Hunting the Resonances in p(γ, K + )Λ Reactions: (Over)Complete Measurements and Partial-Wave Analyses

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1 FACULTY OF SCIENCES Hunting the Resonances in p(γ, K + )Λ Reactions: (Over)Complete Measurements and Partial-Wave Analyses Jannes Nys Jan Ryckebusch (T. Vrancx, L. De Cruz, P. Vancraeyveld, T. Corthals) Electromagnetic production of pseudoscalar Department of Physics and Astronomy, Ghent University, Belgium mesons Nucleon Resonances: From Photoproduction to High Photon Virtualities, Tom Vrancx Trento Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 / 25

2 OVERVIEW Amplitude extraction DATA PWA σ M 2 γ p RPR K + Λ RPR γ p γ K + Λ K + γ... Λ Regge-plus-resonance (RPR) model and VR model p Λ p K + 2 Inferring model-independent reaction amplitudes Multipole decomposition (Partial Wave Analysis - PWA) Alternate (complementary) method: amplitude extraction Amplitude extraction using real data From complete to overcomplete sets Amplitude comparison 3 Conclusions Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 2 / 25

3 Regge-plus-resonance (RPR) approach [PRC86 (22) 522] Regge background: exchange of K(494) and K (892) Regge trajectories in t channel Enrich Reggeized background with N : J = 2, 3 2, 5 2 with M N 2 GeV Bayesian inference of the resonance content of p(γ, K + )Λ [PRL8 (22) 822] 7 parameters S (535), S (65), F 5 (68), P 3 (72), D 3 (875), P 3 (9), P (9), and F 5 (2) Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 3 / 25

4 Probability of a resonance given the p(γ, K + )Λ data Probability of a resonance given the γ(p, K + )Λ data Bayesian analysis: beyond point estimates! Marginalize Marginaliseover overall all possiblemodels with with resonance resonance R: R: P (R D) P (R P (M P (M P (M i ) P (M i D) i D) = = P (D M P (D M i ) i ) }{{ i ) }{{} P (D) } P (D). MM i R M i R M i i M i R M M i R M i i Z i Z i!! Jan Ryckebusch (Ghent University) Amplitude analysis of p(γ, K + )Λ Trento, July, 24 9 / Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 4 / 25

5 Bayesian evidence evidence map for the map 2 model for the variants 2 model variants -ln(z ) 3 2 RPR Number of N* parameters PRL8(22)822 RPR-2 (PDG-2) S (535) S (65) D 5 (675) F 5 (68) D 3 (7) P (7) P 3 (72) D 3 (875) m P 3 (9) P (9) m F 5 (2) Jan Ryckebusch (Ghent University) Amplitude analysis of p(γ, K + )Λ Trento, July, 24 8 / Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 5 / 25

6 RPR predictions for p(e, e K + )Λ RPR predictions for p (e, e K + ) Λ (µb/sr) σ T (µb/sr) σ L * cosθ K. Q 2 =.9 GeV 2 * cosθ K. CLAS Coman 29 RPR 2 Regge 2 Q 2 = 2.35 GeV * Q 2 =.9 GeV 2 * cosθ K. cosθ Q 2 = 2.35 GeV 2 K Data: LNS [PRC8 DATA: PRC8 (2) (2) 522] 522 fix the reaction amplitudes against Test p(γ, K of + )Λ predictive power: fix against p(γ, K + )Λ data, 2 most longitudinal test against p(e, e K + )Λ data couplings can be (no refitting) constrained by means 2 EM of gauge transition invariance form factors: t-channel: dipole (also 3 reasonable electric s-channel Born assumptions for K and N term), electromagnetic s-channel: Inferred from formbonn factors CQM helicity 4 transition amplitudes formusing factors consistent from Lagrangians. consistent Lagrangians Jan Ryckebusch (Ghent University) Amplitude analysis of p(γ, K + )Λ Trento, July, 24 3 / Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 6 / 25

7 RPR for neutral kaon photoproduction from DEUTERON targets Neutral kaon photoproduction from the deuteron Neutral kaon photoproduction from the deuteron Elementary-production Elementary-production operator: RPR model operator: RPR operator: model Parameters RPR for model neutron from Parameters Parameters the ones for offor the neutron neutron proton inferred from from the the ones ones of the of the proton proton using (isospin!) isospin (isospin!) symmetry PLB68(29)428 relativistic PLB68(29)428 Dnp-vertex + FSI relativistic Dnp-vertex + FSI [PLB68 relativistic (29) 428] Dnp-vertex + FSI (µb/gev) (µb/gev) dσ/dp.8 2 lab.8.7 H(γ,K )YN.9<E γ <. [GeV] lab 2 lab.7 H(γ,K )YN.9<E.9<cosθ γ <. [GeV] <. K.6 lab.9<cosθ <. K.6.5 dσ/dp K LEPS-PRC78(28)4 lab.<e K Λ γ <. [GeV] LEPS-PRC78(28)4 + lab K Λ+K Σ +K Σ lab.<e.9<cosθ <. [GeV] <. K Λ γ K Regge + lab K Λ+K Regge Σ +K+ resonances Σ.9<cosθ <. K Regge Regge + resonances p (MeV) 2 3 K p (MeV) K Data: DATA [PRC78, (LNS): PRC78, 4] 4 DATA (LNS): PRC78, 4 Jan Ryckebusch (Ghent University) Amplitude analysis of p(γ, K + )Λ Trento, July, 24 4 / JanJannes Ryckebusch Nys (Ghent (UGent) University) (Over)Completeness Amplitude analysis of p(γ, in p(γ, K + )ΛK + )Λ October Trento, July 3,, / 7 / 25 K

8 FIG. 3. (Color Jannes online) Nys The fitted (UGent) proton cutoff energy as a function (Over)Completeness of W. The data are the cutoff in p(γ, values extracted K + )Λfrom fitting the October VR 3, 25 8 / 25 ABOVE the resonance region: VR model (N(e, e π ± )N ) [PRC89 (24) 2523 (π)] Motivation: models with Reggeized background underestimate σ T Main component: gauged pion-exchange current (missing transverse strength provided by residual effects of nucleon resonances) EM transition FF implements resonance-parton contributions Running cutoff energy Λ γpp (s) for the proton EM transition FF correct on-shell limits lowers number of free parameters (compare: [PRC8(2) 4522]) simple interpretation: p charge radius asymptotically 4for p virtuality s 4. Data Λγpp (s) of Eq. (24) 3. Λγpp Λγpp (GeV)

9 dσ U/dt (µb/gev 2 ) 2 ε = W = 2.9 GeV Q 2 =.75 GeV 2 2 ε = W = 2.65 GeV Q 2 = 2.5 GeV 2 ε =.669 W = 2. GeV Q 2 = 2.65 GeV 2 2 ε = W = 2.9 GeV Q 2 = 2.95 GeV 2 ε =.548 W = 2. GeV Q 2 = 3.85 GeV ε =.589 W = 2.48 GeV Q 2 =.75 GeV 2 ε =.745 W = 2. GeV Q 2 = 2.35 GeV 2 ε =.549 W = 2.32 GeV Q 2 = 2.65 GeV 2 ε =.432 W = 2.43 GeV Q 2 = 2.95 GeV 2 ε =.43 W = 2.2 GeV Q 2 = 3.85 GeV t (GeV 2 ) ε =.744 W = 2.9 GeV Q 2 = 2.5 GeV 2 ε =.654 W = 2.2 GeV Q 2 = 2.35 GeV 2 ε =.348 W = 2.6 GeV Q 2 = 2.65 GeV 2 ε =.576 W = 2.9 GeV Q 2 = 3.35 GeV 2 ε =.266 W = 2.44 GeV Q 2 = 3.85 GeV ε =.63 W = 2.33 GeV Q 2 = 2.5 GeV 2 ε =.499 W = 2.47 GeV Q 2 = 2.35 GeV 2 ε =.68 W =.98 GeV Q 2 = 2.95 GeV 2 ε =.449 W = 2.3 GeV Q 2 = 3.35 GeV 2 ε =.43 W = 2. GeV Q 2 = 4.35 GeV For high t >.5 GeV 2 data [EPJ A49, 6 (23)] KM and previous VR do not show correct t-dependence Additional u-channel trajectories and/or t-dependence for Λ γππ do not considerably improve high t fit. Introduce FF in strong vertex of t-channel Regge amplitudes (monopole in t) p(e, e K + )Λ Use ingredients from π + production to predict observables of K + electroproduction. [PRC89 (24) 6522 (K)] FIG. 8. (Color Jannes online) TheNys t dependence (UGent) of the unseparated cross section dσ(over)completeness U/dt of the p(e, e π + )n reaction at twenty (W, Q 2 in, ε) combinations. p(γ, K + )Λ October 3, 25 9 / 25

10 OVERVIEW Amplitude extraction DATA PWA σ M 2 γ p RPR K + Λ RPR γ p γ K + Λ K + γ... Λ Regge-plus-resonance (RPR) model and VR model p Λ p K + 2 Inferring model-independent reaction amplitudes Multipole decomposition (Partial Wave Analysis - PWA) Alternate (complementary) method: amplitude extraction Amplitude extraction using real data From complete to overcomplete sets Amplitude comparison 3 Conclusions Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 / 25

11 Kinematics & Dynamics Case study of p(γ, K + )Λ Two independent kinematic variables Invariant mass W Kaon angle θ c.m. cm Photon: γ / Proton: p + 2 uud Kaon: K + u s Lambda: Λ + 2 uds Dynamics 2 spin-/2 particles and a real photon 8 combinations Symmetries of the reaction 4 independent COMPLEX REACTION AMPLITUDES M λγ λ p,λ Λ M i=,2,3,4 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 / 25

12 Transversity amplitudes / CGLN / multipoles Transversity Amplitudes (TA) b i=,...,4 cm b y + J y + y b 2 y J y y b 3 y + J x y b 4 y J x + y Normalized TA a i=,...,4 a i = b i = r b ie iαi 2 + b b b 4 2 CGLN amplitudes and multipole decomposition M = m sλ if σ.e P γ F 2 (σ.e p) [σ. (e k e P γ )] if 3 (σ.e k ) (e p.e P γ ) if 4 (σ.e p) (e p.e P γ ) m sp F = l P l+ (cos θc.m.) [E l+ + lm l+ ] + P l (cos θc.m.) [E l + (l + )M l ] F 2 = l P l (cos θc.m.) [(l + )M l+ + lm l ] F 3 = l P l+ (cos θc.m.) [E l+ M l+ ] + P l (cos θc.m.) [E l + M l ] F 4 = l P l (cos θc.m.) [ E l M l E l+ + M l+ ] Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 2 / 25

13 Multipoles for p(γ, K + )Λ (RPR-2): BACKGROUND DOMINANCE Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) E E Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) E M Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) M E Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) M M Figure : RPR-2, RPR-2 (only background) and RPR-2 (only N ). Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 3 / 25

14 Polarization observables in pseudoscalar-meson photoproduction (B, T, R ) (B 2, T 2, R 2 ) Transversity expression Σ (y,, ) (x,, ) r 2 + r2 2 r2 3 r2 4 T (, +y, ) (, y, ) r 2 r2 2 r2 3 + r2 4 P (,, +y) (,, y) r 2 r2 2 + r2 3 r2 4 Cx (+,, +x) (+,, x) 2 Im(a a 4 + a 2 a 3 ) Cz (+,, +z) (+,, z) +2 Re(a a 4 a 2 a 3 ) Ox (+ π 4,, +x) (+ π 4,, x) +2 Re(a a 4 + a 2 a 3 ) Oz (+ π 4,, +z) (+ π 4,, z) +2 Im(a a 4 a 2 a 3 ) E (+, z, ) (+, +z, ) +2 Re(a a 3 a 2 a 4 ) F (+, +x, ) (+, x, ) 2 Im(a a 3 + a 2 a 4 ) G (+ π 4, +z, ) (+ π 4, z, ) 2 Im(a a 3 a 2 a 4 ) H (+ π 4, +x, ) (+ π 4, x, ) +2 Re(a a 3 + a 2 a 4 ) Tx (, +x, +x) (, +x, x) +2 Re(a a 2 + a 3 a 4 ) Tz (, +x, +z) (, +x, z) +2 Im(a a 2 + a 3 a 4 ) Lx (, +z, +x) (, +z, x) 2 Im(a a 2 a 3 a 4 ) Lz (, +z, +z) (, +z, z) +2 Re(a a 2 a 3 a 4 ) dσ (B,T,R) dω : cross section for given beam (B), target (T ), recoil (R) polarization Asymmetries dω A = dσ dσ dω dσ (,,) dω = ρ 4 (B,T,R ) dσ (B 2,T 2,R 2 ) dω (B,T,R ) + dσ (B 2,T 2,R 2 ) dω 4 i= bi 2 SINGLE asymmetries: MODULI DOUBLE asymmetries: PHASES Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 4 / 25

15 Complete sets 4 complex amplitudes, or 8 real variables There is one arbitrary global phase δ α4 i = α i α 4. Take α 4 = and use normalized transversity amplitudes = a 2 + a a a 4 2 We need 6 real variables and an independent scaling factor Definition COMPLETE SET A complete set is a minimum set of observables from which one can determine the underlying reaction amplitudes unambiguously. [Chiang & Tabakin PRC55 (997) 254]: 8 observables Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 5 / 25

16 .8 Role of resonances for the NTA moduli (r 2 ) RPR-2 - resonance RPR-2 region RPR-2 - res cos θcm Regge + spin-/2 Regge Regge + cos θcm Regge + Regge spin-5/2 + spin-3/2 W(GeV) Regge +

17 RPR-2 predictions for (W, cos θ c.m. ) dependence of NTA moduli for p(γ, K + )Λ r r cos θc.m r 3 r cos θc.m : (Color online) The energy and angular dependence of the moduli r i of the normalized transversity amplitudes f Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 7 / 25

18 Extracted NTA moduli for p(γ, K + )Λ: FORWARD [PRC87 (23) 5525].45 cos θ cm cos θ cm cos θ cm r r r r r 2 : b 2 = y J y y Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 8 / 25

19 Extracted NTA moduli for p(γ, K + )Λ: BACKWARD [PRC87 (23) 5525] r cos θ cm GRAAL.4 RPR cos θ cm cos θ cm r r r cos θ cm cos θ cm cos θ cm.86 r 2 : b 2 = y J y y Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 9 / 25

20 RPR-2 predictions for (W, cos θ c.m. ) dependence of NTA relative phases δ i = α i α 4 for p(γ, K + )Λ at forward angles the background dominates and the W -dependence of δ i is mild at backward angles large N contributions and the W -dependence of δ i is wild Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 2 / 25

21 Full amplitude extraction (ri, δiα4 ) at single (s, t) [JPG42 (25) 346] π/2 π/2 2 π π 3π/2 3π/2 (a) Complete (b) Discrete amb. π/2 π/ π 3π/2 (c) Unimodal Jannes Nys (UGent) π 3π/2 (d) Improved (Over)Completeness in p(γ, K + )Λ October 3, 25 2 / 25

22 Amplitude distance a (s, t) a2 (s, t) Ma (s, t) a3 (s, t) a4 (s, t) Ma Ma = Q: What is the distance between M and M2? A: D [M, M2 ] = arccos Re M M2 Both Mi=,2 have an unknown α4. Q: How to calculate D [M, M2 ] independent of choice α4? A: α4 = argmin (D [M (α4 ), M2 (α4 = )]) α4 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

23 Model comparison in amplitude space D [M RP R 2 Regge, M Regge ] D [M RP R 2, M Kaon MAID ] π/2 π/2 cos θc.m π/8 π/4 π/8 D [MRPR-2, Mmodel] cos θc.m π/8 π/4 π/8 D [MRPR, MK-M] π/8 5π/8 π/2.86 GeV < W <.88 GeV PD UD M 3π/8 2π/8 π/ cos θc.m. Resolution of the data. Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

24 Required resolution for model falsification? Distance frequency D(RPR-2,Kaon-MAID) (no cuts) D(RPR-2,Kaon-MAID) (with cuts) D(RPR-2, Regge) (with cuts) D(RPR-2, RPR-2 NO D3) (with cuts) To obtain sensible results: Are the models falsifiable? Project information in amplitude space onto observable space (observables are not independent) Clear effect of measurements of individual observables by comparing posterior to prior distributions π/4 π/2 D Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

25 SUMMARY Available models RPR model for Q 2 = over large W range. VR for high virtuality Q 2 above the resonance region. Model-independent amplitude inference Obtaining resonance information in background-dominated reactions requires background-subtraction schemes, such as RPR-2. Hierarchy in the quality/quantity of the data! Quadratic equations connect {Σ, P, T } to the moduli {r, r 2, r 3, r 4 } of the normalized transversity amplitudes Analysis of γp K + Λ with {Σ, T, P } from GRAAL (.65 W.9 GeV) allowed to extract {r, r 2, r 3, r 4} in 95% of considered (W, cos θ c.m.) 2 RPR-2 is in reasonable agreement with the extracted r i Extracting the NTA independent phases {δ, δ 2, δ 3 } is far more challenging (connected to asymmetries by means of non-linear equations) Mathematical Completeness does not imply Practical Completeness!! Overcomplete sets provide a solution! Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

26 Selected publications J. Nys, T. Vrancx and J. Ryckebusch Amplitude extraction in pseudoscalar-meson photoproduction: towards a situation of complete information J. Phys. G 42 (25) 3, 346 D. G. Ireland Information Content of Polarization Measurements Phys. Rev. C 82 (2) 2524 T. Vrancx, J. Ryckebusch, T. Van Cuyck T, P. Vancraeyveld Incompleteness of complete pseudoscalar-meson photoproduction Phys. Rev. C 87 (23) L. De Cruz, J. Ryckebusch, T. Vrancx, P. Vancraeyveld A Bayesian analysis of kaon photoproduction with the Regge-plus-resonance model Phys. Rev. C 86 (22) 522 L. De Cruz, T. Vrancx, P. Vancraeyveld, J. Ryckebusch Bayesian inference of the resonance content of p(γ, K + )Λ Phys. Rev. Lett. 8 (22) 822 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

27 Backup slides Backup slides Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

28 Jannes Nys. (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / PREDICTIONS FOR ELECTROPRODUCTION 29 Electromagnetic form factors from Bonn-CQM ) 2 F (Q D 3 (7) P 3 (72) P 3 (9) Q (GeV ) ) 2 F 2 (Q D 3 (7) P 3 (72) P 3 (9) Q (GeV ).8 D 5 (675) F 5 (68) F 5 (2).8 D 5 (675) F 5 (68) F 5 (2) ) 2.6 ) 2.6 F (Q.4 F 2 (Q Q (GeV ) Q (GeV ) Figure 5.2 The EM transition form factors F (Q 2 ) (left panels) and F 2 (Q 2 ) (right panels) derived from helicity amplitudes calculated by the Bonn CQM [76]. The top panels show the results for the spin- 3/2 resonances D 3 (7), P 3 (72) and P 3 (9), while the lower panels display the results for the spin-5/2 resonances D 5 (675), F 5 (68) and F 5 (2).

29 34 CHAPTER 2. FORMALISM The expression for the amplitude (2.65) can be regarded as an infinite sum of residues that result Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25 Figure 2.6 Chew-Frautschi plots for the two lightest kaon trajectories. Meson masses as listed by the PDG were used [25]. Note that each line represents two trajectories, corresponding with the odd- and even-parity states. Sommerfeld-Watson transformation

30 Reconstructed observables: CLAS check..7 GeV W.76 GeV..76 GeV W.8 GeV..8 GeV W.86 GeV Cx. Cx. Cx Cz. Cz. Cz cos θ c.m cos θ c.m cos θ c.m. Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 3 / 25

31 L max for 5% accuracy in RPR-2 cos θc.m L Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 3 / 25

32 Bayesian evidence map for the 2 model variants -ln(z ) 3 2 RPR Number of N* parameters PRL8(22)822 RPR-2 (PDG-2) S (535) S (65) D 5 (675) F 5 (68) D 3 (7) P (7) P 3 (72) D 3 (875) m P 3 (9) P (9) m F 5 (2) Jan Ryckebusch (Ghent University) Amplitude analysis of p(γ, K + )Λ Trento, July, 24 8 / 35 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

33 (M) (M) (M2) α 4 α α 2 α 3 π 2π α 4 α α 2 α 3 π 2π α 4 α α 2 α 3 π 2π α 4 δ α4 δ α4 2 δ α4 3 π 2π α 4 δ α4 δ α4 2 δ α4 3 π 2π α 4 δ α4 δ α4 2 δ α4 3 π 2π Figure : Example of a situation where a global phase transformation, followed by α 4 = can give a distorted picture of the degree of compatibility of two models. Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

34 Observable # data Experiment Year Reference dσ 56 SLAC 969 Boyarski et al. [38] 72 SAPHIR 24 Glander et al. [39] 377 CLAS 26 Bradford et al. [4] 2 LEPS 27 Hicks et al. [4] 266 CLAS 2 McCracken et al. [32] Σ 9 SLAC 979 Quinn et al. [42] 45 LEPS 23 Zegers et al. [43] 54 LEPS 26 Sumihama et al. [44] 4 LEPS 27 Hicks et al. [4] 66 GRAAL 27 Lleres et al. [3] T 3 BONN 978 Althoff et al. [45] 66 GRAAL 29 Lleres et al. [3] P 7 DESY 972 Vogel et al. [46] 233 CLAS 24 McNabb et al. [33] 66 GRAAL 27 Lleres et al. [3] 77 CLAS 2 McCracken et al. [32] C x, C z 32 CLAS 27 Bradford et al. [34] O x, O z 32 GRAAL 29 Lleres et al. [3] The Search for Missing Resonances in γp K + + Λ and K + + Σ Using Circularly Polarized Photons on a Transversely Polarized Frozen Spin Target (N. Walford, g9b, T, F, T x, T z). The Search for Missing Resonances in γp K + + Λ Using Circularly Polarized Photons on a Longitudinally Polarized Frozen Spin Target (L. Casey, g9a, E, L x, L z ). Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

35 N* photoproduction program at CLAS G T P E F G H T x T z L x L z O x O z C x C z SŒ r q q q q q q Proton targets QŒ + r q q q q q q S r q q q q q q S r q q q q q q Data taking completed May 8, 22 S&3 r q q q q q q æ-published, æ-acquired SS q q K + r q q r q q q q q q q q q q r r K + r q q r q q q q q q q q q q r r K * + r q q q K +* r q SŒ - r q q q q S! - q q q q q K - + q q q q q Neutron targets K q q q q q q q q q q q q K q q q q q q q q q q q q K * q q 45 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

36 Observables for particular experimental setups Table 7: The dσ dω for all possible experimental set ups [2]. For details, see text. Configuration B T R dσ dσ (,,) dω (conf.)/ dω N Y + P P R y L N L Y + P P R y + P T z (Lx P R x + Lz P R z ) T N + T P T y T Y + ΣP T y P R y + T P T y + P P R y + P T x (Tx P R x + Tz P R z ) c N c Y + P P R y + P γ c (Cx P R x + Cz P R z ) c L N EP γ c P T z c L Y + P P R y EP γ c P T z HP γ c P T z P R y + P γ c (Cx P R x + Cz P R z ) + P T z (Lx P R x + Lz P R z ) c T N + T P T y + F P γ c P T x c T Y + ΣP T y P R y + T P T y + P P R y + GP γ c P R y P T x + F P γ c P T x + P γ c P T y (Cx P R z + Cz P R x ) +P γ c P T y (Ox P R z + Oz P R x ) + P T x (Tx P R x + Tz P R z ) l N ΣP γ l cos(2φγ) l Y ΣP γ l cos(2φγ) T P γ l P y R cos(2φγ) + P P R y + P γ l sin(2φγ)(ox P x R + Oz P R z ) l L N ΣP γ l cos(2φγ) + GP γ l P z T sin(2φγ) ) l L Y + P Py R P γ l cos(2φγ) (T Py R + Σ + P T x (Tx P z R Tz P R x ) +P γ l sin(2φγ) (GP T z + F P R y P T z + Ox P R x + Oz P R z ) + P T z (Lx P R x + Lz P R z ) l T N + T P T y P γ l cos(2φγ)(p P T y + Σ) + HP γ l P T x sin(2φγ) l T Y P γ l P y T Py R cos(2φγ) + ΣP T y Py R + T P T y + P Py R + P T x (Tx P x R + Tz P R z ) ) P γ l cos(2φγ) ( Px T (Lx P z R Lz P R x ) + P P T y + Σ + T Py R ) +P γ l sin(2φγ) ((Ox P x R + Oz P R z ) + HP T x + EPy RP T x Py T (Cx P z R Cz P R x ) Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

37 Multipoles (Kaon-MAID) Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) E M Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) E E Re ( 3 /mπ +) Im ( 3 /mπ +) Re ( 3 /mπ +) Im ( 3 /mπ +) M M Figure : Kaon-MAID, Kaon-MAID \Resonances and Kaon-MAID \Bg. Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

38 Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

39 Additional observables In the following, we study the effect of additional observables on the precision of the extracted amplitudes. Set number Observables {C x, O x, E, F } 2 {C x, O x, E, F, C z } 3 {C x, O x, E, F, C z, O z } 4 {C x, O x, E, F, C z, O z, G} 5 {C x, O x, E, F, C z, O z, G, H} 6 {C x, O x, E, F, C z, O z, G, H, T x } 7 {C x, O x, E, F, C z, O z, G, H, T x, L x } 8 {C x, O x, E, F, C z, O z, G, H, T x, L x, T z } 9 {C x, O x, E, F, C z, O z, G, H, T x, L x, T z, L z } Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

40 Cross section Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 4 / 25

41 Σ (R 2 + R2 2 R3 2 R4)/N 2 T (R 2 R2 2 R3 2 + R4)/N 2 P (R 2 R2 2 + R3 2 R4)/N 2 C x 2 (R R 4 sin δ + R 2R 3 sin(δ 2 δ 3)) /N C z +2 (R R 4 cos δ R 2R 3 cos(δ 2 δ 3)) /N O x +2 (R R 4 cos δ + R 2R 3 cos(δ 2 δ 3)) /N O z +2 (R R 4 sin δ R 2R 3 sin(δ 2 δ 3)) /N E +2 (R R 3 cos(δ δ 3) R 2R 4 cos δ 2) /N F 2 (R R 3 sin(δ δ 3) + R 2R 4 sin δ 2) /N G 2 (R R 3 sin(δ δ 3) R 2R 4 sin δ 2) /N H +2 (R R 3 cos(δ δ 3) + R 2R 4 cos δ 2) /N T x +2 (R R 2 cos(δ δ 2) + R 3R 4 cos δ 3) /N T z +2 (R R 2 sin(δ δ 2) + R 3R 4 sin δ 3) /N L x 2 (R R 2 sin(δ δ 2) R 3R 4 sin δ 3) /N L z +2 (R R 2 cos(δ δ 2) R 3R 4 cos δ 3) /N Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, 25 4 / 25

42 ηtotal (σexp =.) ηincorrect (σexp =.).8 cos θcm ηtotal (σexp =.) ηincorrect (σexp =.).8.5 cos θcm (UGent) Jannes Nys 2 (Over)Completeness in p(γ, K + )Λ October 3, / 25

43 Single BR Double T R BT Kinematics nr S T P C x C z O x O z E F G H T x T z L x L z Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25

44 H (bits) H(r ) H(r 2 ) H(r 3 ) H(r 4 ) H(δ ) H(δ 2 ) H(δ 3 ) N obs re 6.24: Shannon entropy H in function of the number of asymmetries in a set. The N observable shown on a log scale with base 2. The results are for W = 2.5 GeV and integrated o Jannes Nys (UGent) (Over)Completeness in p(γ, K + )Λ October 3, / 25