axial-Vector Mesons in a Three-Flavour Sigma Model

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