1 / 40

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

abena
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related