Baryon Resonances in a Coupled Analysis of Meson and Photon induced Reactions

Transcription

1 Baryon Resonances in a Coupled Analysis of Meson and Photon induced Reactions Deborah Rönchen HISKP, Bonn University INT workshop Spectrum and Structure of Excited Nucleons from Exclusive Electroproduction November 6, Seattle, USA Supported by DFG, NSFC HPC support by Jülich Supercomputing Centre Dispersive analysis of D K ππ Dispersive analysis of D K ππ Franz Niecknig

2 of the N Introduction: Baryon spectrum in experiment and -spectrum. theory N -spectrum are now true predictions. In the subsequent subsection 7.3 we will then illustrate in some more detail, how instanton-induced effects due to t Hooft s quark-quark interaction are in fact responsible for the phenomenology 7. Discussion of the complete N-spectrum above.8 GeV much more states are predicted than observed, Missing resonance problem Lattice calculation (single hadron approximation): Figures 9 and show the resulting positions of the positive- and negative-parity nucleon resonances with total spins up to J = 3 obtained in model A and B, respectively. These are compared with the experimentally observed positions of all presently known resonances of each status taken from the Particle Data Group [37]. Again, the resonances in each column are classified by the total spin J and the parity π, where left in each column the results for at most ten excitations in model A or B are shown. In comparison the experimental positions [37] are displayed on the right in each column N with the uncertainties of the resonance positions indicated by the shaded boxes and the rating of each resonance denoted spectrum by the corresponding innumber a relativistic of stars and a differentquark shading of the model: error box. In addition we also display the determined resonance positions of the three new states that have been recently discovered by the SAPHIR collaboration [54,56,5,53]. These states are indicated by the symbol S. In the following, we turn to a shell-by-shell discussion of the complete nucleon spectrum. According to their assignment to a particular shell, we additionally summarized the explicit positions of the excited model states in tables,, 4, 5, 6 and ** 6 *** Mass [MeV] 5 * S ** 9 ** ** *** **** **** 44 **** **** 9 8 * ** S S 7 65 *** **** **** **** ** 675 **** 9 **** 5 ****..8.6 [Edwards et al., Phys.Rev. D84 ()] only about half of the states have or status 939 **** J π /+ 3/+ 5/+ 7/+ 9/+ /+ 3/+ /- 3/- 5/- 7/- 9/- /- 3/- L T J P P3 F5 F7 H9 H K 3 S D3 D5 G7 G9 I I 3 Fig. 9. The calculated positive and negative parity N-resonance spectrum (isospin T = and strangeness S = ) in model A (left part of each column) in comparison to the experimental spectrum taken from Particle Data Group [37] (right part of each column). The resonances are classified by the total spin J and parity π. The experimental resonance position is indicated by a bar, the corresponding uncertainty by the shaded box, which is darker the better a resonance is established; the status of each resonance is additionally indicated by stars. The states labeled by S belong to new SAPHIR results [54,56,5,53], see Löring text. et al. EPJ A, 395 (), experimental spectrum: PDG PDG listing: major part of the information from πn elastic (Exception: BnGa multi-channel PWA) large coupling to inelastic channels?

3 N and now Experimental studies of hadronic reactions: major progress in recent years Photoproduction: e.g. from JLab, ELSA, MAMI, GRAAL, SPring-8 source: ELSA; data: ELSA, JLab, MAMI enlarged data base with high quality for different final states (double) polarization observables alternative source of information besides πn X towards a complete experiment: unambiguous determination of the amplitude (up to an overall phase) Electroproduction: e.g. from JLab, MAMI, MIT/Bates electroproduction of πn, ηn, KY, ππn access the Q dependence of the amplitude, information on the internal structure of resonances e(ki) γ (k) N(pi) e(kf) N(pf) m(q) 3

4 Complete Experiment Photoproduction of pseudoscalar mesons: CGLN Phys. Rev. 6, 345 (957) ˆM = if σ ɛ + F σ ˆq σ (ˆk ɛ) + if 3 σ ˆkˆq ɛ + if 4 σ ˆqˆq ɛ q: meson k ( ɛ): photon (polarization) F i : complex functions of θ, W, constructed from multipoles E L±, M L± 6 polarization observables: asymmetries composed of beam, target and/or recoil polarization measurements Complete Experiment: unambiguous determination of the amplitude 8 carefully selected observables Chiang and Tabakin, PRC 55, 54 (997) e.g. {σ, Σ, T, P, E, G, C x, C z } Electroproduction e.g. Berends, Donnachie, Weaver NPB4, (967) ˆM = if σ ɛ + F σ ˆq σ (ˆk ɛ) + if 3 σ ˆkˆq ɛ + if 4 σ ˆqˆq ɛ + if 5 σˆkˆk ɛ + if 6 σˆqˆk ɛ F i = F i (W, θ, Q ), multipoles E L±, M L±, L L± (or E L±, M L±, S L± ) 36 polarization observables 4

5 Different analyses frameworks: a few examples [Edwards et al., Phys.Rev. D84 ()] GWU/SAID approach: PWA based on Chew-Mandelstam K -matrix parameterization unitary isobar models: unitary amplitudes + Breit-Wigner resonances MAID, Yerevan/JLab, KSU multi-channel K -matrix: BnGa (mostly phenomenological Bgd, N/D approach), Gießen (microscopic Bgd) dynamical coupled-channel (DCC): 3-dim scattering eq., off-shell intermediate states ANL-Osaka (EBAC), Dubna-Mainz-Taipeh, Jülich-Bonn 5

6 Different analyses frameworks: a few examples [Edwards et al., Phys.Rev. D84 ()] GWU/SAID approach: PWA based on Chew-Mandelstam K -matrix parameterization unitary isobar models: unitary amplitudes + Breit-Wigner resonances MAID, Yerevan/JLab, KSU multi-channel K -matrix: BnGa (mostly phenomenological Bgd, N/D approach), Gießen (microscopic Bgd) dynamical coupled-channel (DCC): 3-dim scattering eq., off-shell intermediate states ANL-Osaka (EBAC), Dubna-Mainz-Taipeh, Jülich-Bonn 5

7 The Jülich-Bonn DCC approach

8 The Jülich-Bonn DCC approach EPJ A 49, 44 (3) Dynamical coupled-channels (DCC): simultaneous analysis of different reactions The scattering equation in partial-wave basis L S p T IJ µν LSp = L S p V IJ µν LSp + γ,l S dq q L S p V IJ µγ L S q E E γ(q) + iɛ L S q T IJ γν LSp potentials V constructed from effective L s-channel diagrams: T P genuine resonance states t- and u-channel: T NP dynamical generation of poles partial waves strongly correlated 7

9 The Jülich-Bonn DCC approach EPJ A 49, 44 (3) Dynamical coupled-channels (DCC): simultaneous analysis of different reactions The scattering equation in partial-wave basis L S p T IJ µν LSp = L S p V IJ µν LSp + γ,l S dq q L S p V IJ µγ L S q E E γ(q) + iɛ L S q T IJ γν LSp free parameters fitted to data: s-channel: resonances (T P ) t- and u-channel exchange: background (T NP ) Λ K K Λ, Σ Λ, Σ K Σ K N K Σ, Σ Λ N π π N π N π N m bare + f πnn ( ) Λ m n cut offs Λ in form factors ex Λ + q (couplings fixed from SU(3)) 7

10 The Jülich-Bonn DCC approach Resonance states: Poles in the T -matrix on the nd Riemann sheet pole position E is the same in all channels residues branching ratios Re(E ) = mass, -Im(E ) = width Analytic structure (P).3 GeV (-body) unitarity and analyticity respected 3-body ππn channel: - parameterized effectively as π, σn, ρn - πn/ππ subsystems fit the respective phase shifts branch points move into complex plane Pl(x) from PW decomposition, e.g. Vu = dx u mn + iɛ, 8

11 Photoproduction EPJ A 5, (5) Multipole amplitude γ π, η γ m π, η M IJ µγ = V IJ µγ + T IJ µκ GκV IJ κγ κ (partial wave basis) N V πγ N N V κγ B G T N m = π, η, B = N, T µκ: Jülich hadronic T -matrix Watson s theorem fulfilled by construction analyticity of T: extraction of resonance parameters Photoproduction potential: approximated by energy-dependent polynomials γ m γ m V µγ = (E, q) N P NP µ + B N P P i N, γ a µ B = γa µ (q) P NP µ m (E) + N i γ a µ;i (q)pp i (E) E m b i γ a µ, γa µ;i : hadronic vertices correct threshold behaviour, cancellation of singularity at E = mb i γ a µ;i affects pion- and photon-induced production of final state mb i: resonance number per multipole; µ: channels πn, ηn, π, KY Polynomials 9

12 Data analysis and fit results

13 Combined analysis of pion- and photon-induced reactions Fit parameters: s-channel: resonances (T P ) Λ K πn πn π p ηn, K Λ, K Σ, K + Σ π + p K + Σ + N N π 8 free parameters N resonances ( m bare + couplings to πn, ρn, ηn, π, K Λ, K Σ)) + resonances ( m bare + couplings to πn, ρn, π, K Σ) m bare + f πnn γp π p, π + n, ηp, K + Λ 5 free parameters couplings of the polynomials N γ P NP µ m γ + B N P P i N, γ a µ B m 4. data points calculations on the JURECA supercomputer: parallelization in energy ( 3-4 processes)

14 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ γp K + Λ: Differential cross section Recoil polarization MeV JU4 345 MeV. MC MeV MeV MC JU4: Jude PLB 735 (4), MC: McCracken PRC 8 () Beam asymmetry MeV LL MeV ZE LL7: Lleres EPJA 3 (7), ZE3: Zegers PRL (3) MC MC4: McNabb PRC 69 (4), MC: McCracken PRC 8 () Target asymmetry MeV LL LL9: Lleres EPJA 39 (9) MeV LL

15 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ γp K + Λ: C x C z MeV.5 69 MeV MeV BR BR7: Bradford PRC 75 (7) MeV BR BR BR7: Bradford PRC 75 (7) -.5 BR O x O z 649 MeV 883 MeV.5 LL LL MeV LL MeV LL LL9: Lleres EPJA 39 (9) LL9: Lleres EPJA 39 (9) 3

16 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ Prediction for new CLAS data (Paterson et al. Phys. Rev. C 93, 65 (6)):.5 Σ E cm =7 MeV Θ [deg] 4

17 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ Prediction for new CLAS data (Paterson et al. Phys. Rev. C 93, 65 (6)): E cm =7 MeV T Θ [deg] 5

18 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ Prediction for new CLAS data (Paterson et al. Phys. Rev. C 93, 65 (6)): E cm =7 MeV O x

19 Preliminary: K + Λ photoproduction in the JüBo model simultaneous fit of γp π p, π + n, ηp, K + Λ and πn πn, ηn, K Λ, K Σ Prediction for new CLAS data (Paterson et al. Phys. Rev. C 93, 65 (6)): E cm =7 MeV O z

20 Impact of new polarization data

21 Impact of new polarization data on γp πn multipoles - A joint analysis of the SAID, BnGa and JüBo groups - EPJ A 5, 84 (6) Recent new data on γp πn: E, G, H, P, T in γp π p from ELSA Thiel et al. PRL 9, (); Gottschall et al. PRL, 3 (4); Hartmann et al. PLB 748, (5); Thiel et al. arxiv:64.9 Σ in γp π p and γp π + n from JLab Dugger et al. PRC 88, 653 (3) 89, 99(E) (4) Σ in γp π p from MAMI Hornidge et al. PRL, 64 (3) included in the SAID, BnGa, JüBo fits compare multipoles before and after the inclusion of the new data conversion to a common solution? 9

22 The SAID, BnGa and JüBo approaches All three approaches: coupled channel effects unitarity ( body) amplitudes are analytic functions of the invariant mass SAID PWA based on Chew-Mandelstam K -matrix K -matrix elements parameterized as energy-dependent polynomials resonance poles are dynamically generated (except for the (3)) masses, width and hadronic couplings from fits to pion-induced πn and ηn production Bonn-Gatchina (BnGa) PWA Multi-channel PWA based on K -matrix (N/D) mostly phenomenological model resonances added by hand resonance parameters determined from large experimental data base: pion-, photon-induced reactions, 3-body final states Jülich-Bonn (JüBo) DCC model based on a Lippmann-Schwinger equation formulated in TOPT hadronic potential from effective Lagrangians photoproduction parameterized by energy-dependent polynomials resonances as s-channel states (dynamical generation possible) resonance parameters determined from pionand photon-induced data

23 Selected new data and predictions EPJ A 5, 84 (6) Fig.. Selected data and the predictions from the four different PWAs: black solid line: BnGa-, blue dashed: JüBo5B, green dotted: MAID7, red dash-dotted: SAID CM. The predictions are based on fits which did not yet use these new data. TheData: new data CBELSA/TAPS are shown for the Collaboration beam asymmetry (T : ΣHartmann for γp etπ + al. n PLB [8] (st 748, row), (5) for the, beam E: Gottschall asymmetry al. Σ in PRL the, low-energy region [8] and at higher energies (nd row) for γp π p, (nd and 3rd row). The next three rows show T [8], G [38,83], and 3 (4), G: E [37,84] for γp π Thiel et al. PRL 9, (), Thiel et al. arxiv:64.9) p. Note that the data from refs. [8] and [8] are included in the fits of JüBo5B and SAID CM. Predictions: black solid lines: BnGa, red dash-dotted: SAID, blue dashed: JüBo, green dotted: MAID covers also KAON MAID [98]. Data on πn and ηp (and view of Particle Properties, RPP, (MAID). The BnGa and K + Λ) are fitted independently. JüBo groups use pion and photo-induced reactions and determine the properties of the contributing resonances in Particle properties. The SAID and MAID PWA groups

24 Fit results EPJ A 5, 84 (6) Fig.. The new fit results of the different PWAs in comparison with the new data: black solid line: BnGa, blue dashed: JüBo, red dash-dotted: SAID. New data are shown for the beam asymmetry Σ for γp π + n [8] (st row), for the beam asymmetry Σ in Data: the low-energy CBELSA/TAPS region [8] Collaboration and at higher (T energies : Hartmann (nd row) et al. for PLB γp748, π p, (nd (5) and, E: 3rdGottschall row). Theetnext al. PRL three, rows show T [8], 3 G [38,83], (4), and G: E Thiel [37,84] et al. forprl γp 9, π p. The BnGa (), fitthiel did not et al. yetarxiv:64.9) use the data on the beam asymmetry Σ for γp π p in the low-energy region [8]. Nevertheless, the new fit is fully consistent with the new data. Fits: black solid lines: BnGa, red dash-dotted: SAID, blue dashed: JüBo The M multipole (fig. 3(c), (d)) drives the excitation of the J P =/ + partial wave containing the Roper evidences clearly N(44)/ +, the contributions from the higher-mass resonances are small. The new data lead to

25 Im A [ Im A [ Comparison of multipoles before & after including the new data: Selected examples Eur. 84 J. A (6) 5: 84 Eur.5: Phys. Eur. Phys. J. A (6) Before E+ (π+n) n) E +(π.4 b) b) M (π p).5 c) E+(3/) Re AA [mfm] [mfm] Re M (π p) E+(3/) c) W [MeV] W [MeV] W [MeV] ++ 4 W [MeV] ++ M (π n) M (πthe n) MFig. M n) real (top) E E+presents (/)p 4. Each block and imaginary (bottom) part of (π n) (π +(/)p d) (right) including new d) data. Black solid line: BnGa, blue dashed: Ju Bo, red da d).6 (b)) presents the I = 3/ (I = /) multipole; block c) and e) show the γp [MeV] W M+(3/) (3/) M +.5 e) e) W [MeV] M (3/) M (πm p)+(3/) 3 + M3 (πp) e) 3 3 ] ] 8.4 W [MeV] M (/)p M+ +(/)p f) f) W [MeV] + M (/)p +(/)p M (πm n) 3 + M3 (π+n) black solid lines: BnGa, red dash-dotted: SAID, blue dashed: Ju Bo, green dotted: MAID ImAA[mfm] [mfm] Im -3-3 Re A [mfm] - - Im A [mfm] Im ImAA[mfm] [mfm] Re Re AA [mfm] [mfm] Re A [mfm] Im A [mfm] 8 8 Im A [mfm] Im A [mfm] Im A [mfm] Im ImAA[mfm] [mfm] E (/)p (π p) M + Re A [mfm]. 8 After + E (/)p (π E p) E+ (π+n) n) M +(π + e) b). Re A [mfm] -4-4 Before M+(3/) Page 3 of 8 Im A [mfm].4 M+(3/) E+(π p) a) Re ReAA[mfm] [mfm] Re A [mfm] Re A [mfm] After E+(π p).8 a) Page of of 8 8 Page f) 3

26 Consistency of the results EPJ A 5, 84 (6) Page 6 of 8 Eur. Phys. J. A (6) 5: 84 Pairwise variances between two PWAs: var(, ) = 6 i= (M (i) M (i)) (M (i) M (i)) (M: γp π p multipoles up to L = 4) Fig. 8. The variances taken pairwise between two PWAs Fig. 9. The variance of all three PWAs summed over all γp π p multipoles up to L = 4. The range covered by the new double-polarization observables is indicated by shaded areas. Over the largest part of the energy range the new data have enforced now an improvement in closerof agreement the overall consistency. The improvement is displayed as a light green area and, separately as difference of the variance. The contribution to the improvement from the E+ wave is shown as the dashed curve. Ranges.5 to.7 GeV: with an overall deterioration are marked in red. beyond.7 GeV: BnGa, SAID, JüBo multipoles - BnGa agrees well with SAID and with JüBo - larger discrepancies between SAID and JüBo This quantity is plotted in fig. 8(a) for the amplitudes before and in fig. 8(b) for the amplitudes after the new data were included. The spike in fig. 8(a) slightly below W =.5GeV reflects the discrepancies in the description of the ηp cusp between the approaches. Indeed, this is also directly visible for E+ shown in fig. 3. Once the new data are included, this discrepancy becomes smaller (fig. 8(b)). A wider peak below W =.7 GeV might stem from slightly different N(68)5/ + properties used in the three PWAs. Also the wider peak becomes less pronounced 4

27 Summary Progress in experimental and theoretical study of the baryon spectrum Jülich-Bonn model: - DCC approach that respects analyticity and ( body) unitarity - simultaneous analysis of pion- and photon-induced reactions - preliminary results for K + Λ photoproduction Impact of new polarization data for pion photoproduction from ELSA, CLAS, MAMI: - joint analysis of the BnGa, SAID and JüBo groups - comparison of the multipoles before and after the inclusion of the new data agreement between the three analyses is improved! 5

28 Thank you for your attention!