Overview of Light-Hadron Spectroscopy and Eotics Stefan Wallner Institute for Hadronic Structure and Fundamental Symmetries - Technical University of Munich March 19, 018 HIEPA 018 E COMPASS 1 8
Introduction Light-Meson Sector PDG meson listings 80 light non-strange mesons (47 in summary table) > 100 possible further states 8 strange mesons (15 in summary table) [PDG 017] Important quantum numbers J PC J: Spin P: Eigenvalue under space inversion C: Eigenvalue under charge conjugation /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Light-Meson Sector PDG meson listings 80 light non-strange mesons (47 in summary table) > 100 possible further states 8 strange mesons (15 in summary table) [PDG 017] Important quantum numbers J PC J: Spin P: Eigenvalue under space inversion C: Eigenvalue under charge conjugation /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Naïve Quark Model Light-quark mesons qq states of u, d, and s (anti)quarks SU(3) flavor nonets Ground-state nonets Many more nonets for orbital and radial ecitations 3/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Naïve Quark Model Light-quark mesons qq states of u, d, and s (anti)quarks SU(3) flavor nonets Ground-state nonets Many more nonets for orbital and radial ecitations 3/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Naïve Quark Model Light-quark mesons qq states of u, d, and s (anti)quarks SU(3) flavor nonets Ground-state nonets Many more nonets for orbital and radial ecitations 3/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Beyond the Constituent Quark Model QCD permits additional color-neutral configurations Physical mesons: linear superpositions of all allowed basis states with same J PC Amplitudes in principle determined by QCD interactions Disentanglement of contributions difficult Light mesons: no definitive eperimental evidence yet 4/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Beyond the Constituent Quark Model QCD permits additional color-neutral configurations Physical mesons: linear superpositions of all allowed basis states with same J PC Amplitudes in principle determined by QCD interactions Disentanglement of contributions difficult Light mesons: no definitive eperimental evidence yet 4/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Meson Production h beam X 1 h. n 1 h n h target h recoil Ecited mesons appear as intermediate states 5/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Meson Production h beam X h 1 h. h n 1 h n h target h recoil Various final states: π π π + ηπ... 5/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Meson Production h beam X h 1 h. h n 1 h n h target h recoil Various reactions to produce them: Heavy-meson decays τ decays t-channel production in high-energy scattering... 5/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Meson Production h beam X h 1 h. h n 1 h n h target h recoil Various reactions to produce them: Heavy-meson decays τ decays t-channel production in high-energy scattering... 5/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Introduction Production Eperiments VES COMPASS I 9 GeV/c π beam I 190 GeV/c π beam I Be target I Solid-state, `H targets JLab: GlueX 1 GeV linearly polarized γ-beam I I `H target https://halldweb.jlab.org/wiki/inde.php/gluex Project Overviews 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Motivation [Adolph et al., PRD 95, 03004 (017)] π p P X π π + π p recoil Rich spectrum of overlapping and interfering X Dominant states Hidden states with lower intensity Events / (5 MeV/c ) 0.4 0.3 0. 0.1 6 10 a 1 (160) Also structure in ππ subsystem Successive -body decay via ππ resonance called isobar Also structure in angular distributions a (130) π (1670) 0 0.5 1 1.5.5 m [GeV/c 3π ] 7/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Motivation [Adolph et al., PRD 95, 03004 (017)] π P π π + X π p p recoil Rich spectrum of overlapping and interfering X Dominant states Hidden states with lower intensity Also structure in ππ subsystem Successive -body decay via ππ resonance called isobar Also structure in angular distributions 7/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Motivation [Adolph et al., PRD 95, 03004 (017)] π P X ξ π π + π p p recoil Rich spectrum of overlapping and interfering X Dominant states Hidden states with lower intensity Also structure in ππ subsystem Successive -body decay via ππ resonance called isobar Also structure in angular distributions 7/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Motivation [Adolph et al., PRD 95, 03004 (017)] 1640 < m3π < 1680 MeV/c I Rich spectrum of overlapping and interfering X I I Dominant states Hidden states with lower intensity I Also structure in ππ subsystem å Successive -body decay via ππ resonance called isobar I Also structure in angular distributions 7/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Isobar Model [Adolph et al., PRD 95, 03004 (017)] π π p P X ξ π + π p recoil For given partial wave J PC M ε ξ π L at a fied mass m 3π Calculate 5D decay phase-space distribution of final-state particles Measured phase-space distribution contains coherent contributions of various partial waves waves I(τ) = T i ψ i (τ) Perform maimum-likelihood fit in bins of m 3π ( mass-independent fit ) Decompose data into partial waves Etract m 3π dependence of partial-wave amplitudes 8/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics i
Partial-Wave Analysis Isobar Model [Adolph et al., PRD 95, 03004 (017)] π π [J P C M ε ] L π + P X ξ π p p recoil For given partial wave J PC M ε ξ π L at a fied mass m 3π Calculate 5D decay phase-space distribution of final-state particles Measured phase-space distribution contains coherent contributions of various partial waves waves I(τ) = T i ψ i (τ) Perform maimum-likelihood fit in bins of m 3π ( mass-independent fit ) Decompose data into partial waves Etract m 3π dependence of partial-wave amplitudes 8/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics i
Partial-Wave Analysis Isobar Model [Adolph et al., PRD 95, 03004 (017)] π π [J P C M ε ] L π + P X ξ π p p recoil For given partial wave J PC M ε ξ π L at a fied mass m 3π Calculate 5D decay phase-space distribution of final-state particles Measured phase-space distribution contains coherent contributions of various partial waves waves I(τ) = T i ψ i (τ) Perform maimum-likelihood fit in bins of m 3π ( mass-independent fit ) Decompose data into partial waves Etract m 3π dependence of partial-wave amplitudes 8/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics i
Partial-Wave Analysis Isobar Model [Adolph et al., PRD 95, 03004 (017)] π π [J P C M ε ] L π + P X ξ π p p recoil For given partial wave J PC M ε ξ π L at a fied mass m 3π Calculate 5D decay phase-space distribution of final-state particles Measured phase-space distribution contains coherent contributions of various partial waves waves I(τ) = T i ψ i (τ) Perform maimum-likelihood fit in bins of m 3π ( mass-independent fit ) Decompose data into partial waves Etract m 3π dependence of partial-wave amplitudes 8/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics i
Partial-Wave Analysis Isobar Model [Adolph et al., PRD 95, 03004 (017)] π π [J P C M ε ] L π + P X ξ π p p recoil For given partial wave J PC M ε ξ π L at a fied mass m 3π Calculate 5D decay phase-space distribution of final-state particles Measured phase-space distribution contains coherent contributions of various partial waves waves I(τ) = T i ψ i (τ) Perform maimum-likelihood fit in bins of m 3π ( mass-independent fit ) Decompose data into partial waves Etract m 3π dependence of partial-wave amplitudes 8/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics i
Partial-Wave Analysis t Binning [Adolph et al., PRD 95, 03004 (017)] π t [J P C M ε ] X ξ L π π + π p p recoil Challenge Production also depends on t Large data set ( 50 M eclusive events) Perform PWA also in narrow bins of t (t -resolved analysis) Etract m 3π AND t dependence of partial-wave amplitudes 9/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis t Binning [Adolph et al., PRD 95, 03004 (017)] Events / (5 MeV/c ) 10 60 40 0 3 0.10 < t' < 0.1 (GeV/c) Events / (5 MeV/c ) 40 30 0 10 3 10 0.44 < t' < 1.00 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 0 0.5 1 1.5.5 m [GeV/c 3π ] Challenge Production also depends on t Large data set ( 50 M eclusive events) Perform PWA also in narrow bins of t (t -resolved analysis) Etract m 3π AND t dependence of partial-wave amplitudes 9/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis t Binning [Adolph et al., PRD 95, 03004 (017)] Events / (5 MeV/c ) 10 60 40 0 3 0.10 < t' < 0.1 (GeV/c) Events / (5 MeV/c ) 40 30 0 10 3 10 0.44 < t' < 1.00 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 0 0.5 1 1.5.5 m [GeV/c 3π ] Challenge Production also depends on t Large data set ( 50 M eclusive events) Perform PWA also in narrow bins of t (t -resolved analysis) Etract m 3π AND t dependence of partial-wave amplitudes 9/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Results [Adolph et al., PRD 95, 03004 (017)] Events / (5 MeV/c ) 0.4 0.3 0. 6 10 a 1 (160) a (130) π (1670) 1 ++ 0 + ρ(770) π S a1(160) ++ 1 + ρ(770) π D a(130) + 0 + f (170) π S π(1670) 0.1 0 0.5 1 1.5.5 m [GeV/c 3π ] 10/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Results [Adolph et al., PRD 95, 03004 (017)] 1 ++ 0 + ρ(770) π S a1(160) ++ 1 + ρ(770) π D a(130) + 0 + f (170) π S π(1670) Events / (5 MeV/c ) 0.4 0.3 0. 0.1 6 10 a 1 (160) a (130) π (1670) 0 0.5 1 1.5.5 m [GeV/c 3π ] π P [1 ++ 0 + ] Intensity / (0 MeV/c ) 6 10 1.5 3.7% 1 0.5 ρ(770) + + + 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] S π π + π p p recoil 10/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Results [Adolph et al., PRD 95, 03004 (017)] 1 ++ 0 + ρ(770) π S a1(160) ++ 1 + ρ(770) π D a(130) + 0 + f (170) π S π(1670) Events / (5 MeV/c ) Intensity / (0 MeV/c ) 0.4 0.3 0. 0.1 6 10 a 1 (160) a (130) π (1670) 0 0.5 1 1.5.5 m [GeV/c 3π ] 6 10 1 7.7% 0.5 + + + 1 ρ(770) π D 0.100 < t' < 1.000 (GeV/c) Intensity / (0 MeV/c ) 6 10 1.5 3.7% 1 0.5 + + + 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 0 0.5 1 1.5.5 m [GeV/c 3π ] 10/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Results [Adolph et al., PRD 95, 03004 (017)] 1 ++ 0 + ρ(770) π S a1(160) ++ 1 + ρ(770) π D a(130) + 0 + f (170) π S π(1670) Events / (5 MeV/c ) Intensity / (0 MeV/c ) 0.4 0.3 0. 0.1 6 10 a 1 (160) a (130) π (1670) 0 0.5 1 1.5.5 m [GeV/c 3π ] 6 10 1 7.7% 0.5 + + + 1 ρ(770) π D 0.100 < t' < 1.000 (GeV/c) Intensity / (0 MeV/c ) Intensity / (0 MeV/c ) 6 10 1.5 3.7% 1 0.5 + + + 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 0.3 0. 6 10 6.7% + + 0 f (170) π S 0.100 < t' < 1.000 (GeV/c) 0.1 0 0.5 1 1.5.5 m [GeV/c 3π ] 0 0.5 1 1.5.5 m [GeV/c 3π ] 10/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Partial-Wave Analysis Results [Adolph et al., PRD 95, 03004 (017)] Events / (5 MeV/c ) Intensity / (0 MeV/c ) 0.4 0.3 0. 0.1 0.5 6 10 a 1 (160) a (130) π (1670) Intensity / (0 MeV/c ) Intensity / (0 MeV/c ) 6 10 1.5 3.7% Wave1 ++ set0 for + ρ(770) π + pπ S π π π + + p recoil 0 a1(160) 88 partial waves 0.5 1 1.5.5 m [GeV/c 3π ] ++ 1 + ρ(770) π D Most comprehensive analysis + + + 6 so far in 10 PWA 1 ρ(770) of π 3π D final state 6 10 a(130) Spin J up to 6 1 7.7% 0.100 < t' < 1.000 (GeV/c) 6.7% + 0 Angular + f (170) momentum π S L up to 6 0.3 π(1670) 6 different π π + isobars 1 0.5 + + + 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 0. + + 0 f (170) π S 0.100 < t' < 1.000 (GeV/c) 0.1 0 0.5 1 1.5.5 m [GeV/c 3π ] 0 0.5 1 1.5.5 m [GeV/c 3π ] 10/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method Data Resonance Parameters Masses and widths of the meson resonances 11/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method Data (I) Partial-Wave Decomposition Partial Waves Intensities and relative phases of the partial waves Resonance Parameters Masses and widths of the meson resonances 11/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method Data (I) Partial-Wave Decomposition Partial Waves Intensities and relative phases of the partial waves (II) Resonance-Model Fit Resonance Parameters Masses and widths of the meson resonances 11/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] Modeling m 3π dependence Parameterize m 3π dependence of partial-wave amplitudes (intensity & phase) T α (m 3π, t ) = Cα(t k ) D k (m 3π, t ; ζ k ) k Comp α Dynamic functions D k (m 3π, t ; ζ k ) For resonances: Breit-Wigner amplitude For non-resonant term: Phenomenological parameterization Coupling amplitudes Cα(t k ) Determine strength and phase of components Independent coupling amplitude for each t bin 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] The fit Describes large fraction of data consistently Simultaneous fit of 14 waves ( 60 %) Described by 11 resonances: a1, a, a 4, π, π 1, π Etract t dependence of model components 13/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] 13/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method 13/6 [arxiv:180.05913] S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Resonance-Model Fit Method [arxiv:180.05913] The fit Describes large fraction of data consistently Simultaneous fit of 14 waves ( 60 %) Described by 11 resonances: a1, a, a 4, π, π 1, π Etract t dependence of model components 13/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States π π π + Final State [arxiv:180.05913] Intensity / (0 MeV/c ) 1 0.5 + + + 6 10 1 ρ(770) π D 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. a (130) 0.5 1 1.5.5 m [GeV/c 3π ] Good description of clear peak Very stable with respect to variations of the fit model Potential a (1700) appearing Strongest evidence in f(170) π P decay 14/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States π π π + Final State [arxiv:180.05913] Intensity / (0 MeV/c ) 1 0.5 + + + 6 10 1 ρ(770) π D 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. Intensity / (0 MeV/c ) 5 10 4 10 3 10 10 + + + 1 ρ(770) π D 0.100 < t' < 0.113 (GeV/c) 10 0.5 1 1.5.5 m [GeV/c 3π ] a (130) and a (1700) Good description of clear peak Very stable with respect to variations of the fit model 0.5 1 1.5.5 m [GeV/c 3π ] Potential a (1700) appearing as destructive interference at low t Strongest evidence in f(170) π P decay 14/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States π π π + Final State [arxiv:180.05913] Intensity / (0 MeV/c ) 1 0.5 + + + 6 10 1 ρ(770) π D 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. Intensity / (0 MeV/c ) 0 10 + + + 3 10 1 f (170) π P 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0.5 1 1.5.5 m [GeV/c 3π ] a (130) and a (1700) Good description of clear peak Very stable with respect to variations of the fit model 0.5 1 1.5.5 m [GeV/c 3π ] Potential a (1700) appearing as destructive interference at low t Strongest evidence in f(170) π P decay 14/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States ηπ Final State at COMPASS [Phys.Lett. B740 (015) 303-311] ηπ invariant mass distribution Clear a (130) signal D-wave contribution dominant Possible a(1700) in high-mass shoulder of a (130) 15/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States ηπ Final State at COMPASS [Phys.Lett. B740 (015) 303-311] D-wave intensity Clear a (130) signal D-wave contribution dominant Possible a(1700) in high-mass shoulder of a (130) 15/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States Test Analytic and Unitary Models on ηπ Final State [Phys.Lett. B779 (018) 464-47] Models have to include principles of analyticity and unitarity Breit-Wigner models only for narrow isolated resonances Improve the employed models collaboration with JPAC Developed analytic model based on relativistic S-matri principles J PC = ++ wave in ηπ a (130) pole In agreement with π π π + analysis a (1700) pole Mass in agreement with π π π + analysis Width is 160 MeV/c larger in π π π + analysis Possible reasons: Breit-Wigner model assumptions Only intensity fitted in ηπ analysis... 16/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States Test Analytic and Unitary Models on ηπ Final State [Phys.Lett. B779 (018) 464-47] Models have to include principles of analyticity and unitarity Breit-Wigner models only for narrow isolated resonances Improve the employed models collaboration with JPAC Developed analytic model based on relativistic S-matri principles J PC = ++ wave in ηπ a (130) pole In agreement with π π π + analysis a (1700) pole Mass in agreement with π π π + analysis Width is 160 MeV/c larger in π π π + analysis Possible reasons: Breit-Wigner model assumptions Only intensity fitted in ηπ analysis... Intensity 10 3 140 0 10 100 10 80 0 60 1.4 1.6 1.8.0 40 0 0 0.5 1.0 1.5.0.5 3.0 s [GeV] 16/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = ++ States ηπ Final State at GlueX COMPASS [Phys.Lett. B740 (015) 303-311] GlueX [J. Stevens, Kπ-workshop, 018, JLab] GlueX data on ηπ final state Similar data-set size as COMPASS more data epected in 018 [J. Stevens, Kπ-workshop, 018, JLab]: https://www.jlab.org/conferences/pki018/talks/wed/stevens.pdf 17/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Partial-Wave Decomposition [Adolph et al., PRD 95, 03004 (017)] π P [1 + 1 + ] ρ(770) P π π + π p p recoil 1 + : spin-eotic π 1 -like quantum numbers Forbidden quantum numbers for q q system (non-rel.) Lattice-QCD: lightest hybrid predicted with 1 + quantum numbers Broad intensity distribution Strong evolution with t 18/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Partial-Wave Decomposition [Adolph et al., PRD 95, 03004 (017)] Intensity / (0 MeV/c ) 0 10 3 10 0.8% + + 1 1 ρ(770) π P 0.100 < t' < 1.000 (GeV/c) 0 0.5 1 1.5.5 m [GeV/c 3π ] 1 + : spin-eotic π 1 -like quantum numbers Forbidden quantum numbers for q q system (non-rel.) Lattice-QCD: lightest hybrid predicted with 1 + quantum numbers Broad intensity distribution Strong evolution with t 18/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Partial-Wave Decomposition [Adolph et al., PRD 95, 03004 (017)] Low t High t 1 + : spin-eotic π 1 -like quantum numbers Forbidden quantum numbers for q q system (non-rel.) Lattice-QCD: lightest hybrid predicted with 1 + quantum numbers Broad intensity distribution Strong evolution with t 18/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History BNL E85 1 waves Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History BNL E85 1 waves BNL E85 36 (high) vs 1 (low) waves Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History COMPASS 008 1 waves COMPASS 008 36 waves ) Intensity / (0 MeV/c 3 10 50 + + 1 1 ρ(770) π P 0.100 t' 1.000 (GeV/c) 40 30 0 π preliminary p π π π + p (COMPASS 008) ) Intensity / (0 MeV/c 3 10 + + 6 1 1 ρ(770) π P 0.189 t' 0.0 (GeV/c) 5 4 3 π preliminary p π π π + p (COMPASS 008) 1 Waves 36 Waves 10 1 0 0.8 1 1. 1.4 1.6 1.8..4 Mass of the π π π + System (GeV/c ) 0 1. 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Mass of the π π π + System (GeV/c ) Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History COMPASS 008 88 waves Intensity / (0 MeV/c ) 0 10 3 10 0.8% + + 1 1 ρ(770) π P 0.100 < t' < 1.000 (GeV/c) VES 0 0.5 1 1.5.5 m [GeV/c 3π ] Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History COMPASS 008 88 waves (low t ) BNL E85 36 (high) vs 1 (low) waves Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State History COMPASS 008 88 waves (low t ) BNL E85 36 (high) vs 1 (low) waves t -resolved analysis is crucial Wave set used in PWA model is crucial Work in progress: Methods to infer wave-set from data Narrow peak at 1.6 GeV/c in BNL E85 analysis [Chung S., Phys.Rev. D65 (00)] No peak in later BNL E85 analysis using more data [Dzierba A., Phys.Rev. D73 (006)] Main features reproduced in COMPASS data using the same model Similar results in analysis of VES data [Zaitsev A., Nucl.Phys A675 (000) 155C-160C] Strongest evidence for possible π 1 (1600) in high-t region 19/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Resonance-Model Fit [arxiv:180.05913] Intensity / (0 MeV/c ) 0 10 + + 3 10 1 1 ρ(770) π P 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0.5 1 1.5.5 m [GeV/c 3π ] π 1 (1600), m 0 = 1600 +100 50 MeV/c, Γ 0 = 610 +70 40 MeV/c Large non-resonant contribution in spin-eotic 1 + wave, but... Strong modulation with t is eploited in t -resolved analysis No description of data at high t without Breit-Wigner component 0/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Resonance-Model Fit [arxiv:180.05913] Intensity / (0 MeV/c ) 4 + + 3 10 1 1 ρ(770) π P 0.100 < t' < 0.113 (GeV/c) Model curve Resonances Nonres. comp. Intensity / (0 MeV/c ) 3 10 1 1 ρ(770) π P 1 0.74 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0.5 + + 0.5 1 1.5.5 m [GeV/c 3π ] π 1 (1600), m 0 = 1600 +100 50 MeV/c, Γ 0 = 610 +70 40 MeV/c 0.5 1 1.5.5 m [GeV/c 3π ] Large non-resonant contribution in spin-eotic 1 + wave, but... Strong modulation with t is eploited in t -resolved analysis No description of data at high t without Breit-Wigner component 0/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 + State Resonance-Model Fit [arxiv:180.05913] [deg] φ 100 0 100 00 + + + + + [1 1 ρ(770) π P] [1 0 ρ(770) π S] 0.74 < t' < 1.000 (GeV/c) Intensity / (0 MeV/c ) 3 10 1 1 ρ(770) π P 1 0.74 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0.5 + + 300 0.5 1 1.5.5 m [GeV/c 3π ] π 1 (1600), m 0 = 1600 +100 50 MeV/c, Γ 0 = 610 +70 40 MeV/c 0.5 1 1.5.5 m [GeV/c 3π ] Large non-resonant contribution in spin-eotic 1 + wave, but... Strong modulation with t is eploited in t -resolved analysis No description of data at high t without Breit-Wigner component 0/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method [arxiv:1711.1088] π P [J P C M ε ] [j pc ] L π π + π p p recoil Allows to study π π + isobar amplitude for specific j pc of π π + isobar system for specific J PC of π π π + system as a function of m3π Study many different isobar amplitudes simultaneously 1/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method J PC = 1 + Wave with freed j pc = 1 Isobar Amplitude.0 Preliminary 1 + 1 + [ππ] 1 πp 0.36 < t < 1.000(GeV/c) 105000 90000 75000 j pc = 1 mπ [GeV/c ] 1.5 1.0 60000 45000 30000 0.5 15000 0.5 1.0 1.5.0.5 0 m 3π [GeV/c ] J PC = 1 + /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method J PC = 1 + Wave with freed j pc = 1 Isobar Amplitude.0 Preliminary 1 + 1 + [ππ] 1 πp 0.36 < t < 1.000(GeV/c) 105000 90000 75000 j pc = 1 mπ [GeV/c ] 1.5 1.0 60000 45000 30000 0.5 15000 0.5 1.0 1.5.0.5 0 m 3π [GeV/c ] J PC = 1 + /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method J PC = 1 + Wave with freed j pc = 1 Isobar Amplitude 10 6 1.58 < m 3π < 1.6GeV/c 1 + 1 + [ππ] 1 πp Corrected zero mode Full range Fied shape Intensity [Events/(GeV/c )] 3 0.36 < t < 1.000(GeV/c) 1 Preliminary 0 0.5 1.0 m π π + [GeV/c ] Study π π + amplitude as a function of m 3π m π π + spectrum shows good agreement with ρ(770) Breit-Wigner Etract m π π + dependence of comple-valued amplitude Shape of m 3π spectrum is in fair agreement with fied-isobar analysis π 1 (1600) signal at about 1.6 GeV/c robust /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method J PC = 1 + Wave with freed j pc = 1 Isobar Amplitude 10 3 1.58 < m 3π < 1.6GeV/c 1 + 1 + [ππ] 1 πp Corrected zero mode Full range Fied shape Im(Tbin)[(Events/(GeV/c )) 1/ ] 1 0 0.36 < t < 1.000(GeV/c) 0.79 0.89 0.30 0.69 Preliminary 1 0 1 Re(T bin)[(events/(gev/c )) 1/ ] 10 3 10 6 1.58 < m 3π < 1.6GeV/c 1 + 1 + [ππ] 1 πp Corrected zero mode Full range Fied shape Intensity [Events/(GeV/c )] 3 0.36 < t < 1.000(GeV/c) 1 0 Preliminary 0.5 1.0 m π π + [GeV/c ] Study π π + amplitude as a function of m 3π m π π + spectrum shows good agreement with ρ(770) Breit-Wigner Etract m π π + dependence of comple-valued amplitude Shape of m 3π spectrum is in fair agreement with fied-isobar analysis π 1 (1600) signal at about 1.6 GeV/c robust /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Freed-Isobar Method J PC = 1 + Wave with freed j pc = 1 Isobar Amplitude 10 4 1 + 1 + [ππ] 1 πp Intensity [Events/40 MeV] 1 Fied isobars 0.36 < t < 1.000(GeV/c) Freed isobars Preliminary 10 6 1.58 < m 3π < 1.6GeV/c 1 + 1 + [ππ] 1 πp Corrected zero mode Full range Fied shape Intensity [Events/(GeV/c )] 3 0.36 < t < 1.000(GeV/c) 1 Preliminary 0 0.5 1.0 1.5.0.5 m 3π[GeV/c ] 0 0.5 1.0 m π π + [GeV/c ] Study π π + amplitude as a function of m 3π m π π + spectrum shows good agreement with ρ(770) Breit-Wigner Etract m π π + dependence of comple-valued amplitude Shape of m 3π spectrum is in fair agreement with fied-isobar analysis π 1 (1600) signal at about 1.6 GeV/c robust /6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States f 0 (980) π P Decay [arxiv:180.05913] a 1 (140) m 0 = 1411 +4 5 MeV/c, Γ 0 = 151 +11 14 MeV/c Narrow peak at about 1.4 GeV/c Modeled by Breit-Wigner resonance: a 1 (140) Mass too close to a 1 (160) ground state a 1 (140) does not fit into q q spectrum Nature of this signal still unclear? Tetra-quark state [Phys. Rev. D 91, 0940 (015), Phys.Rev. D96 (017) no.3, 034030] Interference effect between a1(160) and Deck-like contributions [Phys.Rev.Lett. 114 (015)] Anomalous triangle singularity in a 1(160) K K (89) f 0(980)π [Phys. Rev. D 91, 094015 (015), Phys. Rev. D 94, 096015 (016)] Intensity / (0 MeV/c ) 3 10 1 0 f (980) π P 0 30 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0 10 + + + 0.5 1 1.5.5 m [GeV/c 3π ] 3/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States f 0 (980) π P Decay [arxiv:180.05913] a 1 (140) m 0 = 1411 +4 5 MeV/c, Γ 0 = 151 +11 14 MeV/c Narrow peak at about 1.4 GeV/c Modeled by Breit-Wigner resonance: a 1 (140) Mass too close to a 1 (160) ground state a 1 (140) does not fit into q q spectrum Nature of this signal still unclear? Tetra-quark state [Phys. Rev. D 91, 0940 (015), Phys.Rev. D96 (017) no.3, 034030] Interference effect between a1(160) and Deck-like contributions [Phys.Rev.Lett. 114 (015)] Anomalous triangle singularity in a 1(160) K K (89) f 0(980)π [Phys. Rev. D 91, 094015 (015), Phys. Rev. D 94, 096015 (016)] Intensity / (0 MeV/c ) 3 10 1 0 f (980) π P 0 30 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0 10 + + + 0.5 1 1.5.5 m [GeV/c 3π ] 3/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States ρ(770) π S Decay Intensity / (0 MeV/c ) 1.5 1 0.5 + + + 6 10 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. [arxiv:180.05913] 0.5 1 1.5.5 m [GeV/c 3π ] a 1 (160), m 0 = 199 +1 8 MeV/c, Γ 0 = 380 ± 80 MeV/c Broad peak in intensity spectrum Large spread in a 1 (160) parameters from previous measurements Imperfections in the model systematic uncertainties dominant 4/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States ρ(770) π S Decay Intensity / (0 MeV/c ) 1.5 1 0.5 + + + 6 10 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. [arxiv:180.05913] 0.5 1 1.5.5 m [GeV/c 3π ] a 1 (160), m 0 = 199 +1 8 MeV/c, Γ 0 = 380 ± 80 MeV/c Broad peak in intensity spectrum Large spread in a 1 (160) parameters from previous measurements Imperfections in the model systematic uncertainties dominant 4/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States ρ(770) π S Decay Intensity / (0 MeV/c ) 1.5 1 0.5 + + + 6 10 1 0 ρ(770) π S 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. Need to combine information from different measurements [arxiv:180.05913] 0.5 1 1.5.5 m [GeV/c 3π ] a 1 (160), m 0 = 199 +1 8 MeV/c, Γ 0 = 380 ± 80 MeV/c Broad peak in intensity spectrum Large spread in a 1 (160) parameters from previous measurements Imperfections in the model systematic uncertainties dominant 4/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
J PC = 1 ++ States πππ States in τ Decays CLEO [Phys.Rev. D61 (000) 0100] BELLE [Phys.Rev. D81 (010) 113007] Observation of τ πππ + ν τ in τ + τ production Clean data samples Tagging of τ decay via the second τ No other hadrons involved No non-resonant contributions Clarify nature of a 1 (160), a 1 (140), a 1 (1640),... 5/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Conclusion Light-hadron spectroscopy is a active field High-precision measurement of ground and ecited states: a (130), a (1700), a 1(160),... Study of eotic states: π1(1600), a 1(140),... Many high-precision data upcoming GlueX, Belle II,... Limited by systematic effects develop advanced methods and models Tight collaboration with theorists 5 10 + + + 1 ρ(770) π D 0.100 < t' < 0.113 (GeV/c) Intensity / (0 MeV/c ) 4 10 3 10 10 10 0.5 1 1.5.5 m [GeV/c 3π ] 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Conclusion Light-hadron spectroscopy is a active field High-precision measurement of ground and ecited states: a (130), a (1700), a 1(160),... Study of eotic states: π1(1600), a 1(140),... Many high-precision data upcoming GlueX, Belle II,... Limited by systematic effects develop advanced methods and models Tight collaboration with theorists Intensity / (0 MeV/c ) 0 10 3 + + 10 1 1 ρ(770) π P 0.100 < t' < 1.000 (GeV/c) Model curve Resonances Nonres. comp. 0.5 1 1.5.5 m [GeV/c 3π ] 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Conclusion Light-hadron spectroscopy is a active field High-precision measurement of ground and ecited states: a (130), a (1700), a 1(160),... Study of eotic states: π1(1600), a 1(140),... Many high-precision data upcoming GlueX, Belle II,... Limited by systematic effects develop advanced methods and models Tight collaboration with theorists 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Conclusion Light-hadron spectroscopy is a active field High-precision measurement of ground and ecited states: a (130), a (1700), a 1(160),... Study of eotic states: π1(1600), a 1(140),... Many high-precision data upcoming GlueX, Belle II,... Limited by systematic effects develop advanced methods and models Tight collaboration with theorists 10 3 140 0 10 Intensity 100 80 60 40 10 0 1.4 1.6 1.8.0 0 0 0.5 1.0 1.5.0.5 3.0 s [GeV] 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
Conclusion Light-hadron spectroscopy is a active field High-precision measurement of ground and ecited states: a (130), a (1700), a 1(160),... Study of eotic states: π1(1600), a 1(140),... Many high-precision data upcoming GlueX, Belle II,... Limited by systematic effects develop advanced methods and models Tight collaboration with theorists Future results from COMPASS Etended freed-isobar analysis π π + j pc : 0 ++, 1,.. π π π + J PC : 0 +, 1 ++, 1 +,... Spectroscopy of kaons... K + p K π π + + p recoil... 6/6 S. Wallner Overview of Light-Hadron Spectroscopy and Eotics
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