Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Nature of Light Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450)

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Presentation transcript:

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Nature of Light 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 Institut für Theoretische Physik Goethe-Universität Frankfurt am Main

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Motivation: Effective Theories of QCD and Linear 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 T C

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia 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 under 1 GeV → f 0 (600), a 0 (980) Scalar states above 1 GeV → f 0 (1370), a 0 (1450) – additional scalar states under 1 GeV required (tetraquarks?) f 0 (600), „sigma“f 0 (1370)

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I: Scalars under 1 GeV N f = 2 Scalars → Pseudoscalars → Vectors → Axialvectors → scalars pseudoscalars vectors axialvectors

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Lagrangian of a Linear Sigma Model with Vector and Axialvector Mesons (N f =2) 12 parameters photon

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Spontaneous Symmetry Breaking (SSB): Shift: Shift (Diagonalise): Renormalise Pseudoscalar Wave Functions: [R. Pisarski, hep-ph/ (1995)] [S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)] 11 parameters

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Parameter Determination Masses: Pion Decay Constant Five Parameters: Z, g 2, m 1, h 2, m σ Three Parameters: Z, m 1, m σ Isospin Angular Momentum (s wave) [NA48/2 Collaboration, 2009]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I – Results Z = ± 0.205, m σ = (332 ± 456) MeV, quark condensate~ gluon condensate

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I – Results Boundaries of m σ ← scattering lengths

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I – Sigma Decay Γ σ→ππ [H. Leutwyler et al.] [J. R. Peláez et al.]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I - Results Our Result Experimental Value [KLOE Collaboration, hep-ex/ v3] [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario II: Scalars above 1 GeV N f = 2 Scalars → Pseudoscalars → Vectors → Axialvectors → scalars pseudoscalars vectors axialvectors

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Decay Width f 0 (1370) → ππ [D. V. Bugg, arXiv: [hep-ex]] [S. Janowski (Frankfurt U.) – Diploma Thesis (preliminary results)]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia The Rho Mass Contributions

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario II – Scattering Lengths Scattering lengths saturated Additional scalars: tetraquarks, quasi- molecular states Glueball

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Including Baryons [S. Gallas, F. Giacosa and D. H. Rischke, arXiv: [hep-ph]]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Summary LSM with global U(2) R x U(2) L invariance: scattering lengths, low-energy meson decay widths General phenomenology in agreement with experiment (ρ→ππ, a 1 →πγ, f 1 →a o π, a 0 →ηπ decay, ππ scattering lengths) The f 0 (600) → ππ decay width fails to match experiment ↔ quarkonium structure of f 0 (600), a 0 (980) excluded Quarkonium structure of f 0 (1370), a 0 (1450) favoured, f 0 (1370) → ππ in agreement with experiment Scalar states under 1 GeV required for correct description of pion-pion scattering lengths

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Outlook Consequences of Global Invariance up to 4 th Order Mixing in the Scalar Sector Chiral Models With Three Flavours 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.) Excited QCD 2010, Tatranska Lomnica/Slovakia Spare Slides

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I – Sigma Decay m 1 = 0 → m ρ generated from the quark condensate only; our result: m 1 = 652 MeV a 1 →σπ

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I: a 1 → ρπ Decay [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario II: Parameter Determination Masses: Pion Decay Constant Five Parameters: Z, h 1, h 2, g 2, m σ

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Comparison: the Model with and without Vectors and Axial-Vectors

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Relevant Vertices for Pion-Pion Scattering Feynman Diagrams At Tree Level:

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Tree-Level Scattering Amplitude s-channel isospin I components of the scattering amplitude: scattering lengths (on the threshold): partial wave amplitude

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Results I

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Calculation of Scattering Lengths Feynman Diagrams At Tree Level: Scattering Length = ± J. R. Batley et al. [NA48/2 Collaboration], Eur. Phys. J. C 54, 411 (2008)

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Results I: as function of E865 NA48/2 Ke4

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Calculation of Pion-Pion Scattering Lengths and Decay Widths (Local Invariance) Feynman Diagrams At Tree Level: ππ Scattering Lengths: m σ ≈ ( ) MeV [D. Parganlija, F. Giacosa and D. Rischke, AIP Conf. Proc. 1030, 160 (2008)] 100 MeV Width at 800 MeV Mass [H. Leutwyler et al.]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Results from the Locally Invariant Lagrangian: ππ Scattering Lengths and Low-Energy Meson Decay Widths Pion-pion scattering lengths correspond to experiment (NA48/2 data) → m σ = ( ) MeV f 0 (600) decay width: Γ σ→ππ < 100 MeV even at m σ = 800 MeV [Leutwyler: m σ – iΓ σ /2 = (441-i272) MeV] Γ ρ→ππ = 86.5 MeV [PDG: Γ ρ→ππ = (149.4 ± 1.0) MeV] Decay widths for sigma and rho do not match experiments How to improve decay widths? [D. Parganlija, F. Giacosa and D. Rischke, AIP Conf. Proc. 1030, 160 (2008) ]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia 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), U. G. Meissner (1988), P. Ko and S. Rudaz (1994)] [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)] [D. Parganlija, F. Giacosa and D. Rischke, AIP Conf. Proc. 1030, 160 (2008) ] [D. Parganlija, F. Giacosa and D. Rischke, arXiv: [hep-ph] ]

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Parameter Determination k Three Parameters: Z, m σ and h 1 Find global minimum of Look for per D.O.F. at minimum Parameter errors: diagonal elements of at global minimum for all parameters

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia s-wave, isospin-two scattering length

Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Renormalisation Constant Z