Summary Project B1

Table of contents

  1. Associated strangeness photoproduction K+ Λ photoproduction
  2. K0 Λ photoproduction
  3. K0 Σ+ photoproduction
    1. Excited hyperon photoproduction
    2. K photoproduction
    3. Simulated analysis of proposed experiments
    4. ω and φ vector mesons
    5. η′ meson

Associated strangeness photoproduction K+ Λ photoproduction

KPlusLambdaCrossSec.png
Figure 3.13: Differential cross sections for γp → K+ Λ. Closed circles, open squares and open triangles are LEPS [44], SAPHIR [40] and CLAS [41, 42] data respectively. The dotted and dash-dotted curves are Regge models with only K exchange, and K and K exchange respectively, from Guidal et al. [46]. The solid line is the isobar plus Regge model of Mart and Bennhold [45]

The search for missing resonances, and the goal of a complete, model independent measurement have provided motivation for the most extensively measured associated strangeness channel, γp → K+ Λ. Differential cross section data with high statistics have been measured with the SAPHIR detector [39, 40] at ELSA and CLAS detector [41, 43] at Jefferson Lab. Discrepancies between these data however leave ambiguities to the contributing s-channel resonances, with the most notable difference around the structure at √s = 1.9 GeV. The LEPS collaboration [44] measured the K+ Λ differential cross section for centre of mass energies 1.945-2.28 GeV (photon beam energy of 1.5-2.4 GeV) and forward angular range (centre of mass K+ polar angle of 0 − 60° ). The data was consistent with the CLAS data in the energy overlap region (see fig. 3.13) and partially reproduces the peak structure at √s = 1.9 GeV, however this is at the lower limit of the energy range. The data extends beyond the angular acceptance of the CLAS data (approximately 25° in the centre of mass).

γp → K+ Λ differential cross section measurements, and the polarisation observables Σ, CX, CZ, OX and OZ are planned for the BGO-OD experiment. The data will cover the overlap region between CLAS and LEPS, and provide important statistics at the observed structure at W = 1.9 GeV. Data will also cover very forward centre of mass angles, where only LEPS data exists beyond a photon beam energy of 1.5 GeV. The disagreement of either Regge model [46] at forward angles in fig. 3.13 and above W = 2 GeV suggests that there is still significant s-channel contributions in this region, and a reggeisation of only t-channel contributions cannot describe this data. The measurement, and in particular an understanding of K+ identification in the BGO, will provide a basis for the analysis of further channels, for example, excited hyperons and φ photoproduction.

K0LambdaCS.png
Figure 3.14: γ(n, K0 differential cross section as a function of K0 momentum for photon beam energy (a) 0.9-1.0 GeV and (b) 1.0-1.1 GeV, for laboratory frame polar angles smaller than 25°. Solid black line is a Kaon-MAID fit [6], dotted black line the Saclay-Lyon A isobar model [48], dotted red and dot-dashed red are phenomenological models described in [47], and the blue dashed and dot dashed lines are Kaon-MAID fits to K0 Σ0 and K0 Σ+. Taken from [47].

K0 Λ photoproduction

Determining s-channel resonances contributing to the γp → K+ Λ spectrum is complicated by large t-channel contributions. As explained in reference [4], K0 photoproduction in this sense is easier to understand due to the absence of t-channel K0 exchange. Charged and neutral strangeness channels, and the associated hadronic coupling constants are linked via SU(3) symmetry. Cross sections and polarisation observable data for γn → K0 Λ for example, provide important constraints upon the γp → K+ Λ reaction mechanism. Despite these advantages, there is limited data for the γn → K0 Λ channel. The first cross section data for γn → K0 Λ using a deuterium target was measured with the Neutral Kaon Spectrometer at the Laboratory of Nuclear Science (LNS) at Tohoku University [47]. The experiment had an acceptance of approximately π steradians, covering forward angles up to a photon beam energy of 1.1 GeV. K0 were identified via the decay K0 → π+ π, where the K0 invariant mass was reconstructed from pion momenta. Fig 3.14 shows the measured cross section for the inclusive reactions γN → K0 Y (where Y is either Λ, Σ0 or Σ+ ). The data suggests a more backward peaking angular distribution than what was predicted with the Kaon-MAID parameterisation [6].

The BGO-OD experiment will measure differential cross sections and polarisation observables for this channel, vastly improving the limited data set. Statistics will be greatly improved over previous experiments, as the BGO-OD experiment is able to reconstruct K0 via both neutral and charged pion decay modes. Recoil polarisation, P , will be measured from the self analysing Λ weak decay. A linearly polarised beam will be used to measure the beam asymmetry, Σ, and the double beam-recoil polarisation observables, OX and OZ. With a circularly polarised beam, the beam-recoil polarisation observables, CX and CZ will be extracted from threshold to a beam energy of approximately 1.7 GeV. Polarisation observables for γn → K0 Σ0 will also be extracted from the same data set. It is interesting to note that the peak observed in η photoproduction off the neutron at W = 1680 MeV is close to the K0 Σ0 photoproduction threshold at 1691 MeV.

K0 Σ+ photoproduction

The BGO-OD experiment will study the channel γp → K0 Σ+ and provide complementary data to the differential cross sections, beam asymmetry and recoil polarisations measured with the Crystal Barrel (analyses page). The beam asymmetry will be measured over the K production threshold, testing the hypothesis of t-channel mechanisms described in the Analyses section. The new SciFi photon tagger will cover a large energy range over where the cusp was observed in the cross section. The high beam energy resolution will allow high energy resolution differential cross sections, and accurate measurement of linear beam polarisation for extracting Σ over this region. Recent solutions for the Bonn-Gatchina Partial Wave Analysis ([49], references therein and the A2 scientific program of this proposal) give widely varying results over this energy range (fig. 3.15).

Excited hyperon photoproduction Constituent quark models with three quenched quark states cannot accurately describe the mass differences of excited hyperons. The lowest excitation energy of a baryon of approximately 450 MeV is too high to describe the Λ(1405), and the mass difference to the spin orbit partner, Λ(1520) is too large. It is also difficult to reconcile the Λ(1405) mass to be lower than the non-strange N(1535). These mass differences however can be described using unquenched quark models with five components [50, 51, 52]. These can either be interpreted as a meson cloud or a pentaquark molecule with di-quark structure. The N(1535) for example can be described as a bound KΛ − KΣ system and Λ(1405) as a dynamically generated KN − Σπ resonance. Alternatively within a penta-quark description, N(1535) can be described as [ud][ud]d– and Λ(1405) as [ud][sq]q– with qq– = (uu– + dd–)/ √2. These descriptions have important implications for the entire spectrum of hyperon resonances. Within the penta-quark model for example, a Σ with J π = 1/2 is expected close in mass to Σ(1385).

PWA_Revised.png
Figure 3.15: Partial wave analysis solutions for beam asymmetry for γp → K0 Σ+ for centre of mass energy 1900 and 2050 MeV. Discriptions of the two solutions, BG2011 02 and BG2011 01 are in [49], references therein and the A.2 scientific program of this proposal. Figure created from [49].

Old data (pre 1980) for K p → Λπ+ π [53] has been re-examined in a search for Σ states with J π = 1/2 [52], in light of a potential Σ(1/2 ) structure observed in J/ψ decays [51]. A fit to the Λπ mass spectrum favours the inclusion of a second resonance close in mass but with a width of approximately 120 MeV. Including the second resonance also improves the fit to the angular distribution between the incident K and Λ (the Σ(1385) with J = 3/2+ gives an angular distribution of the form (1 + 3 cos θ)/2, and the addition of a resonance with J = 1/2 gives a flat distribution component).

Wu, Dulat and Zou [50] proposed that the existence of a Σ (1/2 ) state close to the Σ(1385) can be tested via the decay Λ(1520) → Σ π → Λπ+ π. The Λπ invariant mass is sensitive to the inclusion of the extra resonance due to the final state particles being either in relative P-wave or S-wave for Λ(1520) → Σ+3/2 π and Λ(1520) → Σ∗−1/2 π+ respectively. Model fits to data were promising, however it was concluded that higher statistics data is required to establish this resonance. The LEPS collaboration measured differential cross section and beam asymmetry data for K+ Σ∗− photoproduction off the deuteron [54]. The beam asymmetries were small and negative, in contrast to the positive values predicted by Oh, et al. [55], who included weakly established resonances predicted by quark models to accurately describe cross section data.

Recent analyses of previous Crystal Ball data for K p → π0 Λ [56, 57] fitted effective Lagrangians to differential cross sections and Λ polarisation data. After including t-channel K exchange, u-channel proton exchange and four star Σ resonances, the best fit to the data required an extra Σ resonance with J π = 1/2+ , mass 1635 MeV and width 120 MeV.

Recent advances in chiral unitary formalism for meson baryon interactions [58, 59, 60, 61] described the Λ(1405) as a two-pole structure, with the contributions interfering on the real energy axis. The Λ(1405) can only be observed via the decays: Λ(1405) → πΣ with I = 0, however, it was found that there is different coupling of the two poles to different meson-baryon channels, leading to a difference in the Λ(1405) line shape depending upon the decay it is observed via.

The Λ(1405) mass was reconstructed from all three decay modes using recent data from the CLAS detector [62]. It is clear that the line shape differs depending upon the decay mode, however they do not agree with theoretical predictions where the Σ π+ line shape is at a higher mass.

Due to the limited data on excited hyperons and the ambiguity as to their structure, a detailed search with the BGO-OD experiment is proposed. Σ resonances close in mass to Λ(1405) can be identified via Σ → πΛ, and avoid misidentified background from Λ(1405). Differential cross sections, and polarisation observables, Σ, P , CX and CZ will be used to disentangle reaction mechanisms. Resonant structures can be studied via the photoproduction of K, K+ and K0 . The reaction γp → K+ Λ(1520) will also be studied to constrain potential Σ1/2 resonances close to Σ(1385), and provide differential cross section data up to 2.8 GeV. The BGO-OD experiment will identify all three Λ(1405) decay modes, providing differential cross section, and t dependence data for each. The experimental setup is ideal to identify all particles in the final state for the decay Λ(1405) → Σ0 π0, the only decay channel with no background from Σ(1385) (isospin forbidden).

K photoproduction can be used to search for contributions of the κ(800) scalar meson [63]. Due to the non-zero strangeness, pomeron t-channel exchange, which dominates non-strange vector meson photoproduction, cannot contribute, leaving only K, K and, potentially, κ t-channel exchanges. Differential cross sections for K∗+ Λ and K∗0 Σ+ exhibited similar distributions in energy and angle [64, 65], despite the K∗+ Λ cross section predicted to be larger by a factor of three due to differences in hadronic coupling constants and isospin factors. To compensate these differences, particularly at forward angles and high energies where s-channel contributions are not expected, it was argued by Oh and Kim [63] that κ(800) t-channel exchange has a strong contribution to γp → K∗0 Σ+.

Fig. 3.16(a,b,c) are examples for γp → K∗0 Σ+ differential cross section with two model fits, including t-channel K , K, κ exchange, s-channel resonances and u-channel hyperon resonances. The dashed line is derived from the model fit to K∗+ Λ, where there is only a small contribution from t-channel κ exchange. For a reasonable fit to K∗0 Σ+ however, a larger contribution from t-channel κ exchange is required.

KappaEvidence_Revised.png
Figure 3.16: (a,b,c) Differential cross sections for γp → K0 Σ+ [64], Fitted models described in the text and in more detail in [63] (larger κ t-channel contribution with the solid line). Figure adapted from [63].

Due to the different parity of the κ and the pseudoscalar K, a parity exchange asymmetry, Pσ can be extracted (given in [63]). At forward angles and high energies (to limit s and u-channel contributions), this is predicted to be positive with κ t-channel exchange, or negative without (fig. 3.16(d,e)), with similar behaviour predicted for the photon beam asymmetry, Σ. Preliminary data have been taken from the LEPS collaboration for K∗0 Σ+ [66], with the intention of extracting spin-density matrix elements and Pσ , however this is still in preliminary stages.

The BGO-OD experiment will measure both K∗+ Λ and K∗0 Σ+ channels. Differential cross section data for K∗0 Σ+ at forward angles will constrain model fits in the region most susceptible to the inclusion of the κ t-channel exchange. Data for K∗+ Λ will contribute to the limited world data set for this channel, and can be used as a ratio to K∗0 Σ+ to check normalisation procedures. A linearly polarised photon beam will allow the extraction of Pσ and Σ.

Simulated analysis of proposed experiments Fig. 3.17 shows simulated data analysis of particles with strangeness (descriptions given in the caption). These identification procedures will form the basis of all associated strangeness experiments described in the BGO-OD physics proposal.

ω and φ vector mesons The interest in vector meson photoproduction is strongly motivated by the problem of the so-called “missing resonances” of the baryon excitation spectrum. Recently, there is evidence (ω single and double polarisation observables section) that s-channel resonances do indeed contribute in ω photoproduction in the threshold energy region – on top of dominating t-channel processes. Understanding the latter is important to reliably extract resonance information. Despite ρ photoproduction having a higher cross section, ω and φ can be better identified and discriminated above background due to their smaller widths. Moreover, ω and φ are isospin-singlets and they act as isospin-filters, simplifying the interpretation of data.

StrangenessID.png
Figure 3.17: Simulated analysis of associated strangeness channels (analysed channels inset). Missing mass from K+ detection in (a) the Forward Spectrometer and (b) the BGO (Black lines). K+ identification in the BGO used the new weak decay identification method described on the Analyses page. Identification of the decay Σ0 → γΛ yields a blue peak at the Σ0 mass, and the red peak at the Λ mass for when no decay is identified. (c) Σ0 decay γ energy in the Σ0 rest frame versus the missing mass from K+ γ momentum reconstruction. A peak in the photon energy is evident at the 0 −mΛ mass difference. (d) K0 invariant mass reconstruction from pionic decay (neutral and charged).

ω photoproduction off the proton has been investigated at several facilities ([67]-[74],[2]). Measurements of the differential cross sections revealed pomeron and π0 t-exchange dominance at small momentum transfers. The relative increase of the differential cross section at higher t is ascribed to the contribution of resonant states. Full understanding of the ω photoproduction process requires disentangling t-exchange from s and u-channel processes. Details of their contributions are sensitively probed by polarisation observables (see e.g. [75, 76]). Thus, polarisation observables are considered a fundamental tool to extract resonance information. To date, the most comprehensive and statistically significant data set in ω photoproduction [15] is based on measurements with unpolarised beams however. It is our goal to improve this unsatisfactory situation.

Theoretical interpretations of the available experimental cross section and beam asymmetry results are strongly model dependent ([75]-[78], [16]). New high precision polarisation results will constrain these models. It will be essential to completely understand the t-exchange mechanisms. This shall be achieved by simultaneous study of φ photoproduction. Here, (almost) pure t-exchange dynamics is probed, since the φ meson is a pure ss– state and its direct coupling to the nucleon is strongly inhibited (OZI rule [79]). Due to this, the total cross section for φ photoproduction is over an order of magnitude smaller than the one of ω photoproduction (σ(γp → ωp) ≅ 8−9µb at threshold; σ(γp → φp) ≅ 0.2−0.3µb at threshold). The differential cross sections ([80] and [81]) show the diffractive behavior typical for vector meson photoproduction which is associated with pomeron exchange. LEPS results on the decay angular distributions [82] reveal additional contributions of unnatural parity exchange terms close to threshold, as would be expected from π0 or η exchange. In Fig. 3.18 the energy dependence of (dσ/dt)t=−|t|min is shown from threshold up to Eγ = 6 GeV. The LEPS data (full circles) show an unexpected bump structure around 2 GeV (almost 400 MeV above threshold) which corresponds to a centre of mass energy W ≅ 2.1 GeV. The azimuthal decay distributions over the bump structure seem to indicate that the non monotonic behavior in Fig. 3.18 is not due to additional unnatural parity exchange processes in the corresponding energy range, leading to the interpretation that “new dynamics” are invoked.

phi_dsdt_proton.png
Figure 3.18: Energy dependence of the differential cross section of the reaction γ + p → φ + p (figure from Ref.[81]). Data from LEPS (full circles) show a bump structure at ≅ 2 GeV. The solid curve represents the prediction from Ref.[83], including Pomeron trajectory and π and η-exchange.

It is a further goal of our investigation, to better understand the mechanism of φ photoproduction in this energy regime. An experimental way to disentangle the role of π0-exchange is offered by coherent photoproduction off (isoscalar) deuteron targets (Ethγ (γd → φd) ≅ 1.30 GeV), where the π0 term is forbidden due to isospin conservation. If a bump structure in the energy dependence of the differential cross-section still appears, it can not be related to π0-exchange. LEPS results for the energy dependence of the differential cross section dσ/dt(tmin) of coherent φ photoproduction off the deuteron [84] may indeed indicate a bump structure at Eγ = 1.7 GeV, i.e. 400 MeV above the threshold, as for the free proton case. However, more statistics is necessary to reach a final conclusion. The possibility that, even in the φ channel, the bump structure in Fig. 3.18 is due to intermediate s-resonance contributions was investigated in Ref.[85]. In order to couple to the φ, the authors introduced a resonant state with strange content (ss– uud) and a mass of ≅ 2.1 GeV. With intrinsic angular momentum of J P = 3/2± it is possible to describe the LEPS data. The parity of such a state could be fixed through the beam asymmetry, Σ. At present, no data are available for Σ. If any resonant state is involved in φ photoproduction, it may be expected to play a role also in ω photoproduction. The resonant state introduced in [85] seems to improve the description of the ω differential cross section at 2.1 GeV ([15]).

From these considerations it appears necessary to study ω and φ photoproduction simultaneously. For both channels, ω and φ, it will be important to investigate also the photoproduction off the neutron. Preliminary GRAAL results on the beam asymmetry [74] show important differences between ω photoproduction off the proton and off the neutron. New higher precision polarisation measurements over a larger energy range are necessary to pin this down. Similarly, data on φ photoproduction off the neutron is still scarce.

The BGO-OD set-up is ideal to study ω and φ photoproduction. The high momentum resolution in forward directions combined with charged particle tracking and photon spectroscopy with BGO ball and inner MWPC in the central angular region gives access to complex multi-particle final states. The ω meson will be identified by both, the ω → π+ π0 π (B.R.: 89.2 %) and the radiative ω → π0 γ (B.R.: 8.3 %) decays. This permits internal checks of the analyses by comparing the individual results. As compared to present CB data, which is solely based on the neutral decay, statistics will be vastly improved. The φ meson will be identified by its φ → K+ K decay (B.R.: 48.9 %). The open dipole  allows for simultaneous K+ and K identification. Simulation studies (Fig.3.10) and recent commissioning results (Fig.3.11) show that K+ mesons, in addition to the forward spectrometer, can also be identified in the BGO calorimeter by detecting the delayed weak decay. This increases the geometrical acceptance for φ detection significantly. BGO-OD will thus overlap the acceptance of both, LEPS and CLAS.

The goal is to measure the vector meson decay angular distributions using linearly and circularly polarised beams with sufficient precision to determine the relevant polarisation density matrix elements for the photoproduction off proton, neutron and deuteron. Detailed Monte-Carlo simulations to study the achievable sensitivity are presently ongoing. Unpolarised photon beams – obtained by averaging over both helicities of circularly polarised beams – will yield the polarisation density matrix elements

  • ρ000 , ρ01−1 and Re(ρ010);
    evaluating the circular polarisation of the beam will allow access to
  • ρ300, ρ31−1 and Re(ρ310);
    and with linear polarisation
  • ρ100 , ρ11−1 and Re(ρ110)
    can be obtained, as well as the photon beam asymmetry, Σ, which represents a superposition of density matrix elements.

η′ meson The CLAS and CBELSA/TAPS experiments have produced a rich amount of cross section data for η′ photoproduction on the proton [86, 87, 88] and on the deuteron [89], covering the energy region from threshold (1.447 GeV) up to 2.84 GeV. Two theoretical approaches attempted to describe the data:

  1. in a relativistic meson-exchange model of hadronic interactions [90], Nakayama and Haberzettl consider t-channel mesonic (ρ and ω) together with s- and u-channel nucleon and resonance contributions. S11(1535), P11(1710), D13(1520) and P13(1720) resonances were included, the latter two required to reproduce details of the angular distributions.
  2. in a reggeized model for η and η’ photoproduction [91] of Tiator and co-workers the t-exchanges are treated in terms of Regge trajectories to reproduce the correct high-energy behavior. Both approaches give a reasonable description of the data. They can not be distinguished on the sole basis of cross sections, nor the resonances parameters unambiguously determined. This requires polarisation observables, in particular beam and/or target asymmetries.

The BGO-OD setup is ideally suited for the measurement of both, charged and neutral, decay channels, e.g. (a) η ′ → π+ π η → π+ π 2γ (BR ≅ 17.5%), (b) η′ → 2γ (BR ≅ 2%), and (c) η′ → π0 π0 η → 6γ (BR ≅ 8.2%).

Using a 6 cm long liquid hydrogen target and a tagged photon rate of NγTot ≅ 5 · 107 s−1 we detect about 103 η′ per day of beamtime within the polarised coherent peak. This will allow to measure the beam asymmetry Σ in η′ photoproduction with an error ∆Σ = 0.05 from threshold to 1700 MeV in 6 angular and 4 energy bins within 4 weeks.

[2] R. Lawall et al., Eur. Phys. J. A 24 (2005) 275
[4] R. Ewald et al., Phys. Lett. B 713 (2012) 180
[6] T. Mart, C. Bennhold, H. Haberzettl and L. Tiator, http://portal.kph.uni-mainz.de/MAID/kaon/ (2010)
[15] M.Williams et al., Phys.Rev.C 80 (2009) 065208
[39] K. H. Glander et al., Eur. Phys. J. A 19 (2004) 251
[40] M. Q. Tran et al., Phys. Rev. Lett. B 445 (1998) 20
[41] R. Bradford and R. A. Schumacher et al. (CLAS Collaboration), Phys. Rev. C 73 (2006) 035202
[42] J. C. W. McNabb et al. (CLAS Collaboration), Phys. Rev. C 69 (2004) 042201
[43] M. E. McCracken, M Bellis, C. A. Meyer, M Williams et al., Phys. Rev. C 81 (2010) 025201
[44] M. Sumihama et al. (LEPS Collaboration), Phys. Rev. C 73 (2006) 035212
[45] T. Mart and C. Bennhold, Preprint: arXiv:0412097v1 [nucl-th] (2004)
[46] M. Guidal, J. M. Laget and M. Vanderhaeghen, Phys. Rev. C 68 (2003) 058201
[47] K. Tsukada et al., Phys. Rev. C 78 (2008) 014001
[48] T. Mizutani, C. Fayard, G. H. Lamot and B. Saghai Phys. Rev. C 58 (1998) 75
[49] Bonn-Gatchina Partial Wave Analysis, http://pwa.hiskp.uni-bonn.de/ (2012)
[50] Jia-Jun Wu, S. Dulat and B. S. Zou, Phys. Rev. C 81 (2010) 045210
[51] B. S. Zou, Int. J. Mod. Phys. 21 (2006) 5552
[52] Jia-Jun Wu, S. Dulat and B. S. Zou, Phys. Rev. D 80 (2009) 017503
[53] D. O. Huwe, Phys. Rev. 181 (1969) 1824
[54] K. Hicks, D. Keller, H. Kohri et al. (LEPS Collaboration), Phys. Rev. Lett. 102 (2009) 012501
[55] Y. Oh, C. M. Ko and K. Nakayama, Phys. Rev. C 77 (2008) 045204
[56] S. Prakhov et al. (Crystal Ball Collaboration), Phys. Rev. C 80 (2009) 025204
[57] P. Gao, B. S. Zou, A. Sibirtsev, Nuc. Phys. A 867 (2011) 41
[58] T. Hyodo and D. Jido, Prog. Part. Nuc. Phys. 67 (2012) 55
[59] D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meißner, Nuc. Phys. A 725 (2003) 181
[60] J. C. Nacher, E. Oset, H. Toki, A. Ramos and U. G. Meißner, Phys. Lett. B 455 (1999) 55
[61] M. Mai, U.-G. Meissner, Preprint: arXiv:1202.2030 [nucl-th] (2012)
[62] K. Moriya and R. Schumacher (CLAS Collaboration), Nuc. Phys. A 835 (2010) 325
[63] Y. Oh, H. Kim, Phys. Rev. C 74 (2006) 015208
[64] I. Hleiqawi, K. Hicks et al. (CLAS Collaboration), Phys. Rev. C 75 (2007), 042201
[65] L. Guo and D. P. Weygand (CLAS Collaboration), Preprint:arXiv:hep-ex/0601010v1
[66] S. Hwang, J. K. Ahn and K. Hicks (LEPS Collaboration), Few-Body Syst., published online, 18th April 2012
[67] ABBHHM Collaboration, Phys.Rev. 188 (1969) 5
[68] J.Ballam et al., Phys.Rev.D 7 (1973) 11
[69] F.J.Klein et al., πN Newsletter14 (1998) 141
[70] J.Barth et al., E.P.J.A 18 (2003) 117
[71] H.R.Crouch et al., Phys.Rev.C 155 (1967) 5
[72] Y.Eisenberg et al., Phys.Rev.Lett 22 (1969) 13
[73] M.Battaglieri et al., PRL 90 (2003) 022002 19
[74] V.Vegna et al., International Journal of Modern Physics E 19 (2010) 1241
[75] Q.Zhao, Phys.Rev.C 63 (2001) 025203
[76] Y.Oh, A.I.Titov and T.-S.H.Lee, Phys.Rev.C 63 (2001) 025201
[77] A.I.Titov and T.-S.H.Lee, Phys.Rev.C 66 (2002) 015204
[78] G.Penner and U.Mosel, Phys.Rev.C 66 (2002) 055212
[79] S.Okubo, Phys.Lett.5, 165 (1963); G.Zweig, CERN Report No 8182/TH (1964) 401 (unpublished); CERN Report No 8419/TH (1964) 412(unpublished); J.Iizuka, Prog.Theor.Phys.Suppl. 37/38 (1966) 21
[80] J.Barth et al., E.P.J.A 17 (2003) 269
[81] T.Mibe et al., PRL 95 (2005) 182001
[82] W.C.Chang et al., Phys.Rev.C 82 (2010) 015205
[83] Titov et al., Phys.Rev.C 67 (2003) 065205
[84] W.C.Chang et al., Phys.Lett.B 658 (2008) 209
[85] A.Kiswandhi et al., Phys.Lett.B 691 (2010) 214
[86] M. Dugger et al., Phys. Rev. Lett. 96 (2006) 062001
[87] M. Williams et al., Phys. Rev. C 80 (2009) 045213
[88] V. Crede et al., Phys. Rev. C 80 (2009) 055202
[89] I. Jaegle et al., arXiv:1012.1021v1[nucl-ex]
[90] K. Nakayama and H. Haberzettl, Phys. Rev C 73 (2006) 045211
[91] Wen-Tai Chiang et al., Phys. Rev. C 68 (2003) 045202