The Fascinating Structure of Hadrons: What have we learned about excited protons? Volker Credé Florida State University, Tallahassee, FL Physics Colloquium University of Georgia, 4/4/23
Outline Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances 2 Electromagnetic Probes Mission Goal: Complete Experiments 3 Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions 4
Outline Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances 2 Electromagnetic Probes Mission Goal: Complete Experiments 3 Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions 4
Quarks, QCD, and Confinement Structure of Baryon Resonances The Early Particle Zoo and the Quark Model Name proton given to hydrogen nucleus by Rutherford in 92: He had discovered earlier that the proton was a candidate to be a fundamental particle and building block of nitrogen, and all other heavier atomic nuclei. 932 Neutron 947 First Mesons: π, π, K, K 95 Strange baryons: Λ with uds 964 Ω with sss
Quarks, QCD, and Confinement Structure of Baryon Resonances The Early Particle Zoo and the Quark Model Name proton given to hydrogen nucleus by Rutherford in 92: He had discovered earlier that the proton was a candidate to be a fundamental particle and building block of nitrogen, and all other heavier atomic nuclei. 932 Neutron 947 First Mesons: π, π, K, K 95 Strange baryons: Λ with uds 964 Ω with sss 964 Quark model (based on Flavor SU(3)) 968 Discovery of partons at SLAC after 97: Quantum Chromodynamics (QCD)
Quarks, QCD, and Confinement Structure of Baryon Resonances Non-Perturbative Quantum Chromodynamics (QCD) QCD is the theory of the strong nuclear force which describes the interactions of quarks and gluons making up hadrons. Strong processes at larger distances and at small (soft) momentum transfers belong to the realm of non-perturbative QCD. Hadron multiplets, e.g. Simple ansatz for the quark-antiquark potential: V = 4 3 α S (r) c r k r arxiv:hep-ex/6635
Quarks, QCD, and Confinement Structure of Baryon Resonances Non-Perturbative Quantum Chromodynamics (QCD) QCD is the theory of the strong nuclear force which describes the interactions of quarks and gluons making up hadrons. Strong processes at larger distances and at small (soft) momentum transfers belong to the realm of non-perturbative QCD. Quarks are confined within hadrons. Confinement of quarks and gluons within nucleons is a non-perturbative phenomenon, and QCD is extremely hard to solve in non-perturbative regimes: Knowledge of internal structure of nucleons is still limited. This is particularly true for excited nucleons.
Non-Perturbative QCD Quarks, QCD, and Confinement Structure of Baryon Resonances How does QCD give rise to excited hadrons? Interaction between quarks fairly unknown throughout > 98 % of a hadron s volume. Explaining the excitation spectrum of hadrons is central to our understanding of QCD in the low-energy regime (Hadron Models, Lattice QCD, etc.) Complementary to Deep Inelastic Scattering (DIS) where information on collective degrees of freedom is lost.
Non-Perturbative QCD Quarks, QCD, and Confinement Structure of Baryon Resonances How does QCD give rise to excited hadrons? What is the origin of confinement? 2 How are confinement and chiral symmetry breaking connected? 3 Would the answers to these questions explain the origin of 98% of observed matter in the universe? Excited Baryons: What are the fundamental degrees of freedom inside a proton or a neutron? How do they change with varying quark masses?
Understanding Excited Baryons The excitation spectrum of the hydrogen atom: Quarks, QCD, and Confinement Structure of Baryon Resonances Study of the hydrogen spectrum has shown that the understanding of the structure of a bound state and of its excitation spectrum go hand in hand.
Understanding Excited Baryons Quarks, QCD, and Confinement Structure of Baryon Resonances N 3 5 6 8 2 3 7 3 6 7 6 5 PDG 22 W Nomenclature: P 33 (232) (old) (232) 3 2 (new)
3 Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances Spectrum of Nucleon Resonances S. Capstick and N. Isgur, Phys. Rev. D34 (986) 289 Perhaps only the tip of the iceberg has been discovered? ** 25 *** **** ** **** **** Mass [MeV] 2 5 * S *** **** ** **** ** ** **** 2. Excitation Band: (56, 2 ), (56, 2 2 ) (7, 2 ), (7, 2 2 ) ( ) (2, 2 )? * ** S S *** **** **** **** ****. Excitation Band: (7, ) Theory Experiment **** J π /2 3/2 5/2 7/2 9/2 /2 3/2 /2-3/2-5/2-7/2-9/2- /2-3/2-
3 Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances Spectrum of Nucleon Resonances S. Capstick and N. Isgur, Phys. Rev. D34 (986) 289 Perhaps only the tip of the iceberg has been discovered? ** 25 *** **** ** **** **** Mass [MeV] 2 5 * S *** **** ** **** ** ** **** 2. Excitation Band: (56, 2 ), (56, 2 2 ) (7, 2 ), (7, 2 2 ) ( ) (2, 2 )? * ** S S *** **** **** **** ****. Excitation Band: (7, ) Theory Experiment **** J π /2 3/2 5/2 7/2 9/2 /2 3/2 /2-3/2-5/2-7/2-9/2- /2-3/2-
Quarks, QCD, and Confinement Structure of Baryon Resonances Excited-State Baryon Spectroscopy from Lattice QCD R. Edwards et al., Phys. Rev. D 84, 7458 (2) Missing states? (7) N(938) (232) (62) m π = 4 MeV Exhibits broad features expected of SU(6) O(3) symmetry Counting of levels consistent with non-rel. quark model, no parity doubling
Quarks, QCD, and Confinement Structure of Baryon Resonances Components of the Experimental N Program The excited baryon program has two main components: Probe resonance transitions at different distance scales Electron beams are ideal to measure resonance form factors and their corresponding Q 2 dependence. Provides information on the structure of excited nucleons and on the confining (effective) forces of the 3-quark system. Establish the systematics of the spectrum Current medium-energy experiments use photon beams to map out the baryon spectrum (JLab, ELSA, MAMI, SPring-8, etc.). Provides information on the nature of the effective degrees of freedom in strong QCD and also addresses the issue of previously unobserved or so-called missing resonances.
Quarks, QCD, and Confinement Structure of Baryon Resonances Helicity Amplitudes for the Roper Resonance A /2 ( 3 GeV /2 ) 8 6 4 2-2 -4-6 -8 2 3 4 Q 2 (GeV 2 ) S /2 ( 3 GeV /2 ) 7 6 5 4 3 2 2 3 4 Q 2 (GeV 2 ) Consistency between both channels (Nππ, Nπ): sign change, magnitude,... At short distances (high Q 2 ), Roper behaves like radial excitation. Low Q 2 behavior not well described by LF quark models: e.g. meson-baryon interactions missing Gluonic excitation likely ruled out! Data from CLAS A /2 and S /2 amplitudes: e.g. V. Mokeev et al., PRC 86, 3523 (22); PRC 8, 4522 (29). Quark-model calculations: - q 3 radial excitation - - - - q 3 G hybrid state
A /2 ( 3 GeV /2 ) Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances Helicity Amplitudes for γ p N(52)D 3 Transition -2-4 -6-8 - -2 V. Mokeev et al., PRC bf 86, 3523 (22). 2 3 4 5 Q 2 (GeV 2 ) A 3/2 ( 3 GeV /2 ) 8 6 4 2 8 6 4 2 2 3 4 5 Q 2 (GeV 2 ) L. Tiator et al. There is clear evidence for helicity switch from λ = 3/2 (at photon point) to λ = /2 at high Q 2 : Rapid change in helicity structure when going from photo- to electroproduction of a nucleon resonance Stringent prediction of the CQM! A hel = A /2 2 A 3/2 2 A /2 2 A 3/2 2 Helicity asymmetry.75.25 -.25 - -.75 -.5 2 2.5 3 3.5 4 4.5 Q 2 (GeV 2 )
Quarks, QCD, and Confinement Structure of Baryon Resonances Components of the Experimental N Program The excited baryon program has two main components: Probe resonance transitions at different distance scales Electron beams are ideal to measure resonance form factors and their corresponding Q 2 dependence. Provides information on the structure of excited nucleons and on the confining (effective) forces of the 3-quark system. Establish the systematics of the spectrum Current medium-energy experiments use photon beams to map out the baryon spectrum (JLab, ELSA, MAMI, SPring-8, etc.). Provides information on the nature of the effective degrees of freedom in strong QCD and also addresses the issue of previously unobserved or so-called missing resonances.
Outline Introduction Electromagnetic Probes Mission Goal: Complete Experiments Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances 2 Electromagnetic Probes Mission Goal: Complete Experiments 3 Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions 4
Electromagnetic Probes Mission Goal: Complete Experiments E γ [GeV] Reaction Thresholds 3, W [GeV] 2.6 2.6 In addition: SPring-8 Saphir.66.6 γp pηη γp pπ ω γp pπ η γp pη γp pπππ γp pππ γp pπ 2, γp KΛ KΣ,.9.7 Common efforts at ELSA, JLab, and MAMI (Double-)polarization measurements, γp & γn reactions, etc.., ELSA CLAS MAMI-C GRAAL
Experimental Facilities Electromagnetic Probes Mission Goal: Complete Experiments CBELSA/TAPS at ELSA Jefferson Laboratory Meson photoproduction: γp pπ pγγ γp pη pγγ, p 3π, pπ π π γp pω pπ γ, π π π
Electromagnetic Probes Mission Goal: Complete Experiments Double-Polarization: Toward Complete Experiments Calorimeter system at ELSA is optimized for neutral particles. Crystal Barrel Setup at ELSA Close to 4π coverage Frozen-Spin Target: Butanol (C 4 H 9 OH). Crystal Barrel (23 CsI crystals) Inner Detector (53 scintillating fibers) Forward Plug (9 CsI crystals with PM s) MiniTAPS (26 BaF 2, - 2 )
Electromagnetic Probes Mission Goal: Complete Experiments The CLAS Spectrometer at Jefferson Laboratory g8b linear beam polarization FROST double polarization
Electromagnetic Probes Mission Goal: Complete Experiments Double-Polarization: Frozen Spin Targets Horizontal cryostat with integrated solenoid to freeze the proton spin. DNP at high B-field (2.5 T), holding mode at.4 T Relaxation time at ELSA 5 h ELSA CLAS Transverse Target Polarization (race-track coil - Dipole Magnet) Longitudinally-Polarized Target (P z 8 %)
Electromagnetic Probes Mission Goal: Complete Experiments Extraction of Resonance Parameters Double-polarization measurements Measurements off neutron and proton to resolve isospin contributions: A(γN π, η, K) I=3/2 2 A(γN π, η, K) I=/2 N Re-scattering effects: Large number of measurements (and reaction channels) needed to extract full scattering amplitude. Coupled Channels Maid Said BoGa... Jülich, Gießen, EBAC, etc. http://ebac-theory.jlab.org
Electromagnetic Probes Mission Goal: Complete Experiments Why are Polarization Observables Important? From π threshold up to (232) region dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) s- & p-wave approximation Λ y ( T δ l P cos 2φ) Fermi-Watson Theorem Λ z ( δ l G sin 2φ δ E)} Two observables sufficient, e.g. dσ/dω, Σ. Chiang & Tabakin, Phys. Rev. C55, 254 (997) 2 Above the ππ threshold More observables needed. In order to determine the full scattering amplitude without ambiguities, one has to carry out eight carefully selected measurements: four double-spin observables along with four single-spin observables. Eight well-chosen measurements are needed to fully determine production amplitudes F, F 2, F 3, and F 4.
Electromagnetic Probes Mission Goal: Complete Experiments Why are Polarization Observables Important? From π threshold up to (232) region dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) s- & p-wave approximation Λ y ( T δ l P cos 2φ) Fermi-Watson Theorem Λ z ( δ l G sin 2φ δ E)} Two observables sufficient, e.g. dσ/dω, Σ. Chiang & Tabakin, Phys. Rev. C55, 254 (997) 2 Above the ππ threshold More observables needed. In order to determine the full scattering amplitude without ambiguities, one has to carry out eight carefully selected measurements: four double-spin observables along with four single-spin observables. Eight well-chosen measurements are needed to fully determine production amplitudes F, F 2, F 3, and F 4.
Example: Ambiguities in γ p pπ Electromagnetic Probes Mission Goal: Complete Experiments Bonn-Gatchina (BnGa) SAID MAID dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) Λ y ( T δ l P cos 2φ) Λ z ( δ l G sin 2φ δ E)} Example: E = N N 2Λ z δ N N Total cross section: γp pπ
Example: Ambiguities in γ p pπ Electromagnetic Probes Mission Goal: Complete Experiments Bonn-Gatchina (BnGa) PWA SAID MAID σ /2 σ σ 3/2
Electromagnetic Probes Mission Goal: Complete Experiments Helicity Asymmetry E in γ p pπ (Data from ELSA) E E = σ /2 σ 3/2 σ /2 σ 3/2 E γ [.6, 2.2] GeV CBELSA/TAPS Maid Said BoGa Angular distributions sensitive to interference between resonances. M. Gottschall et al. [CBELSA/TAPS] cosθ π
Example: Ambiguities in γ p pη Electromagnetic Probes Mission Goal: Complete Experiments D 3 (52) dσ dω = σ { δ l Σ cos 2φ} CLAS ga CBELSA/TAPS MAMI GRAAL P 3 (72) BoGa-PWA.45 MAMI CLAS LNS GRAAL CBELSA/TAPS.4-.45 -.6.45.6-.7.4.4.4.4 E γ = 25 MeV P 3 (72) dσ/dω [nb/sr].3.2.4.35.3.25.2.5.45.4.7-.8.35.35.3.3.25.25.2.2.5.5.5..5.2.25.3.35.4.5..5.2.25.3.35.4.45.4.8-.9.45.4.9-..35.35.35.3.3.3 D 3 (52) η-maid.2.25.25.25.2.2.2.5.5.5....8.2.4 D. Elsner et al. [CBELSA/TAPS], EPJ A 33, 47 (27).8.2.4 E γ [GeV].8.2.4
Electromagnetic Probes Mission Goal: Complete Experiments Helicity-Dependent Cross Section for γ p p η E = σ /2 σ 3/2 σ /2 σ 3/2 Very preliminary: Data are positive M. Gottschall et al. [CBELSA/TAPS] B. Morrison et al. [CLAS Collaboration]
Electromagnetic Probes Mission Goal: Complete Experiments Systematics in Photoproduction (Normalization) dσ dω = N events Φ γ ǫ MC ρ t Γ Ω.4.45.4 MAMI CLAS LNS GRAAL CBELSA/TAPS.4-.45.4 -.6.45.4.6-.7.35.35.35 dσ/dω [nb/sr].3.2.4.2.3.25.2.5.45.4.35.3.25.2.7-.8.3.3.25.25.2.2.5.5.5..5.2.25.3.35.4.5..5.2.25.3.35.4.45.4.35.3.25.2.8-.9.45.4.35.3.25.2.9-. p p ω) b / sr] (γ dσ/dω[µ ω p SLAC 973 (E γ CLAS 29 (E γ = 2.8 GeV) = 2.795 GeV) s = 2.48 GeV.5.5.5...8.2.4.8.2.4.8.2.4 E γ [GeV] γp pη : O. Bartholomy, V. C. et al. [ELSA] PRL 94 (25), EPJ A 33 (27), PRC 8 (29).. - - - cosθ ω
Electromagnetic Probes Mission Goal: Complete Experiments Fascinating Discovery in Reactions off the Neutron σ[µb] 5 5 σ n /σ p 2.5 2.5 6 8 2 22 W[MeV] 6 8 2 22 W[MeV] σ(ηp), free proton σ(ηp), quasi-free proton 3/2σ(ηn), quasi-free neutron Neutron measurements important: Different resonance contributions Study of isospin composition of el.-magn. couplings Narrow structure in γd nη p with M 67 MeV and σ = 25 MeV: Interference effect of the S (535) and S (535) resonances Coupled channel effect of S (535) and P (7) New narrow state? I. Jaegle et al. [CBELSA/TAPS], Eur. Phys. J. A 47, 89 (2)
Outline Introduction Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances 2 Electromagnetic Probes Mission Goal: Complete Experiments 3 Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions 4
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Isospin Filter: γ p N (I = /2) pω A. Wilson et al. [CBELSA/TAPS], Ph.D. thesis (Florida State)..9.9.8.8.7.7.6 CBELSA/TAPS CLAS (29) dσ/dω dσ/dω [µb [µb/sr] / ].5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5.6.4.4.3.3.2.2..... Preliminary.5 2 2.5.5 2 2.5.5 2 2.5 E γ [ GeV ].5 2 2.5..2.5 2 2.5 Good agreement between experiments Excellent statistics Great progress in our understanding of the differences between experiments.
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Isospin Filter: γ p N (I = /2) pω A. Wilson et al. [CBELSA/TAPS], Ph.D. thesis (Florida State)..9.9.8.8.7.7.6 CBELSA/TAPS CLAS (29) dσ/dω dσ/dω [µb [µb/sr] / ].5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5.6.4.4.3.3.2 5.5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5 Preliminary 5 5.5 2 2.5.87.9.9.93.93.97.97. 5.5 2 2.5 E γ [ GeV ] 5.5 2 2.5 Good agreement between experiments Excellent statistics New CBELSA/TAPS data extend the world database in the most forward direction.
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Isospin Filter: γ p N (I = /2) pω dσ/dω dσ/dω [µb [µb/sr] / ] A. Wilson et al. [CBELSA/TAPS], Ph.D. thesis (Florida State)..9.9.8.8.7.7.6.5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5.6.4.4.3.3.2 5.5 2 2.5.5 2 2.5 Preliminary 5 5.5 2 2.5.87.9.9.93.93.97.97. 5 5 CBELSA/TAPS CLAS (29) γ p γ * N time? ω p ω.5 2 2.5.5 2 2.5.5 2 2.5.5 2 2.5 E γ [ GeV ] p time p
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Baryon Resonances in the Reaction γ p pω M. Williams et al. [CLAS Collaboration], Phys. Rev. C 8, 6529 (29) PWA fit includes resonances t-channel amplitudes. Strong evidence for (W > 2 GeV): (5/2) N(68) (5/2) N(95) (7/2) N(29) J π /2 3/2 5/2 7/2
Polarization Observables in γ p pω Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Asymmetry Σ for γp pω (P. Collins et al., CUA) Strong evidence for (W > 2 GeV): (5/2) N(68) (5/2) N(95) (7/2) N(29) Oh et al. Paris et al. Sarantsev et al.
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Photoproduction of π Mesons from the Proton Reaction γp pπ remains important for our understanding of baryons. ] µb sr [ dσ dω At ELSA, excellent data with good statistics in the forward direction. Forward region is very sensitive to higher-spin resonances: Observation of N(29)G 7 within the Bonn-Gatchina PWA framework (Important to confirm high-mass states first observed in πn scattering) 2 2.5 35-4 MeV 2.5 2.5 75-8 MeV 2 5 5 5 5 5 5 θ c.m. V. C. et al. [CBELSA/TAPS], Phys. Rev. C 84, 5523 (2).5 9-95 MeV CBELSA/TAPS CB-ELSA CLAS, GRAAL older Bonn data
Beam Asymmetry Σ in γ p pπ Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) Λ y ( T δ l P cos 2φ) Λ z ( δ l G sin 2φ δ E)} SAID MAID CLAS (E γ < 2 GeV,.85 < cosθ π <.35) Serious discrepancies between models and data above.4 GeV. Photoproduction of π mesons still not very well understood. M. Dugger (ASU), CLAS g8b run group, to be published
Beam Asymmetry Σ in γ p pπ Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions SAID MAID CLAS (E γ < 2 GeV,.35 < cosθ π <.85) Combination of pπ and nπ final states can help distinguish between and N resonances: M. Dugger (ASU), CLAS g8b run group, to be published
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Beam Asymmetry Σ in γ p pπ and γp nπ M. Dugger (ASU), CLAS g8b run group, to be published
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Asymmetry G in γ p pπ (Results from ELSA).6.4.2 -.2 dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) Λ y ( T δ l P cos 2φ) Λ z ( δ l G sin 2φ δ E)} -.4 -.6 -.8.6 - - -.8 -.6 -.4 -.2.2.4.6.8.4.2 -.2 -.4 -.6 -.8 Surprisingly, π production also not well understood at lower energies: BoGa - - SAID... MAID A. Thiel et al. [CBELSA/TAPS], PRL 9, 2 (22) - cosθ π
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Asymmetry G in γ p pπ (Results from ELSA) θ π = 9±5 θ π = 3±5 A. Thiel et al. [CBELSA/TAPS], PRL 9, 2 (22) dσ dω = σ { δ l Σ cos 2φ Λ x ( δ l H sin 2φ δ F ) Λ y ( T δ l P cos 2φ) Λ z ( δ l G sin 2φ δ E)} Surprisingly, π production also not well understood at lower energies. Below GeV, discrepancies can be traced to the E and E 2 multipoles, which are related to certain resonances: E : N(535) 2, N(65) 2, (62) 2 E 2 : N(52) 3 2, (7) 3 2
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Transverse Target Polarization: Target Asymmetry T 7 < E γ < 8 MeV 8 < E γ < 9 MeV N.4.3 γ p pπ.2. -. -.2 -.3 -.4-9 8 27 χ 2 / ndf 23.25 / 7 T -.2444 ±.29 Preliminary N.4 γ p pη.3.2. -. -.2 -.3 -.4-9 8 27 χ 2 / ndf 9.97 / 7 T.668 ±.9 Preliminary φ π φ π direction of target pol.: β = 99 N(φ) = f P target N N N N = T sin(φ β) Unprecedented statistical quality. target pol. axis photon pol. x y z unpolarized σ T linear Σ H P G circular F E
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Introduction Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Target Asymmetry T in γ p pπ (Data from ELSA) T 6 MeV < E γ - - - - - 7 MeV < E γ 8 MeV < E γ 9 MeV < E γ < 625 MeV < 725 MeV < 825 MeV 625 MeV < E γ 725 MeV < E γ 825 MeV < E γ < 65 MeV < 75 MeV < 85 MeV 65 MeV < E γ 75 MeV < E γ 85 MeV < E γ < 675 MeV < 775 MeV < 875 MeV 675 MeV < E γ 775 MeV < E γ 875 MeV < E γ < 7 MeV < 8 MeV < 9 MeV preliminary < 925 MeV 925 MeV < E γ < 95 MeV 95 MeV < E γ < 975 MeV 975 MeV < E γ < MeV - - - - - - - - 6 < E γ < MeV in bins of E = 25 MeV CBELSA/TAPS Daresbury (977) Nucl. Phys. B 2 (977), 45 Maid Said Bonn Gatchina Good agreement of experimental data. (improved statistics) J. Hartmann et al. [CBELSA/TAPS] cosθ π
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Introduction Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Target Asymmetry T in γ p pπ (Data from ELSA) T MeV < E γ < 25 MeV 25 MeV < E γ < 5 MeV - - - - - MeV < E γ 233 MeV < E γ 367 MeV < E γ < 33 MeV < 267 MeV 33 MeV < E γ 267 MeV < E γ < 67 MeV < 3 MeV 5 MeV < E γ 67 MeV < E γ 3 MeV < E γ < 75 MeV < 2 MeV < 333 MeV 75 MeV < E γ 2 MeV < E γ 333 MeV < E γ < MeV < 233 MeV < 367 MeV preliminary < 4 MeV 4 MeV < E γ < 433 MeV 433 MeV < E γ < 467 MeV 467 MeV < E γ < 5 MeV - - - - - - - - cosθ π < E γ < 5 MeV CBELSA/TAPS Daresbury (977) Nucl. Phys. B 2 (977), 45 Maid Said Bonn Gatchina Good agreement of experimental data. Model disagreement toward 3 rd resonance region: W >.6 GeV (E, E 2 multipoles?)
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Target Asymmetry T in γ p pη (Data from ELSA) T - 78 MeV < E γ < 733 MeV 733 MeV < E γ < 758 MeV - 783 MeV < E γ < 88 MeV - - very preliminary - 88 MeV < E γ < 833 MeV - 758 MeV < E γ < 783 MeV - - - - - - - 858 MeV < E γ < 883 MeV 883 MeV < E γ < 98 MeV - 833 MeV < E γ < 858 MeV - - - - - - - - - J. Hartmann et al. [CBELSA/TAPS] 98 MeV < E γ < 933 MeV cosθ η 78 < E γ < 933 MeV in bins of E = 25 MeV CBELSA/TAPS PHOENICS (998) Phys. Rev. Lett. 8 (998), 534 Maid Said Bonn Gatchina
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Observables P, H (Results from CBELSA/TAPS) 8 < E γ < 9 MeV N.4.3.2. -. -.2 -.3 -.4 9 8 27 χ 2 / ndf 7.24 / 6 P -.45 ±.8 H.26 ±.76 γ p pπ Preliminary N.4.3.2. -. -.2 -.3 γ p pη -.4 9 8 27 χ 2 / ndf 9.974 / 6 P.275 ±.22 H -.769 ±.23 Preliminary φ π φ π angle of lin. pol. plane: α = 45 direction of target pol.: β = 99 N(φ) = C (N N ) (N N ) (N N )(N N ) = P(sin(φ β) cos(2(φ α)) H(cos(φ β) sin(2(φ α)) target pol. axis photon pol. x y z unpolarized σ T linear Σ H P G circular F E
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Beam-Target Polarization Observables in γ p p ππ I = I {( Λ i P) δ (I Λ i P ) δ l [ sin 2β( I s Λ i P s ) cos 2β( I c Λ i P c )]} W. Roberts et al., Phys. Rev. C 7, 552 (25) Double-Meson Final States (5 Observables) At higher excitation energies: Multi-meson final states important. Search for states in decay cascades!
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Photoproduction of ππ Pairs off the Proton: Kinematics Two mesons in the final state require 5 independent variables! For example: E γ, Θ c.m., φ, θ, M p meson Single-meson reactions: p-meson system in the reaction plane Two-meson reactions: Reaction and decay plane form angle φ
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Beam Asymmetries I s, I c in γ p pπ π First measurements of beam asymmetries I s and I c using linearly-polarized photons in the reaction γp pπ π. Among other things, study of decays into π: BoGa-PWA solution with a dominant (7)D 33 π D-wave... BoGa-PWA solution with a dominant (7)D 33 π S-wave Direct measurements From mirror operation I s (Φ ) I s (2π Φ ) V. Sokhoyan et al. [CBELSA/TAPS], to be published
I - - - - - - - - - - - - - - - - - - - - - - - - - - - Introduction Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions I s in γ p pπ π from JLab: < E γ < 5 MeV I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 Data < cos( θπ of ) < unprecedented -.7 -.7 < cos( ) < -.6 θπ stat. -.6 quality < cos( ) < - θπ Here: 3-dim. phasespace (E γ,θ π,φ π ) - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions Beam Asymmetry I in γ p pπ π from JLab I Analysis of butanol target challenging: Determination of dilution factor (event-based dilution factors possible) W =.6 GeV Preliminary W =.65 GeV Preliminary 45 4 35 3 25 W =.7 2 GeV Preliminary 5 5 Top. γ p -> p π ( π- ) Butanol data Butanol data w/ CLcut Bound Nucleon data Free Proton data Carbon data W =.75 GeV Preliminary 5 5 2 25 3 35 4 45 5 Missing Mass [MeV] W =.8 GeV W =.85 GeV W =.9 GeV W =.95 GeV Preliminary Preliminary Preliminary Preliminary 2 4 6 2 4 6 2 4 6 2 4 6 S. Park et al., CLAS (FROST); CLAS (gc) PRL 95 (25) φ π
Outline Introduction Quarks, QCD, and Confinement Structure of Baryon Resonances 2 Electromagnetic Probes Mission Goal: Complete Experiments 3 Photoproduction of π, η, and ω Mesons Observables in the Photoproduction of Two Pions 4
Our understanding of baryon resonances has made great leaps forward. There is good evidence that most of the known states (listed in the PDG) will be confirmed in photoproduction and that new states will be revealed: Goal of performing (almost) complete experiments has been (almost) achieved; program on neutron ongoing. Advances in both theory and experiment will allow us to finally understand QCD and confinement. N(86) 5 2 N(875) 3 2 N(88) 2 N(895) 2 N(9) 3 2 N(26) 5 2 (94) 3 2 πn γn πn γn ΛK ΣK Nσ πn γn ΛK ΣK πn γn ηn ΛK ΣK New States πn γn ηn ΛK ΣK π πn γn ηn ΣK in PDG 22. πn γn η (!)
Our understanding of baryon resonances has made great leaps forward. There is good evidence that most of the known states (listed in the PDG) will be confirmed in photoproduction and that new states will be revealed: Hadron spectroscopy (e.g. search for exotic mesons) will continue at Jefferson Lab in the 2 GeV era with the GlueX experiment in Hall D:
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I s in γ p pπ π from JLab: < E γ < 5 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 Data < cos( θπ of ) < unprecedented -.7 -.7 < cos( ) < -.6 θπ stat. -.6 quality < cos( ) < - θπ Here: 3-dim. phasespace (E γ,θ π,φ π ) - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 5 < E γ < 2 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 2 < E γ < 25 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 25 < E γ < 3 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 3 < E γ < 35 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 35 < E γ < 4 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 4 < E γ < 45 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 45 < E γ < 5 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 5 < E γ < 55 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 55 < E γ < 6 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 6 < E γ < 65 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 65 < E γ < 7 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 7 < E γ < 75 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 75 < E γ < 8 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 8 < E γ < 85 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 85 < E γ < 9 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 9 < E γ < 95 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 95 < E γ < 2 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 2 < E γ < 25 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π
I s in γ p pπ π from JLab: 25 < E γ < 2 MeV I - - - - - - - - - - - - - - - - - - - - - - - - - - - I s -. < cos( θπ ) < -.9 -.9 < cos( θπ ) < -.8 -.8 < cos( θπ ) < -.7 -.7 < cos( θπ ) < -.6 -.6 < cos( θπ ) < - - < cos( θπ ) < -.4 -.4 < cos( θπ ) < -.3 -.3 < cos( θπ ) < -.2 -.2 < cos( θπ ) < -. -. < cos( θπ ) <. s X. < cos( θπ ) <.. < cos( θπ ) <.2.2 < cos( θπ ) <.3.3 < cos( θπ ) <.4.4 < cos( θπ ) < < cos( θπ ) <.6.6 < cos( θπ ) <.7.7 < cos( θπ ) <.8.8 < cos( θπ ) <.9.9 < cos( θπ ) <. C. Hanretty et al., CLAS-g8b run group, under review -2 φ π