Presentation is loading. Please wait.

Presentation is loading. Please wait.

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)

Published byAngel Fowler Modified over 9 years ago

Similar presentations

Presentation on theme: "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)"— Presentation transcript:

1 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

2 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

3 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)

4 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

5 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

6 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/9503330 (1995)] [S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)] 11 parameters

7 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]

8 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I – Results Z = 1.667 ± 0.205, m σ = (332 ± 456) MeV, quark condensate~ gluon condensate

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

10 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.]

11 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Scenario I - Results Our Result Experimental Value [KLOE Collaboration, hep-ex/0612029v3] [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)]

12 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

13 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Decay Width f 0 (1370) → ππ [D. V. Bugg, arXiv: 0710.4452 [hep-ex]] [S. Janowski (Frankfurt U.) – Diploma Thesis (preliminary results)]

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

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

16 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Including Baryons [S. Gallas, F. Giacosa and D. H. Rischke, arXiv: 0907.5084 [hep-ph]]

17 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

18 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)

19 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Spare Slides

20 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

21 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)]

22 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

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

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

25 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

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

27 Denis Parganlija (Frankfurt U.) Excited QCD 2010, Tatranska Lomnica/Slovakia Calculation of Scattering Lengths Feynman Diagrams At Tree Level: Scattering Length = 0.233 ± 0.023 J. R. Batley et al. [NA48/2 Collaboration], Eur. Phys. J. C 54, 411 (2008)

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

29 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 ≈ (320 - 340) 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.]

30 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 = (315 - 345) 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) ]

31 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:0812.2183 [hep-ph] ]

32 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

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

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

Download ppt "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)"

Similar presentations

Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450) Denis Parganlija.

Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450) Denis Parganlija.
Resent BES Results on Scalar Mesons Zhipeng Zheng (Representing BES Collaboration) Institute of High Energy Physics, CAS GHP-2004, Oct. 25.

Resent BES Results on Scalar Mesons Zhipeng Zheng (Representing BES Collaboration) Institute of High Energy Physics, CAS GHP-2004, Oct. 25.
J. RuppertHot Quarks 2006, May 2006 What does the rho? Lessons from NA60's di-muon measurement. Jörg Ruppert Nuclear Theory, Department of Physics, Duke.

J. RuppertHot Quarks 2006, May 2006 What does the rho? Lessons from NA60's di-muon measurement. Jörg Ruppert Nuclear Theory, Department of Physics, Duke.
1 A Model Study on Meson Spectrum and Chiral Symmetry Transition Da

1 A Model Study on Meson Spectrum and Chiral Symmetry Transition Da
1 Chiral Symmetry Breaking and Restoration in QCD Da Huang Institute of Theoretical Physics, Chinese Academy of

1 Chiral Symmetry Breaking and Restoration in QCD Da Huang Institute of Theoretical Physics, Chinese Academy of
O(N) linear and nonlinear sigma-model at nonzeroT within the auxiliary field method CJT study of the O(N) linear and nonlinear sigma-model at nonzeroT.

O(N) linear and nonlinear sigma-model at nonzeroT within the auxiliary field method CJT study of the O(N) linear and nonlinear sigma-model at nonzeroT.
QCD – from the vacuum to high temperature an analytical approach.

QCD – from the vacuum to high temperature an analytical approach.
José A. Oller Univ. Murcia, Spain Radiative  Decays and Scalar Dynamics José A. Oller Univ. Murcia, Spain Introduction Chiral Unitary Approach Scalar.

José A. Oller Univ. Murcia, Spain Radiative  Decays and Scalar Dynamics José A. Oller Univ. Murcia, Spain Introduction Chiral Unitary Approach Scalar.
The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz, S. Strüber, D. H. Rischke ITP, Goethe University, Frankfurt.

The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz, S. Strüber, D. H. Rischke ITP, Goethe University, Frankfurt.
Scadron70 page 1 Pattern of Light Scalar Mesons a 0 (1450) and K 0 *(1430) on the Lattice Tetraquark Mesonium – Sigma (600) on the Lattice Pattern of Scalar.

Scadron70 page 1 Pattern of Light Scalar Mesons a 0 (1450) and K 0 *(1430) on the Lattice Tetraquark Mesonium – Sigma (600) on the Lattice Pattern of Scalar.
The chiral partner of the nucleon in the mirror assignment University Frankfurt Susanna Wilms in collaboration with: Francesco Giacosa and.

The chiral partner of the nucleon in the mirror assignment University Frankfurt Susanna Wilms in collaboration with: Francesco Giacosa and.
11 Primakoff Experiments with EIC A. Gasparian NC A&T State University, Greensboro, NC For the PrimEx Collaboration Outline  Physics motivation:  The.

11 Primakoff Experiments with EIC A. Gasparian NC A&T State University, Greensboro, NC For the PrimEx Collaboration Outline  Physics motivation:  The.
Relativistic chiral mean field model for nuclear physics (II) Hiroshi Toki Research Center for Nuclear Physics Osaka University.

Relativistic chiral mean field model for nuclear physics (II) Hiroshi Toki Research Center for Nuclear Physics Osaka University.
Masayasu Harada (Nagoya Univ.) based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (2004) M.H., Work in progress at “Heavy Quark Physics in QCD”

Masayasu Harada (Nagoya Univ.) based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, (2004) M.H., Work in progress at “Heavy Quark Physics in QCD”
Sigma model and applications 1. The linear sigma model (& NJL model) 2. Chiral perturbation 3. Applications.

Sigma model and applications 1. The linear sigma model (& NJL model) 2. Chiral perturbation 3. Applications.
In-medium hadrons and chiral symmetry G. Chanfray, IPN Lyon, IN2P3/CNRS, Université Lyon I The Physics of High Baryon Density IPHC Strasbourg, september.

In-medium hadrons and chiral symmetry G. Chanfray, IPN Lyon, IN2P3/CNRS, Université Lyon I The Physics of High Baryon Density IPHC Strasbourg, september.
L. R. Dai (Department of Physics, Liaoning Normal University) Z.Y. Zhang, Y.W. Yu (Institute of High Energy Physics, Beijing, China) Nucleon-nucleon interaction.

L. R. Dai (Department of Physics, Liaoning Normal University) Z.Y. Zhang, Y.W. Yu (Institute of High Energy Physics, Beijing, China) Nucleon-nucleon interaction.
Mass modification of heavy-light mesons in spin-isospin correlated matter Masayasu Harada (Nagoya Univ.) at Mini workshop on “Structure and production.

Mass modification of heavy-light mesons in spin-isospin correlated matter Masayasu Harada (Nagoya Univ.) at Mini workshop on “Structure and production.
XI ｔｈ International Conference on Quark Confinement and the Hadron Petersburg, Russia 8.9.2014 Philipp Gubler (RIKEN, Nishina Center) Collaborator:

XI ｔｈ International Conference on Quark Confinement and the Hadron Petersburg, Russia Philipp Gubler (RIKEN, Nishina Center) Collaborator:
The Baryon octet-vector meson interaction and dynamically generated resonances in the S=0 sector Bao-Xi SUN ( 孙宝玺 ) Beijing University of Technology Hirschegg.

The Baryon octet-vector meson interaction and dynamically generated resonances in the S=0 sector Bao-Xi SUN ( 孙宝玺 ) Beijing University of Technology Hirschegg.

Similar presentations

Ads by Google