Measurement of the Polarization Observables. Spectrometer. I s and I c for γp p π + π using the CLAS. Charles Hanretty.

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1 Measurement of the I s and I c for γp p π + π using the CLAS Spectrometer Charles Hanretty Florida State University, Tallahassee, FL October 3, 2 Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 / 58

2 Outline Theory and Motivation Theory and Motivation Theory: QCD Constituent Quark Models and Missing Resonances 2 Jefferson Lab Hall B 3 Extraction of Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 2 / 58

3 What is the big picture? Theory and Motivation Theory: QCD Constituent Quark Models and Missing Resonances Hadrons: Particles that are held together and interact via the strong force. Exist as bound states of quarks. Are the most fundamental of systems found in nature. Members of this group are Baryons and Mesons. Quark Structure: Baryon: qqq Quark Structure: Meson: q q Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 3 / 58

4 Quantum Chromodynamics (QCD) Theory: QCD Constituent Quark Models and Missing Resonances Properties of QCD Describes the strong force. Introduces a color charge analogous to the electric charge (red, blue, green). Gluons and quarks possess a color charge, antiparticles possess anticolor. All observed particles are white or colorless states. Interactions are mediated by gluons. Since gluons carry a color charge, they mediate AND participate in the interactions. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 4 / 58

5 Quantum Chromodynamics (QCD): Features Theory: QCD Constituent Quark Models and Missing Resonances Two main features of QCD Asymptotic Freedom: When the energy of the system is high (like in a high energy reaction high momentum transfer), the quarks and gluons interact very weakly. Baryon can then be treated as being comprised of three non-interacting quarks pqcd. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 5 / 58

6 Quantum Chromodynamics (QCD): Features Theory: QCD Constituent Quark Models and Missing Resonances Two main features of QCD Asymptotic Freedom: When the energy of the system is high (like in a high energy reaction high momentum transfer), the quarks and gluons interact very weakly. Baryon can then be treated as being comprised of three non-interacting quarks pqcd. Confinement: The attractive force between quarks grows with the distance between them. This means that the quarks are confined to be in the hadron there are no free quarks (non-pqcd). Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 6 / 58

7 Constituent Quark Models (CQMs) N Resonances (I = /2) Theory: QCD Constituent Quark Models and Missing Resonances Constituent quarks are the current or bare valence quarks after they have been dressed with the mass of the sea quarks and the sea gluons. U. Loring, et al., Eur. Phys. J. A, 39 (2), heo-ph/3287 Generated using predictions according to a model view of the baryon. Assumes three quark degrees of freedom. Various models differ in how they treat short-range interactions. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 7 / 58

8 Constituent Quark Models (CQMs) N Resonances (I = /2) Theory: QCD Constituent Quark Models and Missing Resonances U. Loring, et al., Eur. Phys. J. A, 39 (2), heo-ph/3287 Generated using predictions according to a model view of the baryon. Assumes three quark degrees of freedom. Various models differ in how they treat short-range interactions. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 8 / 58

9 CQMs: Missing Resonances Theory: QCD Constituent Quark Models and Missing Resonances N Resonances (I = /2) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 9 / 58

10 Why so many missing resonances? Theory: QCD Constituent Quark Models and Missing Resonances Possible answers and reasons... Most of what is found in the PDG handbooks has come from πn and KN scattering γn. Analyses involved a single meson final state (i.e. K + Λ, K + Σ, Nπ, Nη). Analyze a double-meson final state has the largest cross section. Sequential decay to final ground state particles: ex. γp N ++ π p π + π. Particle mass widths expected to be 5 MeV too big for a two-body (single meson) final state. Possible quark-diquark structure of the baryon. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 / 58

11 Why so many missing resonances? Theory: QCD Constituent Quark Models and Missing Resonances Possible answers and reasons... Most of what is found in the PDG handbooks has come from πn and KN scattering γn. Analyses involved a single meson final state (i.e. K + Λ, K + Σ, Nπ, Nη). Analyze a double-meson final state has the largest cross section. Sequential decay to final ground state particles: ex. γp N ++ π p π + π. Particle mass widths expected to be 5 MeV too big for a two-body (single meson) final state. Possible quark-diquark structure of the baryon. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 / 58

12 Why so many missing resonances? Theory: QCD Constituent Quark Models and Missing Resonances Possible answers and reasons... Most of what is found in the PDG handbooks has come from πn and KN scattering γn. Analyses involved a single meson final state (i.e. K + Λ, K + Σ, Nπ, Nη). Analyze a double-meson final state has the largest cross section. Sequential decay to final ground state particles: ex. γp N ++ π p π + π. Particle mass widths expected to be 5 MeV too big for a two-body (single meson) final state. Possible quark-diquark structure of the baryon. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 2 / 58

13 Why so many missing resonances? Theory: QCD Constituent Quark Models and Missing Resonances Possible answers and reasons... Most of what is found in the PDG handbooks has come from πn and KN scattering γn. Analyses involved a single meson final state (i.e. K + Λ, K + Σ, Nπ, Nη). Analyze a double-meson final state has the largest cross section. Sequential decay to final ground state particles: ex. γp N ++ π p π + π. Particle mass widths expected to be 5 MeV too big for a two-body (single meson) final state. Possible quark-diquark structure of the baryon. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 3 / 58

14 Constituent Quark Models (CQMs) Theory: QCD Constituent Quark Models and Missing Resonances Resonances are both broad and overlapping! Makes it very difficult to determine singular resonance contributions. We need a way to disentangle these resonances and determine which resonances are produced! Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 4 / 58

15 Jefferson Lab Hall B Charles Hanretty (FSU) Measurement of Is and Ic for ~ γ p p π+ π October 3, 2 T HOMAS J EFFERSON N ATIONAL ACCELERATOR FACILITY (JL AB ) The Facility Theory and Motivation 5 / 58

16 Hall B: The CLAS Detector Jefferson Lab Hall B CEBAF Large Acceptance Spectrometer Drift Chambers Time Of Flight Torus Electromagnetic Calorimeters Cherenkov Counters Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 6 / 58

17 Hall B: the CLAS Detector Jefferson Lab Hall B Magnetic field of Torus affects the particle s trajectory (bending it toward or away from the beamline). Particle s path through CLAS is tracked. Q > Q < If trigger requirements are met, event is recorded. Reconstruction code determines particle s trajectory through CLAS. Q > Information regarding the incident particle and final state particles are determined. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 7 / 58

18 Hall B: Photon Tagger Theory and Motivation Jefferson Lab Hall B Electrons from accelerator interact with the radiator, producing photons via bremsstrahlung. Electrons are bent into hodoscope via the Tagger Magnet. Time stamp and energy of electron is measured. Photon energy determined via Eγ = E - E Can tag photons with energies ranging from (.2)E to (.95)E. E Eγ E Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 8 / 58

19 Polarized Photons Theory and Motivation Jefferson Lab Hall B Circularly polarized beam: longitudinal electron beam + amorphous radiator Linearly polarized beam: unpolarized electron beam + oriented diamond radiator Can obtain 9% polarization g8b highly polarized photons at five energies:.3 GeV,.5 GeV,.7 GeV,.9 GeV and 2. GeV. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 9 / 58

20 Charles Hanretty (FSU) Jefferson Lab Hall B Measurement of Is and Ic for ~ γ p p π+ π FROST: Transverse Holding Coil Theory and Motivation October 3, 2 2 / 58

21 Jefferson Lab Hall B Charles Hanretty (FSU) Measurement of Is and Ic for ~ γ p p π+ π FROST: Target Assembly, Testing, Installation Theory and Motivation October 3, 2 2 / 58

22 Extraction of.4 Measurable quantities called are sensitive to resonance contributions. Occur when the constraint of polarization (beam and/or target) is imposed on the reaction(s). Can be predicted according to model calculations..3 Dr. W. Roberts.2 S 3 (9) omitted Full calc I c P 3 (9) omitted I s m pπ m π + π φ = rad φ =.5652 rad φ = rad φ = rad Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 22 / 58

23 Extraction of.4 Measurable quantities called are sensitive to resonance contributions. Occur when the constraint of polarization (beam and/or target) is imposed on the reaction(s). Can be predicted according to model calculations..3 Dr. W. Roberts I c.2 S 3 (9) omitted Polarization Full calc observables are highly sensitive to which resonances P. are present! 3 (9) omitted I s m pπ m π + π φ = rad φ =.5652 rad φ = rad φ = rad Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 23 / 58

24 Extraction of : Single Meson Final State The final state equation relates the differential cross section, dσ dω polarization observables. For a final state with one meson, there are a total of 7 observables. dσ dω = σ { δl Σ cos(2φ), to the +Λx ( δl H sin(2φ) + δ F ) Λy ( T + δl P cos(2φ) ) Λz ( δl G sin(2φ) + δ E )} Definitions dσ dω = differential cross section σ = unpolarized cross section δ l, = degree and orientation of photon beam polarization Λx,y,z = direction and degree of polarization of the target Σ, H, F, T, P, G, E = polarization observables. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 24 / 58

25 Extraction of : Double Meson Final State For a final state with two mesons, there are a total of 5 observables! I = I { ( + Λi P )+δ ( I + Λi P ) +δl [ sin(2β) ( I s + Λi P s ) + cos(2β) ( I c + Λi P c ) ] } Definitions I = unpolarized reaction rate Λ i = direction and degree of polarization of the target δ l, = degree and orientation of photon beam polarization P = observable arising from the use of a polarized target I,s,c = observables arising from the use of polarized photons β = orientation of polarization w.r.t. a final state particle (β = φ lab + φ polarization ) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 25 / 58

26 Reducing the final state equation Extraction of Applying the run conditions of g8b simplifies the final state equation and reduces the number of observables. Linearly polarized photon beam incident on an unpolarized LH2 target. ( Λi =, δ = ) I = I { ( + Λi P )+δ ( I + Λi P ) +δl [ sin(2β) ( I s + Λi P s ) + cos(2β) ( I c + Λi P c ) ] } Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 26 / 58

27 Reducing the final state equation Extraction of Applying the run conditions of g8b simplifies the final state equation and reduces the number of observables. Linearly polarized photon beam incident on an unpolarized LH2 target. ( Λi =, δ = ) I = I { + δl [ I s sin(2β) + I c cos(2β) ] } Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 27 / 58

28 Reducing the final state equation Extraction of Applying the run conditions of g8b simplifies the final state equation and reduces the number of observables. Linearly polarized photon beam incident on an unpolarized LH2 target. ( Λi =, δ = ) I = I { + δl [ I s sin(2β) + I c cos(2β) ] } I s I c (Σ in the single-meson final state equation) Measuring both for γp p π + π Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 28 / 58

29 Analysis of γp p π + π Extraction of While γp p π + π is studied, a total of four topologies are kinematically fitted. p π + (π ) p π (π + ) π + π (p) p π + π Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 29 / 58

30 Theory and Motivation Extraction of Enforces energy-momentum conservation. Varies final state measurements (4-vectors) within resolution limits (errors) of said measurements. Errors (as calculated by the reconstruction code) are extracted from data and used to build the tracking covariance matrix (event by event). Errors are then scaled to actual run-dependent resolutions to make the full covariance matrix. σ 2 Eγ C pp C pλ C pφ C pλ C λλ C λφ C pφ C λφ C φφ C pp k C pλ k C pφ k C pλ C pφ k C λλ k C λφ k C λφ k k C φφ k Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 3 / 58

31 Theory and Motivation Extraction of Quality of the fit is judged by examining the confidence level and pull distributions. Every diagonal element of the covariance matrix has a pull value associated with it. Systematics affect pull means (µ s), errors contained in the covariance matrix affect pull widths (σ s) and the slope of confidence level plots. Produced using one full run for each coherent edge energy. Produced using one full.3 GeV run. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 3 / 58

32 Momentum Corrections and Tagger Sag Extraction of Momentum Corrections: Kinematic fitter is highly sensitive to systematic effects good tool for determining momentum corrections. Corrections are needed to account for variations in torus B field and misalignments of Drift Chambers. Determined by examining momentum pull distributions for the proton for γp p π + π fits/events. Correction factor and pulls binning: 7 bins in θlab ( θlab 7 ), 8 bins in φlab 6 bins in momentum (.2 GeV p.7 GeV) Tagger Sag Occurs due to a physical sagging of the support structure for Tagger Hodoscope. Affects the determination of photon energy. Has been seen in several runs in Hall B. Requires energy-dependent correction M. Dugger, C. Hanretty, CLAS-Note 29-3 Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 32 / 58

33 Check the pull distributions Extraction of µ =.3534 σ =.8 µ = σ =.22 µ =.545 σ =.997 µ = σ =.987 µ =.4893 σ =.2 µ = σ =.9942 µ = σ =.9883 µ = σ =.24 µ = σ =.996 µ = σ =.7 γp p π + π (Run #48326) p λ φ Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 33 / 58

34 Kinematics Theory and Motivation Extraction of The analysis of the (double-meson) γp p π + π channel requires the use of 5 independent kinematic variables: (mpπ or mππ), cosθ p CM, k, cosθ π, φ + π. + Production plane Plane formed by the two pions Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 34 / 58

35 Extracting I s and I c : φ-distributions Extraction of Three types of (photon) polarization settings were used: PARA PERP AMO PARA PERP Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 35 / 58

36 Extracting I s and I c : φ-distributions Extraction of Three types of (photon) polarization settings were used: PARA PERP AMO The polarization of the photon beam breaks the usual φ symmetry. Events are plotted as a function of lab angle φ π + for each polarization setting. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 36 / 58

37 Extracting I s and I c : φ-distributions Extraction of Three types of (photon) polarization settings were used: PARA PERP AMO The polarization of the photon beam breaks the usual φ symmetry. Events are plotted as a function of lab angle φ π + for each polarization setting. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 37 / 58

38 Extracting I s and I c : Method Extraction of Characteristic: use of AMO φ-distributions. To remove (divide out) the effects of the experimental setup and acceptance, the φ-distributions for PARA and PERP are divided by the AMO φ-distributions (for matching bin combinations). Fit to I = I { + δl [ I s sin(2β) + I c cos(2β) ] } where β = φlab + φpolarization.25 GeV < Eγ.3 GeV - cosθ π φ π Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 38 / 58

39 Extracting I s and I c : Method 2 Extraction of Characteristic: No use of AMO data uses asymmetry between PARA and PERP. Asymmetry between PARA and PERP is formed for matching bin combinations. Fit to: A(k,cosθ π,φ + π ) = PARA PERP + PARA+PERP = I PARA IPERP IPARA + IPERP Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 39 / 58

40 Extracting I s and I c : Method 2 Extraction of Characteristic: No use of AMO data uses asymmetry between PARA and PERP. Asymmetry between PARA and PERP is formed for matching bin combinations. Fit to: A(k,cosθ π +,φ π + ) = (δ PARA + δ PERP ) I s sin(2β) + (δ PARA + δ PERP ) I c cos(2β) l PARA l PERP l PARA l PERP 2 + (δ PARA δ PERP ) I s sin(2β) + (δ PARA δ PERP ) I c cos(2β) l PARA l PERP l PARA l PERP.25 GeV < Eγ.3 GeV - cosθ π φ π GeV < Eγ.5 GeV -.9 cosθ π φ π + 62 Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 4 / 58

41 Preliminary Measurement: I s Extraction of.2 GeV < Eγ <.25 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < I s < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 4 / 58 φ π +

42 Preliminary Measurement: I s Extraction of.4 GeV < Eγ <.45 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < I s < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 42 / 58 φ π +

43 Preliminary Measurement: I s Extraction of.6 GeV < Eγ <.65 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < I s < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 43 / 58 φ π +

44 Preliminary Measurement: I c Extraction of.2 GeV < Eγ <.25 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Σ < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 44 / 58 φ π +

45 Preliminary Measurement: I c Extraction of.4 GeV < Eγ <.45 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Σ < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 45 / 58 φ π +

46 Preliminary Measurement: I c Extraction of.6 GeV < Eγ <.65 GeV -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) <. -. < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Σ < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < < cos( θπ + ) < Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 46 / 58 φ π +

47 Summary Theory and Motivation Extraction of Hadrons form the basis of most matter. These hadrons are systems containing quarks and gluons. Through the study of these systems when excited, the internal dynamics of the hadron may be demystified. Polarization observables are sensitive to these dynamics. Measured for γp p π + π : I c (first for a two-charged-pion final state) I s (first for a two-pion final state) These observable measurements as well as future measurements will aid in the refinement of CQMs as well aid in the revelation of the internal dynamics of the baryon. The FROST experiment will provide access to all 5 observables for a double-meson final state. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 47 / 58

48 Extraction of END Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 48 / 58

49 Extraction of Backup Slides Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 49 / 58

50 Cuts Theory and Motivation Extraction of Vertex -4 cm < zvertex < cm (for all detected particles) All z-vertices must be within 4 cm of each other. Cut on (event) x,y-vertex requiring it originates in the target cell. ns < tvertex < 2 ns (for all detected particles) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 5 / 58

51 Cuts Theory and Motivation Extraction of Vertex -4 cm < zvertex < cm (for all detected particles) All z-vertices must be within 4 cm of each other. Cut on (event) x,y-vertex requiring it originates in the target cell. ns < tvertex < 2 ns (for all detected particles) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 5 / 58

52 Cuts Theory and Motivation Extraction of Vertex -4 cm < zvertex < cm (for all detected particles) All z-vertices must be within 4 cm of each other. Cut on (event) x,y-vertex requiring it originates in the target cell. ns < tvertex < 2 ns (for all detected particles) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 52 / 58

53 Cuts Theory and Motivation Extraction of Photon Energy. GeV < Eγ <.3 GeV.3 GeV < Eγ <.5 GeV.5 GeV < Eγ <.7 GeV.7 GeV < Eγ <.9 GeV.9 GeV < Eγ < 2. GeV Momentum and Angle pproton > 32 MeV/c p π ± > 25 MeV/c θ > θ π ± < 2 Other Cuts Confidence level cut of 5%. ngrf = for all particles. tagrid same for all particles. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 53 / 58

54 Cuts Theory and Motivation Extraction of Photon Energy. GeV < Eγ <.3 GeV.3 GeV < Eγ <.5 GeV.5 GeV < Eγ <.7 GeV.7 GeV < Eγ <.9 GeV.9 GeV < Eγ < 2. GeV Momentum and Angle pproton > 32 MeV/c p π ± > 25 MeV/c θ > θ π ± < 2 Other Cuts Confidence level cut of 5%. ngrf = for all particles. tagrid same for all particles. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 54 / 58

55 Cuts Theory and Motivation Extraction of Photon Energy. GeV < Eγ <.3 GeV.3 GeV < Eγ <.5 GeV.5 GeV < Eγ <.7 GeV.7 GeV < Eγ <.9 GeV.9 GeV < Eγ < 2. GeV Momentum and Angle pproton > 32 MeV/c p π ± > 25 MeV/c θ > θ π ± < 2 Other Cuts Confidence level cut of 5%. ngrf = for all particles. tagrid same for all particles. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 55 / 58

56 Cuts Theory and Motivation Extraction of Photon Energy. GeV < Eγ <.3 GeV.3 GeV < Eγ <.5 GeV.5 GeV < Eγ <.7 GeV.7 GeV < Eγ <.9 GeV.9 GeV < Eγ < 2. GeV Momentum and Angle pproton > 32 MeV/c p π ± > 25 MeV/c θ > θ π ± < 2 Other Cuts Confidence level cut of 5%. ngrf = for all particles. tagrid same for all particles. Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 56 / 58

57 Examination of the behavior of I s and I c Extraction of The behavior of the measured observables is predicted to be either even (I c ) or odd (I s ) as a function of φ. To check the behavior, measurements were fit with expansions of sine and cosine for each cosθ bin. Contributions from the different terms were examined. f(φ ) = A + Acos(φ ) + A2cos(2φ ) + A3cos(3φ ) + A4cos(4φ ) + A5cos(5φ ) + A6cos(6φ ) + A7cos(7φ ) + A8sin(φ ) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 57 / 58

58 Examination of the behavior of I s and I c Extraction of The behavior of the measured observables is predicted to be either even (I c ) or odd (I s ) as a function of φ. To check the behavior, measurements were fit with expansions of sine and cosine for each cosθ bin. Contributions from the different terms were examined. f(φ ) = A + Asin(φ ) + A2sin(2φ ) + A3sin(3φ ) + A4sin(4φ ) + A5sin(5φ ) + A6sin(6φ ) + A7sin(7φ ) + A8cos(φ ) Charles Hanretty (FSU) Measurement of I s and I c for γp p π + π October 3, 2 58 / 58