The Quest for Light Scalar Quarkonia from elsm

Transcription

1 Institut für Theoretische Physik Goethe-Universität Frankfurt am Main The Quest for Light calar Quarkonia from elm Denis Parganlija [Based on arxiv: ] In collaboration with Francesco Giacosa and Dirk H. Rischke (Frankfurt) György Wolf and Péter ovács (Budapest) NCNP tockholm

2 Introduction: Definitions and Experimental Data Mesons: quark-antiquark states calar mesons: J PC = ++ More scalars than predicted by quarkantiquark picture look for tetraquarks, glueballs Mesons: hadronic states with integer spin NCNP tockholm

3 Motivation: PDG Data on J PC = ++ Mesons n n u u + dd Five states up to.8 GeV (isoscalars) tate Mass [MeV] Width [MeV] ss f (6) f (98) 98± 4 - f (37) f (5) 55±6 9±7 f (7) 7±6 35±8 q q qq Glueball NCNP tockholm meson - meson bound state

4 Linear igma Model Implements features of QCD: U(N f ) L x U(N f ) R Chiral ymmetry Explicit and pontaneous Chiral ymmetry Breaking; Chiral U() A Anomaly Vacuum calculations calculations at T Chiral Partners Degeneration above T C order parameter for restoration of chiral symmetry New in our model: N f = 3 with vector and axialvector mesons extended Linear igma Model - elm Vacuum spectroscopy first Extend to T as a next step NCNP tockholm

5 L igma Model Lagrangian with Vector and Axial-Vector Mesons (N f = 3) calars and Pseudoscalars = Tr [( D Φ) ( D Φ)] m Tr ( Φ Φ) λ[tr ( Φ Φ)] λ Tr ( Φ + Tr [ H( Φ + Φ )] + c[(det Φ + det Φ ) 4det( ΦΦ )] P Φ) Explicit ymmetry Breaking n n = σ N + a a σ N a a D Φ = Φ + ig( ΦR L Φ) Where are scalar qq states? + σ + P = ss η N + π π NCNP tockholm η Chiral Anomaly N π π Under GeV? + η + Φ = Above + ip GeV?

6 V igma Model Lagrangian with Vector and Axial-Vector Mesons (N f = 3) Vectors and Axial-Vectors L L R = = m Tr ( L + ) + Tr + ( + ) 4 ν R ν L R ν ig (Tr { Lν [ L, L ]} + Tr{ Rν [ R, R ]}) = = Lν ν δn( mu, d) = R VA ν ν L ν ν ν R ω N + ρ ρ ω ρ N + ρ ω + A = N a + a NCNP tockholm f δ ( m n f u, d ) a N δ ( m + s a s ) f + L + R = V A = V A

7 igma Model Lagrangian with Vector and Axial-Vector Mesons (N f = 3) More (Pseudo)scalar (Axial-)Vector Interactions h INT. = Tr ( Φ Φ) Tr ( L + R ) + h Tr [( L Φ) + ( ΦR ) ] h Tr ( ΦR Φ L ) L + 3 L = L + L + P VA L INT. Perform pontaneous ymmetry Breaking (B): σ N σ N + ϕ N, σ σ + ϕ Nine parameters, none free fixed via fit of masses (except the two sigmas) NCNP tockholm

8 Fit of Masses Mass m π m m η m η' m ρ m Our value [MeV] PDG Value [MeV] Resonances favoured to be qq states Mass m ϕ() m f (4) m a (6) m (7) m a (45) m (45) NCNP tockholm Our value [MeV] PDG Value [MeV] What about the sigmas?

9 calar Mesons in Our Model n n = Mixing between σ N and σ mixing angle θ N a Two states emerge: σ 95% n n σ 95% s s σ N + a a σ N a + σ + and 5% ss and 5% nn NCNP tockholm ss Interpretation depends m σ andγ, σ, on

10 Predominantly Non-trange igma PDG : m f Γ f (37) (37) = = ( 5) MeV, ( 5) MeV Experimental datafavour f (37) as predominantly nn NCNP tockholm

11 Predominantly trange igma PDG: Γ f (7) = (9.3 ± ππ m f (7) = (7 ± 6.5) MeV 6) MeV Our values: m f = th. (7 ) th. (7 ) m f = MeV MeV f (7) predominantly ss calar qq states above GeV! NCNP tockholm

12 ummary Linear igma Model N f = 3 and vector and axial-vector mesons Global fit of all masses except the sigmas Obtained masses ~3% w.r.t. experimental data NCNP tockholm

13 ummary: Our Results on J PC = ++ Mesons tate Mass [MeV] Width [MeV] f (6) tetraquark? 4 - f (98) tetraquark? 98± f (37) predominantly nn - 5 f (5) 55±6 predominantly glueball f (7) predominantly ss 7±6 NCNP tockholm ±7 35±8 [. Janowski, D. Parganlija, F. Giacosa and D. H. Rischke, arxiv:3.338 ]

14 Outlook Lagrangian With Three Flavours + Glueball + Tetraquarks Mixing in the calar ector: Quarkonia, Tetraquarks and Glueball Extension to Non-Zero Temperature: tudy Chiral ymmetry Restoration Include Tensor, Pseudotensor Mesons, Baryons (Nucleons) NCNP tockholm

15 pare lides NCNP tockholm

16 Motivation: QCD Features in an Effective Model QCD Lagrangian Chirality Projection Operators NCNP tockholm

17 Motivation: QCD Features in an Effective Model Global Unitary Transformations invariant not invariant Chiral ymmetry Explicit ymmetry Breaking pontaneously Broken in Vacuum In addition: Chiral U() A Anomaly NCNP tockholm

18 Motivation: Reasons to Consider Mesons More scalar mesons than predicted by quark-antiquark picture Classification needed Restoration of chiral invariance and decofinement Degeneration of chiral partners π and σ σhas to be a quark-antiquark state Identify the scalar quark-antiquark state σ Need a model with scalar and other states NCNP tockholm

19 Motivation: tructure of calar Mesons pontaneous Breaking of Chiral ymmetry Goldstone Bosons (N f = π) Restoration of Chiral Invariance and Deconfinement Degeneration of Chiral Partners (π/σ) f (6), sigma f (37) Nature of scalar mesons calar qq states under GeV f (6), a (98) not preferred by N f = results calar qq states above GeV f (37), a (45) preferred by N f = results [Parganlija, Giacosa, Rischke in Phys. Rev. D 8: 544, ; arxiv: ] NCNP tockholm

20 Calculating the Parameters hift the (axial-)vector fields: f f + w η f f + w r a N N fn r r a + wa π N Canonically normalise pseudoscalars and : η Z N, η r r ηn, N, π Zππ Z Z Perform a fit of all parameters except g (fixed via ρ ππ) 9 parameters, none free fixed via masses m π, m ω m m m m m m, NCNP tockholm f + w η mη, mη ' mη, m m, N η ρ m, * m f m f (4 ) ) m m (7 ) m m ϕ ( ) a a ( 6, a a (45 ) (43 ) + w [Parganlija, Giacosa, Rischke in Phys. Rev. D 8: 544, ; arxiv: ] Preliminary : no fit with m a GeV, m GeV < <

21 Other Results η η mixing angle θ η = 43.9 LOE Collaboration: θ η = 4.4 ±.5 Rho meson mass has two contributions: m φ N ρ = m + [ h + h + h3 ] + NCNP tockholm h φ ~ Gluon Condensate Quark Condensates We obtain m 76 MeV * π Data: 48.7 MeV Our value: 44. MeV φ() + - Data:.8 MeV Our value:.33 MeV

22 Note: N f = Limit The f (6) state not preferred to be quarkonium [Parganlija, Giacosa, Rischke in Phys. Rev. D 8: 544, ; arxiv: ] NCNP tockholm

23 Note: N f = Limit Experimental data favours f (37) as predominantly qq PDG : m f Γ f (37) (37) = = ( 5) MeV, ( 5) MeV [Parganlija, Giacosa, Rischke in Phys. Rev. D 8: 544, ; arxiv: ] NCNP tockholm

24 cenario II (N f =): cattering Lengths cattering lengths saturated Additional scalars: tetraquarks, quasimolecular states Glueball NCNP tockholm

25 cenario II (N f =): Parameter Determination Masses: m Pion Decay Constant π, m, m, m, m η a ρ a Five Parameters: Z, h, h, g, m σ f NCNP tockholm π = Γ ρ ππ = (49.4 ±.) MeV g = g( Z Γ ( a (45) = 65 ± 3) MeV h = h ( Z) h ( h, 3 small) Γ a πγ [ Z] = mσ m f (37) (.64± free.46) MeV φ Z Z )

26 cenario I (N f =): Other Results Γ Our Result Γ a η η' A a ρ ππ [ Z, g ], f a π [ Z, ]exact =.64 MeV πγ a =.8 a =.454 = 333MeV ηπ c mixing angle Γ h : deg [LOE Collaboration, hep-ex/69v3]: [D. η η' mixing angle : 4.4 ±.5 deg Experimental Value Γ a =.64 MeV πγ a =.8 (NA48/) a =.457 (NA48/) A a ηπ = 333 MeV V. Bugg et al., Phys. Rev. D 5, 44 (994)] NCNP tockholm

27 cenario I (N f =): a σπ Decay m = m ρ generated from the quark condensate only; our result: m = 65 MeV a σπ PDG : Γ a (total) = (5 6) MeV NCNP tockholm

28 Comparison: the Model with and without Vectors and Axial-Vectors (N f =) Include values vectors decrease NCNP tockholm Note: other observables (ππ scattering lengths, a (98) ηπ decay amplitude, phenomonology of a, and others) are fine [Parganlija, Giacosa, Rischke, Phys. Rev. D 8: 544, ]

29 cenario I (N f =): a ρπ Decay PDG : (5 6) MeV Γ σ ππ < 6 MeV if m < σ 5 MeV [M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 ()] NCNP tockholm

30 cenario I (N f =) : Parameter Determination Three Independent Parameters: Z, m, m σ Γa [ Z] = (.64 ±.46) MeV πγ φ m ρ = m + [ h + h ( Z) + h3 ( Z)] a [ Z, m NCNP tockholm ~ Gluon Condensate Quark Condensate Isospin [. Janowski (Frankfurt U.), Diploma Thesis, ], m σ ] =.8 ±. [ mπ Angular Momentum (s wave) m σ m Z =.67± = [88, ] [NA48/ Collaboration, 9]. MeV 477] MeV

31 L VA L R ν ν vectors Lagrangian of a Linear igma Model with Vector and Axial-Vector Mesons (N f =) Vectors and Axial-Vectors ν m = Tr [( L ν ) + ( R ) ] + + Tr [( L ) + ( R ) ] 4 ν ν ig (Tr { L ν [ L, L ]} + Tr{ R ν [ R, R ]}) 3 3 g3{tr [( Lν iea [ t, Lν ] + ν L ieaν [ t,l ]){ L, 3 + Tr [( R iea [ t, R ] + R iea [ t, R ]){ R, = = L R ν ν L 3 ν ν ν ν ν R ν 3 ν ν 3 L ( iea [ t, L ] iea [ t, L ]) 3 ν ν 3 R ( iea [ t, R ] iea [ t, R ]) ν NCNP tockholm δn( m u, d ν }] }]} = ) δ ( m n u, d δ ( ) s ms axialvectors )

32 L Lagrangian of a Linear igma Model with Vector and Axial-Vector Mesons (N f =) calars and Pseudoscalars = Tr [( D Φ) ( D Φ)] m Tr ( Φ Φ) λ[tr ( Φ Φ)] λ Tr ( Φ + Tr [ H( Φ + Φ )] + c[(det Φ + det Φ ) 4det( ΦΦ )] P Φ) Explicit ymmetry Breaking scalars Chiral Anomaly D Φ = pseudoscalars 3 Φ + ig( ΦR L Φ) iea [ t, Φ] photon { σ, a} { f(6), a(98)}or { f(37), a(45)} Where is the scalar qq state? NCNP tockholm