Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Mesons in non-perturbative and perturbative regions of QCD Denis Parganlija Thanks to: F. Giacosa, S. Janowski and D. H. Rischke (Frankfurt) Gy. Wolf and P. Kovács (Budapest) D. Bugg (London) Institut für Theoretische Physik Technische Universität Wien [D. Parganlija et al., ] [PhD Thesis of D. Parganlija, arXiv: ]

Building Blocks of Nature Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Atom Proton ~0.5 fm Quarks: u, d, s, c, b, t Leptons Gauge Bosons

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Theory

Quantum Chromodynamics: QCD Symmetries of the QCD Lagrangian Poincare Symmetry Local SU(3) c Colour Symmetry CPT Symmetry Global Chiral U(N f )x U(N f ) Symmetry Z 3 Symmetry Dilatation Symmetry Note: not all symmetries are exact Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Strong Interaction Strong Coupling g ~ 1 Strongly Nonperturbative Effective Models

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Experiment

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Mesons: Definitions and Experimental Data Mesons: quark-antiquark states Quantum numbers: J PC Scalar mesons: J PC = 0 ++ [σ or f 0 (500), a 0 (980), a 0 (1450)…] Pseudoscalar mesons: J PC = 0 -+ [π, K, η, η´…] Vector mesons: J PC = 1 -- [ρ, K*, ω, φ(1020)…] Axial-Vector mesons: J PC = 1 ++ [ a 1 (1260), f 1 (1285), K 1 (1270), K 1 (1400)…] Total Spin ParityCharge Conjugation

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Motivation: Data on IJ PC = Mesons Six states up to 1.8 GeV (isoscalars) StateMass [MeV]Width [MeV] f 0 (500) f 0 (980)980 ± f 0 (1370) f 0 (1500)1505 ± 6109 ± 7 f 0 (1710)1720 ± 6135 ± 8 f 0 (1790)

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Motivation: More Reasons to Consider Mesons Nucleon-nucleon interaction modelled via exchange of a scalar isosinglet 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 formalism with scalar and other states

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Model

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Framework to Consider Mesons: Linear Sigma Model Implements features of QCD:  SU(N f ) L x SU(N f ) R Chiral Symmetry  Explicit and Spontaneous Chiral Symmetry Breaking; Chiral U(1) A Anomaly Vacuum calculations → calculations at T≠0 Chiral partners degenerate above T C → order parameter for restoration of chiral symmetry The model contains: N f = 3 (mesons with u, d, s quarks) in scalar, pseudoscalar, vector and axial- vector channels → extended Linear Sigma Model – eLSM Current calculations: in vacuum

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Best Fit of Resonances from eLSM

Introducing Scalar Glueball Dilatation symmetry: an exact feature of QCD Lagrangian if m f = 0 Introduce dilaton potential in sigma-model Lagrangian Dilaton field and its condensate ↔ Glueball field and its condensate Dilaton affects meson phenomenology Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD [S. Janowski, D. Parganlija, F. Giacosa and D. H. Rischke, PR D 84 (2011) ]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Data on IJ PC = Mesons StateMass [MeV]Width [MeV] f 0 (500) f 0 (980)980 ± f 0 (1370) f 0 (1500)1505 ± 6109 ± 7 f 0 (1710)1720 ± 6135 ± 8 f 0 (1790)

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Future Facilities: FAIR and NICA

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scalar Ambiguities I

Assume that they are the same resonance Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scalar Ambiguities II [M. Ablikim et al. (BES II Collaboration), Phys. Lett. B 603, 138 (2004) and Phys. Lett. B 607, 243 (2005)]

Denis Parganlija (Vienna UT) Model Studies of QCD in non-perturbative and perturbative regions It is impossible to consider glueball only: f 0 (1370), f 0 (1500), f 0 (1710) too close Additional complication: f 0 (1790) would interfere… if it exists Look for f 0 (1790)! PANDA Experiment at FAIR

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Vectors at Finite T and μ Rho meson mass has two contributions: We obtain 640 MeV ≤ m 1 ≤ m ρ → Rho mass decreases by ~(10-15)% → Mass of φ(1020) also decreases by ~(10-15)% (in the region where only the chiral condensate decreases) Resonances become broader ~ Gluon Condensate Quark Condensates

Explore QCD in non-perturbative and perturbative regions by means of effective models Essential to understand meson properties already in vacuum Suggestion for PANDA: inevitable to measure all scalars in order to search for glueballs CBM: insight into vector/axial-vector order parameters ↔ interaction with theory Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Summary and Outlook

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Excited QCD V Sarajevo, February 3 – 9, 2013 indico.cern.ch/event/exqcd2013

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Spare Slides

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD What We Did Not Find

Introducing Baryons Nucleon N and its chiral partner N(1535) Mirror assignment Data for N(1535) → N π, a 1 → πγ and axial coupling of the chiral partner Only ~50% of the nucleon mass originates from the chiral condensate Nucleon-nucleon scattering sensitive to the nature of the scalar state Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD

Comparison: the Model with and without Vectors and Axial-Vectors (N f =2) Note: other observables (ππ scattering lengths, a 0 (980)→ηπ decay amplitude, phenomonology of a 1, and others) are fine [Parganlija, Giacosa, Rischke, Phys. Rev. D 82: , 2010]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Chiral Symmetry of QCD Left-handed and right-handed quarks: Chirality Projection Operators Transform quark fields Quark part of the QCD Lagrangian: invariant Chiral Symmetry Explicit Breaking of Chiral Symmetry

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Chiral Currents Noether Theorem: Vector current V μ = (L μ + R μ )/2 Axial-vector current A μ = (L μ - R μ )/2 Vector transformation of Axial-vector Transformation of ρ(770)-like a 1 (1260)-like

Spontaneous Breaking of Chiral Symmetry Transform the (axial-)vector fields Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Theory: ρ and a 1 should be degenerate Experiment: Spontaneous Breaking of Chiral Symmetry (SSB) via → Goldstone Bosons (pions, kaons…)

Resonances I Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Pseudoscalars Vectors

Resonances II Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Axial-Vectors Scalars

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD The Lagrangian I Scalars and Pseudoscalars Explicit Symmetry Breaking Chiral Anomaly

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD The Lagrangian II Vectors and Axial-Vectors

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Sigma Model Lagrangian with Vector and Axial-Vector Mesons (N f = 3) More (Pseudo)scalar – (Axial-)Vector Interactions What about Scalars?

Isospin 1 Isospin ½ Isospin 0 (Isoscalars) Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Possible Assignments Check all possibilities

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD

Calculating the Parameters Shift the (axial-)vector fields: Canonically normalise pseudoscalars and K S : Perform a fit of all parameters except g 2 (fixed via ρ → ππ) 9 parameters, none free → fixed via masses [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Note: N f = 2 Limit The f 0 (600) state not preferred to be quarkonium [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Note: N f = 2 Limit [Parganlija, Giacosa, Rischke in Phys. Rev. D 82: , 2010; arXiv: ]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario II (N f =2): Scattering Lengths Scattering lengths saturated Additional scalars: tetraquarks, quasi- molecular states Glueball

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario II (N f =2): Parameter Determination Masses: Pion Decay Constant Five Parameters: Z, h 1, h 2, g 2, m σ

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario I (N f =2): Other Results Our Result Experimental Value [KLOE Collaboration, hep-ex/ v3]: [D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario I (N f =2): a 1 →σπ Decay m 1 = 0 → m ρ generated from the quark condensate only; our result: m 1 = 652 MeV a 1 →σπ

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario I (N f =2): a 1 → ρπ Decay [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Scenario I (N f =2) : Parameter Determination Three Independent Parameters: Z, m 1, m σ Isospin Angular Momentum (s wave) [NA48/2 Collaboration, 2009] ~ Gluon Condensate Quark Condensate [S. Janowski (Frankfurt U.), Diploma Thesis, 2010]

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (N f =2) vectors axialvectors Vectors and Axial-Vectors

Denis Parganlija (Vienna UT) Mesons in non-perturbative and perturbative regions of QCD Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (N f =2) Scalars and Pseudoscalars pseudoscalars scalars Explicit Symmetry Breaking Chiral Anomaly photon