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Extending the Linear Sigma Model to Nf = 3

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Presentation on theme: "Extending the Linear Sigma Model to Nf = 3"— Presentation transcript:

1 Extending the Linear Sigma Model to Nf = 3
Institut für Theoretische Physik Goethe-Universität Frankfurt am Main Extending the Linear Sigma Model to Nf = 3 Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke (Frankfurt) György Wolf and Péter Kovács (Budapest) [Based on arXiv: ] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

2 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Motivation QCD Lagrangian Chirality Projection Operators Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

3 Explicit Symmetry Breaking Spontaneously Broken in Vacuum
Motivation Global Unitary Transformations invariant not invariant Chiral Symmetry Explicit Symmetry Breaking Spontaneously Broken in Vacuum In addition: Chiral U(1)A Anomaly Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

4 Motivation: Linear Sigma Model
Treats chiral partners on the same footing Vacuum calculations → calculations at T≠0 Vanishing chiral condensate and degeneration of chiral partners above TC → order parameter for restoration of chiral symmetry New in our model: Nf = 3 with vector and axial-vector mesons extended Linear Sigma Model - eLSM Vacuum spectroscopy first → Extend to T≠0 as a next step Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

5 Sigma Model Lagrangian with Vector and Axial-Vector Mesons (Nf = 3)
Scalars and Pseudoscalars Explicit Symmetry Breaking Chiral Anomaly photon Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

6 Sigma Model Lagrangian with Vector and Axial-Vector Mesons (Nf = 3)
Vectors and Axial-Vectors Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

7 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 SSB leads to mixings: Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

8 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) and g3 (fixed via K* → Kπ) 12 parameters, none free → fixed via masses [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

9 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Masses Mass Our value [MeV] PDG Value [MeV] 136.68 139.57 524 493.68 541.48 547.85 957.81 957.78 775.51 775.49 891.66 Mass Our value [MeV] PDG Value [MeV] 992.6 1019.5 1420.5 1426.4 1213.9 1230 1320.6 1272 1459 1474 1556.6 1425 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

10 PDG Data on JPC = 0++ Mesons
Five states up to 1.8 GeV State Mass [MeV] Width [MeV] f0(600) f0(980) 980±10 f0(1370) f0(1500) 1505±6 109±7 f0(1710) 1720±6 135±8 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

11 Scalar Mesons in Our Model
Mixing between σN and σS → mixing angle θNS ≈ 11° Two states emerge: Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

12 Predominantly Non-Strange Sigma
Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

13 Predominantly Strange Sigma
Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

14 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Other Results η – η’ mixing angle θη = 40.3° ↔ KLOE Collaboration: θη = 41.4° ± 0.5° Rho meson mass has two contributions: Decays K* → Kπ, φ(1020) → K+ K- agree with data (preliminary) ~ Gluon Condensate Quark Condensates Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

15 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Summary Linear Sigma Model Nf = 3 and vector and axial-vector mesons as an effective model of QCD Global fit of all masses except the sigmas Obtained masses within several percent w.r.t. experimental data Scalar meson puzzle: structure of f0(1370) ↔ mostly nonstrange quarkonium and f0(1710) ↔ mostly strange quarkonium Thus: scalar quarkonia above 1 GeV Other results in agreement with other approaches and experiment (preliminary) Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

16 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Outlook Lagrangian With Three Flavours + Glueball + Tetraquarks Mixing in the Scalar Sector: Quarkonia, Tetraquarks and Glueball Extension to Non-Zero Temperature: Study Chiral Symmetry Restoration Low Energy Constants of QCD Pion-Pion Scattering Lengths Include Tensor, Pseudotensor Mesons, Baryons (Nucleons) Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

17 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Spare Slides Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

18 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 under 1 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: , 2010; arXiv: ] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

19 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Note: Nf = 2 Limit The f0(600) state not preferred to be quarkonium [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

20 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Note: Nf = 2 Limit [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

21 Scenario II (Nf =2): Scattering Lengths
Scattering lengths saturated Additional scalars: tetraquarks, quasi-molecular states Glueball Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

22 Scenario II (Nf =2): Parameter Determination
Masses: Pion Decay Constant Five Parameters: Z, h1, h2, g2, mσ Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

23 Scenario I (Nf =2): Other Results
Our Result Experimental Value [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)] [KLOE Collaboration, hep-ex/ v3]: Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

24 Scenario I (Nf =2): a1→σπ Decay
m1 = 0 → mρ generated from the quark condensate only; our result: m1 = 652 MeV a1→σπ Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

25 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
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: , 2010] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

26 Scenario I (Nf =2): a1 → ρπ Decay
[M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)] Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

27 Scenario I (Nf =2) : Parameter Determination
Three Independent Parameters: Z, m1, mσ ~ Gluon Condensate Quark Condensate [S. Janowski (Frankfurt U.), Diploma Thesis, 2010] Isospin [NA48/2 Collaboration, 2009] Angular Momentum (s wave) Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

28 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf =2) Vectors and Axial-Vectors vectors axialvectors Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

29 Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France
Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf =2) Scalars and Pseudoscalars Explicit Symmetry Breaking Chiral Anomaly scalars pseudoscalars photon Denis Parganlija (Frankfurt U.) Excited QCD 2011, Les Houches/France

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