JLAB-MSU Isobar Model for Description of Double Charged Pion Production

1. JLAB-MSU isobar model (JM) for description of double charged pion production off proton by real and virtual photons in N* excitation region. Checked inside kinematics area: W<1.9 GeV, Q2<1.5 GeV2 Version 2005’ (JM05)

2. JLAB-MSU model for 2-p electroproduction(2003’-version). 3-body processes Quasi-2-body mechanisms included • All well established N* with pD decays +P33(1600)&P11(1710)&P13(1720)&P33(1920) 3-star states • Minimal set of Reggetized gauge invariant Born terms • Effective treatment of couplingswith other open channels • All well established N* with rp decays • +P11(1710)&P13(1720) 3-star states. • Diffractive ansatz for non-resonant rp • production

3. Evaluation of 3-body amplitudes The decay amplitudes as well as W-dependence for decay width of intermediate unstable particles have been determined from phenomenological Lagrangians: ,

4. JLAB-MSU model (2003’-version). Residual mechanisms, beyond shown on the plots, were parameterized either as 3-body phase space C(W,Q2) or through a set of partial waves with J<13/2. Both lead to a similar description. Details of the 2003’-version of model may be found in: M.Ripani et. al., Nucl. Phys., A672, 220 (2000); V.Mokeev, et. al., Phys. of Atom. Nucl., 64, 1292 (2001); V.D.Burkert, et.al., Phys. of Atom Nucl.,66, 2199 (2003); V.D.Burkert, et. al., Phys. of Atom Nucl., 67, 1018 (2004);

5. Cross-sections and amplitudes Kinematics variables for final state: Sp+p-, Sp+p, Wp-, a. All angles are determined in CM-frame • Sij=Mij2, GeV2 • is the angle between 2 planes: 1) composed by momenta of photon and p-,2) compo- sed by momenta of p’ & p+

6. Con’t Cross-sections and hadronic currents (unpolarized e- beam): MN=0.938 GeV 3-b phase space inv. flux For unpolarized proton target and the final state density matrixes are: KL,e,eL are equivalent photon vector and virtual photon polarizations W is invariant mass of the final hadronic system dt=dsp+p-dsp+pdWp--da

7. Current and helicity amplitudes Photon polarization vectors For electron scattering lab. frame:

8. Resonant part The strong decay amplitudes Gi are N* hadronic decay widths to the final states of certain helicity; MN* is resonance mass; Pi is the final particle mometum averaged over intermediate unstable particle line. Gi were taken from analyses of experiments with hadronic probes

9. Electromagnetic transition amplitudes transverse photons longitudinal photons are electromagnetic transition N* form factors fitted to the data Multiplicative factors for electromagnetic transition and hadronic decay amplitudes we determined in a way to get Breit-Wigner formula for resonant part of cross-section, expressed through hadronic and electromagnetic N* decay widths (D.Luke, P.Soding, Springer Tract in Modern Physics, 59 (1971)). All these factors were obtained for relations between hel. amplitudes and cross-section on slides 6,7

10. Non-resonantmechanisms in pD isobar channels. Minimal set of Reggetized gauge invariant Born terms Fp Electromagnetic pion (Fp), proton (Fp) and hadronic (FpND) form factors were used for respective vertices FpND Special approach was developed to account for ISI&FSI M.Ripani, et.al., Nucl. Phys., A672, 220 (2000) Fp

11. Non-resonant amplitudes in pD channels. Born terms were evaluated in the effective Lagrangian approach developed in A.Bartl, W. Majerotto, D. Schildknecht, Nuovo Cimento 12A, 703 (1972) . See Born amplitudes in M.Ripani et. al., Nucl. Phys., A672, 220 (2000) p.p. 224-227. New feature: theparticle off-shell behaviour description Vertex functions for Born diagrams on previous slide: SLAC C. J. Bebek e. a. Phys. Rev. D17 (1978) 1693 NN scatteringR. Machleidt in Advances in Nucl. Phys. V19 (1979)

12. Reggezeition and current conservation. Current conservation for Born terms is insured by the relations between vertex functions: Reggeization procedure M. Guidal J.-M. Laget, M. Vanderhaeghen Phys. Lett. B400 (1997) 6 Gauge invariance restoration after Reggezeition

13. Word-Takahashi-Slavnov identity H.Haberzettl, private communication Hadronic vertex Fi Hadronic vertex Fi WTS identity is fulfilled with determined above operators Fi for Born terms of our model, if hadronic vertex functions are related as written on slide 10.

14. THE INITIAL AND FINAL STATE INTERACTIONS. Developed based on approach proposed by K.Gotfried, J. D. Jackson, Nuovo Cimento 34, 736 (1964) • The basic physical assumption: • the reaction mechanisms factorization as sequence of ISI, • main process, FSI • the consideration at ISI & FSI effects absorption of ingoing and • outgoing particles See details in M. Ripani, V. Mokeev, e. a. Nucl. Phys. A672 (2000) 227-234

15. Electroproduction data fit. A possible new 3/2+(1720) baryon state. CLAS data fit Contributions from conventional states only Fit with new 3/2+(1720) state M.Ripani et. al. Phys. Rev. Lett.91, 022002 (2003) Difference between curves due to signal from possible 3/2+(1720) state

16. Fitted differential 2p cross-sections.

17. Description of 1.7 GeV mass region. • Two alternative ways to describe CLAS data inside 1.7 GeV structure: • Modification of hadronic couplings for P13(1720) PDG state • with respect to established values • Implementation of new baryon state withJp = 3/2+.

18. p+D13 0(1520) isobar channel 3-body processes Quasi-2-body mechanisms included • Minimal set of Born terms similar to what was • used for pD states, except an additional g5 matrix • to account for the opposite parities of D and • D13(1520)

19. Description of p+p, p-p mass distributions at W=1.56 GeV. gp→p+D13(1520): absorbed in 3b ph.space included contribution from sub-channel

20. Description of p+p, p-p mass distributions at W=1.79 GeV. Implementation of gp→p+D13(1520) sub-channel allowed to reproduce CLAS data

21. Diagrams for gp→p+D13(1520) channel

22. p+D13(1520) isobar channel in p- angular distributions. Implementation of p+D13(1520) isobar channel keeps description of p- angular distributions reasonably well.

23. The contribution from p+D13 0(1520) isobar channel to the total p+p-p cross-sections. FullJM03 calculations 3/2+(1720) candidate state off p+D13(1520) isobar channel

24. Comparison between various ways to describe structure around 1.7 GeV W. Full JM03 calculations 3/2+(1720) off p+D13(1520) channel 3/2+(1720) off, while p+D13(1520) channel is enhanced to reproduce p-p+p total cross-section around 1.7 GeV W

25. Comparison between various ways to describe structure around 1.7 GeV W. Attempt to substitute the signal from 3/2+(1720) candidate state, enhancing the contribution from p+D13(1520) isobar channel is failed Signal from 3/2+(1720) state exists.

26. Non-resonant mechanisms for rp isobar channel. Modified diffractive ansatz. conv. diffr. ansatz Modifications: insure proper amplitude behavior near threshold accounts for r-line shrinkage at near/sub threshold areas in transition between photon and r meson W in GeV; A0=12, D=0.25 GeV, l0= 0.77 GeV, Dl=0.3 GeV

27. Description of the CLAS data on p+p- inv. mass distributions with W-independent values of magnitude Adiff for non-resonant diffractive rp production. Q2=1.30 GeV2 W=1.79 GeV Adiff=3.0 ds/dM mb/GeV Adiff=12.0 Mp+p- GeV W=2.04 GeV There is no way to describe the data in entire W-area, covered by measurements, with Adiff independent from W ds/dM mb/GeV Mp+p- GeV

28. Description of the CLAS data within the framework of modified diffractive ansatz. N.Shvedunov, et. al., accepted by Phys. of Atom. Nucl.,http://www.jlab.org/~gleb/shvedunov/shvedunov.pdf p+p- mass distributions at various W and Q2=1.30 GeV2 ds/dMp+p mb/GeV Mp+p- GeV

29. Cont’d Reasonable description of p+p- mass distributions and their dependence from W and Q2 was within the framework of developed modification for description of non-resonant rp production.

30. 2p direct production mechanisms at the photon point. JLAB-MSU model 2003-version, described on p.2-29 W=1.45 GeV JLAB-MSU model 05’, see p. 30-60 2pdirect production Preliminary real photon data from: M.Bellis, et. al., (CLAS Collaboration) Proc of NSTAR2004 Workshop, March 24-27,2004, Grenoble, France, World Scientific 2005, ed. by J.-P.Bocquet, V.Kuznetsov, D.Rebreyend, 139

31. Manifestation of 2-p direct production at Q2>0. W=1.49 GeV JLAB-MSU model 05 Q2=0.65 GeV2 Q2=0.95 GeV2 2003’-version 2pdirect production

32. 2p direct production mechanisms and an additional tensor term in pD channels needed to fit data. 2 =1.64 GeV2

33. 2p directproduction and complementary tensor termat the photon point. W=1.63 GeV W=1.78 GeV p+D0 with complementary tensor term

34. Manifestation of complementary tensor term in pD channels at Q2>0. W=1.84 GeV Q2=0.65 GeV2 JLAB-MSU model: improved initial Channels: p-D++ rp p+D13(1520) p+D0 2p direct W=1.84 GeV Q2=0.95 GeV2 Structure around D0 peak in p-p and high mass part in p+p mass distributions are better described, implementing an additional tensor structure for pD chanels

35. Evidence for gpp+F015(1685) and gpp-P++33(1600) channels. gpp-P++33(1600) gpp+F015(1685)

36. The amplitudes for gpp+F015(1685) and gpp-P++33(1600) channels.

37. Fit of 2p photoproduction data at high W after implementation of new isobar channels. Full calculations gpp-D++ gpp+D0 gprp gpp-P++33(1600) gpp+F015(1685) 2p direct

38. Total p+p- photoproduction cross-section off protons. • 3/2+(1720) photocouplings adjusted to the real photon data. Hadronic couplings and mass derived from the fit of virtual photon data. no 3/2+ full calculation Background • Signal from 3/2+(1720) state present, but masked by large background Resonances

39. Isobar channels at Q2=0. GeV2. JLAB preliminary SAPHIR Calculations in JM05 2p direct full p-D++ p+D0 rp p-P++33(1600) Points with bars correspond to SAPHIR data on isobar channels p+F015(1685)

40. Uncertainties in isobar channel separation at Q2=0 GeV2. Parameters of 2p direct production mechanisms as well as magnitude of complementary contact terms in pD channels were varied within 30% s. P33(1600), 3/2+(1720) candidate, P13(1720), F35(1905), F37(1950) photocouplings were varied within 30% s We selected calculated cross- sections for which c2/ d.p.< predetermined value, so they are insight uncertainties for all analyzed observables.

41. Description of single-differential cross-sections at Q2=0. GeV2.

42. Description of single-differential cross-sections at Q2=0. GeV2. Various mechanisms have particular manifestations, which are different for various kind of differential cross-sections. However, reflections of particular mechanisms on observables are highly correlated by mechanism dynamics.

43. Description of single-differential cross-sections at Q2=0. GeV2. Combined fit of all observables enable us to access dynamics of contributing mechanisms.

44. Description of single-differential cross-sections at Q2=0. GeV2.

45. Total p+p- electroproduction cross-section off protons. • Initial values of N* photocouplings were taken from analysis of CLAS 2p data within the framework of 2003’-version of the JLAB-MSU model: V.Burkert et.al., Nucl. Phys. A737, S231 (2004) and further adjusted to the data, using recent version of model. s mb Q2=0.65 GeV2 Q2=0.95 GeV2 • Signal from possible 3/2+(1720) state ~ 1.7 GeV becomes more pronounced at Q2>0.5 GeV2 due to considerable growth of N*/Bckgr. ratio in electroproduction. Q2=1.30 GeV2 W, GeV

46. Description of single-differential cross-sections at Q2=0.65 GeV2. Cross-section calculated in JM03’ All other lines are the same as on slides 40-43.

47. Description of single-differential cross-sections at Q2=0.65 GeV2.

48. Description of single-differential cross-sections at Q2=0.65 GeV2. p+ D13(1520) isobar channel

49. Description of single-differential cross-sections at Q2=0.65 GeV2.

50. Isobar channels at Q2=0.95 GeV2