Dynamical coupled channel calculation of pion and omega meson production

Transcription

1 Dynamical coupled channel calculation of pion and omega meson production INT-JLab Workshop on Hadron Spectroscopy 2009/11/11 Mark Paris Center for Nuclear Studies Data Analysis Center George Washington University

2 Outline Model Dynamical model 6 channel reaction theory for 2 2 particle scattering Fitting πn πn, πn ωn, ΥN πn,υn ωn 1.1 GeV < W < 2.0 GeV [W energy center-of-mass] Predictions Σω photon beam asymmetry ρ0λλ' spin density matrix elements ωn scattering length Conclusion PHYSICAL REVIEW C 79, (2009)

3 Motivation: Jlab 12 GeV Three-body final states: ππn, πηn, πωn, πkλ,... require knowledge of two-particle sub-channel T matrices Meson and baryon resonances excited in two-particle sub-channels γp ππn J. Dudek

4 Motivation: ωn interactions ω interactions are poorly determined SU(3): g /gρnn=3/2 ωnn CD-Bonn realistic NN potential g =8. κωnn=0 ωnn Sato-Lee (Δ) g =10.5 ωnn κωnn=0 Giessen g ~4.6 ωnn κωnn~-1 [Tuchitani, et al. nucl-th/ ] Possible in-medium modification Tω=0 means only T=1/2 N* contribute simplicity can we fit unpol./pol. data and accurately predict other unfitted observables? CBELSA/TAPS Collaboration [Trnka PRL (05)]

5 Dynamical coupled channel approach: overview Assets Deficits relativistic dynamics charge conjugation non-invariant off-shell contribution included analytic structure incomplete two particle unitarity; approx 3PU simultaneous description of pion induced & electromag. reactions Watson's theorem satisfied readily (analytically) continued [not here, though] neglects >3 particle cuts; approx 3PU no renormalization form factor dependence large number of parameters Is it predictive?

6 Model: dynamical equation NB sums:

7 Interaction model Lagrangian: Mesons Interaction Hamiltonian Unitary transformation method Eliminate virtual processes: Baryons

8 Effective interaction Unitary transformed interaction Modified Feynman propagator s-channel N exch u-channel N exch t-channel ρ exch On-shell pair relative momentum

9 Unitary transform method Virtual processes removed from transformed Hamiltonian Does violence to the analytic structure of the nucleon pole term May be acceptable numerically Incorrect to conclude dynamical model not req'd to have same analytic structure as dispersion relations

10 Reaction model: dynamical equation After unitary transformation Projection method few-body approach

11 Scattering equation 2 2 scattering & reactions Ignore

12 Isobar channels ππn ~ πδ,σn,ρn Bakamjian-Thomas construction

13 model: interaction [Hermitian conjugate implied] For 6 channels: Interaction evaluation: evaluate diagrams project into partial wave basis test against plane wave code Propagators: unitary transform modifies Feynman form off-shell on-shell: Feynman 45 Feynman amplitudes

14 Determination of parameters Fit χ2 via conjugate gradient/simplex methods Simultaneous fit of πn and ωn data πn πn: PWA from SAID [energy dep. SP06 solution] π-p ωn: unp. DCS from Nimrod [Karami et.al. '79] Υp ωp: unp. DCS from SAPHIR [Barth et.al. '03] ΥN πn: unp. DCS world data (from SAID) ΥN πn: PBA Σ(E) world data (from SAID) Complete data set ~1800 data points

15 Fit parameters (bare non-resonant) Fixed in 5 channel fits: Phys.Rev.C76:065201,2007

16 Fit parameters (bare resonance) New resonance required to fit D15 compare to PDG D15(2200) ** fixed in 5 channel πn πn fit results of present study

17 Stage 1: πn πn & πn ωn & γn ωn Real Part: T=1/2 cf. SAID PRC74(06) fit to energy dep. soln.

18 Stage 1: πn πn & πn ωn & γn ωn Imag. Part: T=1/2 cf. SAID PRC74(06) fit to energy dep. soln

19 Stage 1: πn πn & πn ωn & γn ωn Real Part: T=3/2 cf. SAID PRC74(06) fit to energy dep. soln

20 Stage 1: πn πn & πn ωn & γn ωn Imag. Part: T=3/2 cf. SAID PRC74(06) fit to energy dep. soln

21 Stage 1: πn πn & πn ωn & γn ωn Data: Nimrod - Rutherford Lab [Karami et al; Binnie et. al. (70's)]

22 Stage 1: πn πn & πn ωn & γn ωn Data: SAPHIR Bonn [Barth et. al. EPJA 18 p117 '03]

23 Total cross section συp ωp Data: SAPHIR Bonn [Barth et. al. EPJA 18 p117 '03]

24 Stage 2: DCS Υp π0p Quality: χ2/n~1 for W< ~1.5 GeV Possible improvements global fit; other non-res mechanisms; more resonances; ππn

25 Stage 2: DCS Υp π+n Quality: χ2/n~1 for E<~1.7 GeV angular dependence okay at high E

26 Stage 2: PBA Σ0 Υp π0p Quality: χ2/n~1 for E<~1.6 GeV

27 Stage 2: PBA Σ+ Υp π+n Quality: χ2/n~1 for E<~1.7 GeV angular dependence poor at high E

28 Prediction for Σω Σω COM angle Data: GRAAL (2006)

29 Spin density matrix elements: ρ0λλ' ω decay amplitude ω decay angular distribution (unpolarized photons)

30 Prediction for ρ000 θ Data: CLAS g11 Mike Williams (CMU/Imperial Coll.) thesis 2007

31 Prediction for ρ01,-1 θ Data: CLAS g11 Mike Williams (CMU/Imperial Coll.) thesis 2007

32 Prediction for ρ010 θ Data: CLAS g11 Mike Williams (CMU/Imperial Coll.) thesis 2007

33 ωn interactions Average scattering length: Klingl/Weise: Lutz: Giessen:

34 Conclusion Coupled channel approach need improvements COM E>~1.6 GeV outlined possible solutions; most likely ππn is important prediction of polarized observables appear only loosely constrained by fits to unpolarized data Outstanding questions pertaining to modeling can model dependencies be identified & controlled? connection to model independent results of χpt? can contact with Lattice QCD be made? NO. valence QCD (K.-F. Liu et. al.)

35 Thank you!