Measurement of double polarisation asymmetries in ω -photoproduction
H. Eberhardt, T. C. Jude, H. Schmieden, A.V. Anisovich, B. Bantes, D. Bayadilov, R. Beck, Yu. Beloglazov, M. Bichow, S. Boese, K.-Th. Brinkmann, Th. Challand, V. Crede, F. Diez, P. Drexler, H. Dutz, D. Elsner, R. Ewald, K. Fornet-Ponse, St. Friedrich, F. Frommberger, Ch. Funke, M. Gottschall, A. Gridnev, M. Gruener, E. Gutz, Ch. Hammann, J. Hannappel, J. Hartmann, W. Hillert, Ph. Hoffmeister, Ch. Honisch, I. Jaegle, D. Kaiser, H. Kalinowsky, F. Kalischewski, S. Kammer, I. Keshelashvili, V. Kleber, F. Klein, E. Klempt, K. Koop, B. Krusche, M. Kube, M. Lang, I. Lopatin, Y. Maghrbi, K. Makonyi, V. Metag, W. Meyer, J. Mueller, M. Nanova, V. Nikonov, R. Novotny, D. Piontek, S. Reeve, G. Reicherz, T. Rostomyan, S. Runkel, A. Sarantsev, St. Schaepe, Ch. Schmidt, R. Schmitz, T. Seifen, V. Sokhoyan, V. Sumachev, A. Thiel, U. Thoma, M. Urban, H. van Pee, D. Walther, Ch. Wendel, U. Wiedner, A. Wilson, A. Winnebeck
aa r X i v : . [ nu c l - e x ] S e p Measurement of double polarisation asymmetries in ω -photoproduction H. Eberhardt a , T. C. Jude a , H. Schmieden a , A.V. Anisovich b,c , B. Bantes a , D. Bayadilov b,c , R. Beck b , Yu. Beloglazov c ,M. Bichow d , S. B¨ose b , K.-Th. Brinkmann e , Th. Challand f , V. Crede g , F. Diez e , P. Drexler e , H. Dutz a , D. Elsner a , R. Ewald a ,K. Fornet-Ponse a , St. Friedrich e , F. Frommberger a , Ch. Funke b , M. Gottschall b , A. Gridnev c , M. Gr¨uner b , E. Gutz b,e ,Ch. Hammann b , J. Hannappel a , J. Hartmann b , W. Hillert a , Ph. Ho ff meister b , Ch. Honisch b , I. Jaegle f , D. Kaiser b , H. Kalinowsky b ,F. Kalischewski b , S. Kammer a , I. Keshelashvili f , V. Kleber a , F. Klein a , E. Klempt b , K. Koop b , B. Krusche f , M. Kube b , M. Lang b ,I. Lopatin c , Y. Maghrbi f , K. Makonyi e , V. Metag e , W. Meyer d , J. M¨uller b , M. Nanova e , V. Nikonov b,c , R. Novotny e , D. Piontek b ,S. Reeve a , G. Reicherz d , T. Rostomyan f , S. Runkel a , A. Sarantsev b,c , St. Schaepe b , Ch. Schmidt b , R. Schmitz b , T. Seifen b ,V. Sokhoyan b , V. Sumachev c , A. Thiel b , U. Thoma b , M. Urban b , H. van Pee b , D. Walther b , Ch. Wendel b , U. Wiedner d ,A. Wilson b , A. Winnebeck b a Physikalisches Institut, Universit¨at Bonn, Germany b Helmholtz-Institut f¨ur Strahlen- und Kernphysik, Universit¨at Bonn, Germany c NRC Kurchatov Institute, Petersburg Nuclear Physics Institute, Gatchina, Russia d Institut f¨ur Experimentalphysik I, Ruhr–Universit¨at Bochum, Germany e II. Physikalisches Institut, Universit¨at Gießen, Germany f Institut f¨ur Physik, Universit¨at Basel, Switzerland g Department of Physics, Florida State University, Tallahassee, USA
Abstract
The first measurements of the beam-target-helicity-asymmetries E and G in the photoproduction of ω -mesons o ff protons at theCBELSA / TAPS experiment are reported. E ( G ) was measured using circularly (linearly) polarised photons and a longitudinallypolarised target. E was measured over the photon energy range from close to threshold ( E γ = E γ = G at a single energy interval of 1108 < E γ < E and G are highly sensitive to the contribution of baryon resonances, with E acting as a helicity filter in the s -channel. The new resultsindicate significant s -channel resonance contributions together with contributions from t -channel exchange processes. A partialwave analysis reveals strong contributions from the partial waves with spin-parity J P = / + , / + , and 3 / − . Keywords:
Meson production, Polarisation in interactions and scattering, Light mesons (S = C = B =
1. Introduction
The excitation spectrum of the nucleon has long been stud-ied to understand the non-perturbative regime of QCD, how-ever this still remains poorly understood. In particular, con-stituent quark models [1, 2, 3] predict significantly more statesthan experimentally observed [4]. This is sometimes referredto as the “missing resonance problem” and is most noticeablefor relatively high lying states. However, masses and parity or-derings of some low lying states are also not well reproduced.These deficits also appear in present Lattice-QCD calculationsand may be due to the fact that the models being used are notfully implementing a treatment of resonance decay [5]. The in-clusion of resonance decays via meson-baryon couplings maya ff ect both the number and ordering of the states [6, 7].The missing resonance problem may also be related to ex-perimental shortcomings. By far most of the observed stateshave been discovered in pion induced processes and thereforestates with small π N couplings may have escaped detection [8].The photoproduction of mesons, in particular non-pionic finalstates, may therefore provide a tool to investigate the existenceof hitherto unobserved resonances.The photoproduction of ω mesons is suitable to address this issue because the reaction threshold lies in the lesser exploredthird resonance region. Furthermore, the ω is isoscalar ( I = s -channel processes, only N ∗ resonances ( I = )couple to the nucleon ground state, with no interference from ∆ ∗ states ( I = ). This greatly simplifies the complexity of thecontributing excitation spectrum.Due to the vector character of the ω meson, at least 23 inde-pendent observables have to be measured to achieve a completeset of observables with respect to the decomposition of the re-action amplitudes [9]. This is much more involved than in pseu-doscalar meson photoproduction where, in principle, only 8 ob-servables su ffi ce, however it is similar to other channels such asdouble pseudoscalar meson photoproduction. It is well knownthat t -channel processes dominate ω photoproduction at highenergies. However, in the threshold vicinity, previous experi-ments indicate that s -channel processes also contribute (see forexample Refs. [10, 11, 12]). Individual double polarisation ob-servables may act as sensitive probes to disentangle these pro-cesses, even if a complete set of observables is not yet available[9].A comprehensive study of ω photoproduction using an unpo-larised liquid hydrogen target and the “charged” ω → π + π − π Preprint submitted to Physics Letters B October 28, 2018 igure 1: ω production via t -channel 0 + (Pomeron) exchange (left), t -channel π exchange (middle) and s -channel intermediate resonance (right). decay was performed at CLAS [13, 14]. Evidence forcontributions from s -channel resonances N (1680)5 / + and N (1700)3 / − was found near threshold, and contributions from N (2190)7 / − were strongly supported. The data also sup-ported 5 / + resonance states around 1.9-2.0 GeV and 3 / + states around 1.8-2.0 GeV. The goal of the present investiga-tion was to further study the possible role of s -channel ex-citations in the threshold region through the measurement ofdouble polarisation observables. The Bonn Frozen Spin hydro-gen (butanol) target [15, 16] was used in longitudinal polarisa-tion mode, in combination with linearly and circularly polarisedphoton beams. The experiments were performed at the ELSAelectron accelerator [17] at the Physics Institute of Bonn Uni-versity. Using the CBELSA / TAPS detector setup, the “neutral”decay ω → π γ was identified, which ideally suits the detectorcapabilities.The paper is organised as follows. Sec. 2 discusses the dou-ble polarisation observables relevant to this study. The exper-iment is briefly described in Sec. 3 and the data analysis inSec. 4, before the results are presented in Sec. 5. The paperconcludes with a summary and outlook in Sec. 6.
2. Double Polarisation Observables and the Mechanism of ω photoproduction It is mandatory to understand the reaction dynamics in orderto extract resonance information from ω photoproduction. Athigh photon energies, ω production is dominated by di ff ractivescattering. The fluctuation of the incoming photon into a q ¯ q -pair produces the vector meson in the vicinity of a strongly in-teracting recoil partner, mediated through the exchange of natu-ral parity quantum numbers of the Pomeron (Fig. 1 (left)). Thecross section shows a characteristic exponential fall o ff withsquared recoil momentum, t . Significant unnatural parity π -exchange (Fig. 1 (middle)) has been expected due to the size-able ω → π γ decay (8.3 % branching ratio) and was indeedreported [14, 18]. Meson exchange models of ω photoproduc-tion [19] have predicted dominant pion exchange processes nearthreshold (for photon beam energies less than 2 GeV), howevera recent partial wave analysis finds a negligible contribution(see below). Neither Pomeron nor π -exchange however, areable to reproduce the strong threshold energy dependence ofthe cross section and the observed ω decay angular distribution(see for example Ref. [14, 20]). This may suggest s -channelcontributions (Fig. 1 (right)), which is further corroborated bymeasurements of the photon beam asymmetry, Σ [10, 11]. For the combination of circularly polarised beam and lon-gitudinally polarised nucleon target, the cross section can bewritten in the form d σ d Ω = d σ d Ω (1 − P ⊙ γ P zT E ) . (1) σ denotes the unpolarised cross section, P ⊙ γ the degree ofcircular beam polarisation, and P zT the degree of longitudinaltarget polarisation. E is the beam-target helicity asymmetry.The sensitivity of E to the reaction mechanism is shown inRef. [21] in an intuitive way: For vector meson photoproduc-tion, it is important which hadron couples to the polarised pho-ton. In the case of Pomeron or π -exchange (Fig. 1 left andmiddle), the photon couples to the vector meson directly but notto the polarised target. With no angular momentum exchangedin the t -channel, this leads to a zero beam-target asymmetry.Conversely, in the case of s -channel production, the photon di-rectly couples to the polarised nucleon. In this case, the helicityasymmetry will reflect the projection onto the beam axis of thespin of the intermediate s -channel state. Such a behaviour ispredicted in Ref. [9]. In the case of mixing Pomeron and π exchange, E may also be non-zero, with a linear dependence incos θ ω CMS [9].
Combining a linearly polarised beam and longitudinally po-larised target, using the notation of Ref. [9], the two beam-targetasymmetries G and G π can be extracted. G is the target asym-metry associated with the azimuthal asymmetry of the produced ω -meson, and G π with that of the π of the neutral decay.Previous data for ω photoproduction at the CBELSA / TAPS-experiment were taken using an unpolarised target. Spin den-sity matrix elements were extracted from this data and the re-sults are described in Ref. [22].
3. CBELSA / TAPS-experiment
Electrons from ELSA with an energy ( E ) of 2.4 and 3.2 GeV(for circular or linear polarisation respectively) were used toproduce photons via bremsstrahlung o ff a thin radiator. To mea-sure the photon energy, electrons which radiated a photon weremomentum analysed using a magnetic dipole (tagging-) spec-trometer, covering a photon energy range of E γ = (0 . − . E [23].Longitudinally polarised electrons were used to produce cir-cularly polarised photons. A Møller polarimeter was integratedinto the tagging spectrometer, using a 20 µ m thick magnetisedfoil which simultaneously acted as a bremsstrahlung radiatorand a Møller target. Symmetric Møller pairs emitted perpen-dicular to the dispersive plane of the tagging spectrometer weremomentum selected by a pair of lead-glass detectors behind thetagger magnet. With this setup the electron beam polarisationwas measured to between 60 - 65% during the duration of thedata taking, with a relative uncertainty of approximately 2%[24]. The degree of polarisation transfer from the beam electron2o the radiated photon can then be calculated [25]. As a guide,using an electron beam energy of 2.4 GeV, the absolute circularpolarisation of the photon beam was 40% and 62% at photonbeam energies of 1200 MeV and 2200 MeV respectively.A 500 µ m thick diamond radiator was used to produce lin-early polarised photons [26]. The radiator was aligned rela-tive to the incident electron beam to select the plane of po-larisation and the energy of the coherent edge. The coherentpeaks were set at photon energies of 950, 1150 and 1350 MeV.The degree of polarisation was determined using the AnalyticalBremsstrahlung Calculation (ANB) software [27], with a typi-cal maximum degree of linear polarisation of 50%, accurate to arelative systematic error of 5%. Ref. [28] describes the methodof coherent bremsstrahlung and the performance of the setup.The linearly or circularly polarised photon beam was incidentupon a 2 cm long longitudinally polarised butanol (C H O)target [15]. The degree of target polarisation was measured viaNMR-techniques and was approximately 70% on average, witha 2% relative systematic error.A three layer scintillating fibre detector [29] to identifycharged particles surrounded the target within the acceptance ofthe Crystal-Barrel calorimeter [30]. This calorimeter consistedof 1230 CsI(Tl) crystals, cylindrically arranged around the tar-get and covering a polar angular range of 30 to 150 degrees. Thedetector was complemented by a forward cone detector of thesame material, which was assembled with scintillating platesfor charge identification, covering a polar angular range of 11.2to 27.5 degrees [31, 32].The 1 to 12 degrees forward cone was covered by the Mini-TAPS detector, set up in a hexagonally shaped wall of 216BaF crystal modules, also assembled with scintillating platesfor charged particle identification.The whole setup was able to detect charged as well as neutralparticles, however it was optimised for the detection of photons.The total coverage is about 96 % of the whole solid angle in thelaboratory frame.
4. Data analysis
The ω was identified through its decay to π γ . Thus duringo ffl ine analysis, four detector hits were required, correspondingto three photons and the proton. The proton (charge) identifi-cation was done using the signals of the inner scintillating fibredetector or the scintillating plates of the forward cone and theMini-TAPS detector. The reconstructed angles of the protonswere used, however the energy information from the calorime-ters was disregarded, since the detector response was very dif-ferent for photons and high energy ( >
400 MeV) protons.Timing cuts according to detector resolutions were appliedbetween the tagged incident photon beam and energy depositsin the detectors. The invariant mass of the summed four mo-menta of two of the photons was required to be between 105-165 MeV (a 3 σ fit due to detector resolutions to the π mass).The invariant mass of the reconstructed π and the other photonwas required to be within 3 σ of the ω mass. There was a smallamount of background from the γ p → π p channel, where a π invariant mass [MeV] γ π
200 300 400 500 600 700 800 900 C oun t s Experimental data ω Simulated p π π Simulated p π Simulated pSum of Simulated data
Figure 2: Typical π γ invariant mass distribution of one bin ( E γ = − θ ω CMS = ( − . − ( − . decay photon caused an extra “split-o ff ” cluster due to the elec-tromagnetic shower in the crystal. These events were removedfrom the data sample by requiring that the photon not originat-ing from the π decay had an energy greater than 200 MeV. Fur-ther kinematic cuts were applied in order to ensure longitudinaland transverse momentum conservation.After all selection cuts, a π γ invariant mass spectrum asshown in Fig. 2 was obtained. Monte Carlo simulations of sig-nal and background events showed that the dominating back-ground channels originated from π and 2 π production. In the ω invariant mass range however, only 2 π was significant forall beam energy and polar angle bins. These background eventsalso carried sizeable asymmetries, which needed to be correctedfor. A dedicated analysis of this channel was performed to ex-tract the asymmetry for every kinematic bin. The fraction of2 π background under the ω mass peak was determined by fit-ting Monte Carlo spectra to the experimental data as in Fig. 2.The asymmetry from the 2 π background was then scaled ac-cordingly and subtracted to leave the asymmetry from the ω channel.The beam-target-helicity asymmetry, E , was extracted by thecombination of the two di ff erent datasets, with either paralleldata ( N ↑↑ ), when the beam and target polarisations point in thesame direction, or antiparallel data ( N ↑↓ ), when the polarisationdirections are opposite: P ⊙ γ P zT E = N ↑↓ − N ↑↑ N ↑↑ + N ↑↓ (2)The beam-target asymmetry using a linearly polarised beam, G (and G π when measuring the asymmetry of the decay π ) was determined by measuring the yield ( N ) as a func-tion of the azimuthal angle between the meson and the tar-get polarisation direction ( ψ ). This was repeated for twodi ff erent azimuthal directions of beam polarisation ( φ γ, l =+ , − ) and either target polarised parallel ( P Tz ) or an-tiparallel ( P T − z ) to the beam direction. G was then ex-3 igure 3: Spectrum used for the determination of the “dilution factor”: Theazimuthal angular di ff erence of the detected proton and the calculated protondirection (using missing momentum techniques) is shown. The curves representthe liquid hydrogen data (blue or dark grey solid line), carbon data (red ordark grey dashed line) and sum of carbon and liquid hydrogen data (green orlight grey solid line) in comparison to the butanol data (black squares). Colouravailable online. tracted from a combined asymmetry of the four combinations: − P l γ P zT G cos(2 ψ ) = (3)[ N ( + , P Tz ) + N ( − , P T − z )] − [ N ( + , P T − z ) + N ( − , P Tz )][ N ( + , P Tz ) + N ( − , P T − z )] + [ N ( + , P T − z ) + N ( − , P Tz )]The polarised target provided a complication to the analy-sis. The frozen spin butanol (C H O) target [16] contained thepolarised hydrogen atoms in which the atomic electron polari-sation was transferred dynamically to the free protons. A meanpolarisation, monitored via NMR techniques, of about 70% wasreached. The protons bound in the carbon and oxygen nucleihowever remained unpolarised. The contribution of the boundprotons (through quasifree processes) required a correction tothe measured target polarisation by what is referred to herein asthe “dilution factor”. The e ff ective dilution factor is related tothe relative contribution of quasifree production, which stronglydepends on the widths of the applied kinematic cuts, on the en-ergy of the beam photon, and on the polar angle of the ω . Thiscontribution is determined by separate measurements on car-bon and hydrogen targets. These data are normalised, usingthe spectra described in Fig. 3, so that the butanol distributionagrees with the sum of liquid hydrogen and Fermi broadenedcarbon distributions [33].Approximately 225k and 5k events were used to determine E and G over the measured kinematic ranges respectively. Thedata was distributed towards forward angles due to the di ff rac-tive nature of the cross section. The statistical error per kine-matic bin has contributions from the number of reconstructed ω events, and the number of subtracted background from 2 π events.The systematic errors consist of uncertainties in the back-ground correction, polarisation determinations and the determi-nation of the dilution factor. The systematic uncertainty be-tween the relative flux of the two polarisation settings was neg- ligible. Furthermore, systematic e ff ects concerning the analysisconditions by the variation of kinematic cut ranges were stud-ied. Individual systematic uncertainties were added linearly fora conservative estimation of the final systematic errors.A more detailed description of the data analysis can be foundin Ref. [34].
5. Results and interpretation
Data for the beam-target-helicity asymmetry, E , are shownin Fig. 4 and 5 for centre-of-mass-energies from 1720 MeV to2280 MeV. At forward angles where t -channel exchange is ex-pected to dominate the reaction, E is close to zero. This isexpected for pure pion or Pomeron exchange but incompatiblewith mixed pion and Pomeron exchange [9]. At more backwardangles, the data show a clear nonlinear behaviour in cos( θ ω CMS ),indicating significant resonance contributions to the ω produc-tion channel.Data for the observables, G and G π are shown in Fig. 6. Bothobservables yield small values in the given mass range, com-patile with zero. The BnGa fit, described below, reproduces themeasured values.A partial wave analysis was performed in the framework ofthe Bonn-Gatchina PWA. A large body of data on pion andphoto-induced reactions was included which defines masses,widths, and coupling constants of nucleon and ∆ resonances.New data on ω photoproduction, which includes di ff erentialcross sections, density matrix elements [22], the beam asymme-try [10, 11], and the present measurement of the observables E , G , and G π were also included. The fit returned a χ = ω photoproduction. The total cross sec-tion receives a large contribution from Pomeron exchange. Thiscontribution rises rapidly from threshold and makes up about50% of the total cross section at 2 GeV. Pion exchange has onlya small contribution to the cross section. Depending on the formfactor used, the contribution is between 5-10% when fitted as afree parameter, however it can be forced to 20% without de-terioration to the description of the data [35]. In addition, theproduction of baryon resonances is found to be important. Be-low 1.9 GeV, the J P = / + partial wave provides the strongestcontribution. If this partial wave is not included in the fit, χ in-creases by 512 units. A J P = / + partial wave is found whichis also required to describe the data reported in [13, 14]; so-lutions without this contribution are worse in χ by 460 units.The contributions from the J P = / − partial wave improve thefit by 331 units in χ . Within the framework of the PWA, u -channel contributions were found to be weak. A full accountof the partial wave analysis, the nucleon resonances contribut-ing to γ p → ω p , and N ∗ → ω N branching ratios will be givenelsewhere [36].It is interesting to note in Fig. 5, the structure in E at a beamenergy of approximately 1650 MeV, where there is evidenceof a change of sign from negative to positive at cos( θ ω CMS ) =+ .
125 and a peak like structure at cos( θ ω CMS ) = − .
375 and − . K ∗ threshold, where a cusp-likestructure was observed in K Σ + photoproduction [37, 38]. It4 CMS ω θ cos( − − − − − − − E
19 MeV ± − − − − − − −
11 MeV ± − − − − − − −
12 MeV ± − − − − − − − − −
15 MeV ±
15 MeV ±
12 MeV ±
11 MeV ± − −
16 MeV ±
15 MeV ±
12 MeV ±
18 MeV ± − −
16 MeV ± Figure 4: Beam-target-helicity asymmetry, E , as a function of cos θ ω CMS . Sys-tematic errors are on the abscissa. The event weighted average beam energy andsystematic error is given for each energy interval, with the energy range givenin parentheses. The solid line is the result of the Bonn-Gatchina PWA whenincluding this data (see text for details). The data are tabulated in Ref. [34]. ) [MeV] γ Photon beam energy (E − − − − − E ) = -0.875 CMS ω θ cos( − − − − − ) = -0.375 CMS ω θ cos( − − − − − ) = +0.125 CMS ω θ cos( − − − − − ) = +0.625 CMS ω θ cos( ) = -0.625 CMS ω θ cos( ) = -0.125 CMS ω θ cos( ) = +0.375 CMS ω θ cos( ) = +0.875 CMS ω θ cos( Figure 5: Beam-target-helicity asymmetry, E , as a function of photon beamenergy (the same data as in Fig. 4). Systematic errors are on the abscissa. Thesolid line is the result of the Bonn-Gatchina PWA when including this data (seetext for details). − − − − − − − G
13 MeV ± − − π G
13 MeV ± ) CMS ω θ cos( Figure 6: Polarisation observables, G and G π versus cos( θ ω CMS ) at an averagebeam energy of 1213 ±
13 MeV (over a range of 1108-1300 MeV). Systematicerrors are on the abscissa. The solid line is the result of the Bonn-GatchinaPWA when including this data (see text for details). The data are tabulated inRef. [34]. K Σ + channel may be re-lated to K ∗ t -channel mechanisms, or dynamically K ∗ -hyperonquasi bound states [39].
6. Summary and outlook
The first measurements of the double polarisation observ-ables E , G , and G π for γ p → p ω have been reported. The beam-target-helicity asymmetry E was measured from threshold to aphoton energy of 2300 MeV, and G and G π were measured ata single bin in photon energy at 1108 < E γ < s -channel contributions, in additionto the expected t -channel contributions, have significant impor-tance in ω photoproduction close to threshold.A fit to the data within the framework of the Bonn-Gatchinapartial wave analysis requires significant contributions of thepartial waves with J P = / + , / + , and 3 / − to ω photopro-duction.A possibility to improve statistics in the ω channel is to ex-ploit the mixed charged decay ( ω → π + π − π ) with a branchingratio of 89.2 % [4]. This cannot be done within the presentCBELSA / TAPS setup but will instead be pursued with the newBGO-OD experiment [40, 41, 21] at ELSA. The BGO-OD ex-periment will also be used to analyse other vector meson chan-nels (for example φ and K ∗ production) o ff the proton and neu-tron, in order to study t -channel exchange processes and thecontributions from nucleon resonances in greater detail.
7. Acknowledgments
We thank the technical sta ff of ELSA and the participatinginstitutions for their invaluable contributions to the success ofthe experiment. We acknowledge support from the DeutscheForschungsgemeinschaft (SFB / TR16) and Schweizerischer Na-tionalfonds.
References [1] N. Isgur and G. Karl, Phys. Rev.
D 18 , 4187 (1978).[2] S. Capstick and N. Isgur, Phys. Rev.
D 34 , 2809 (1986).[3] U. L¨oring, K. Kretzschmar, B. Ch. Metsch, H. R. Petry, Eur. Phys. J.
A10 , 309 (2001).[4] K. A. Olive et al. [Particle Data Group Collaboration], Chin. Phys.
C 38 ,090001 (2014).[5] R.G. Edwards et al. , Phys. Rev.
D 84 , 074508 (2011).[6] M. Doring, J. Haidenbauer, U. G. Meissner, and A. Rusetsky, Eur. Phys.J.
A 47 , 163 (2011).[7] C. B. Lang and V. Verduci, Phys. Rev.
D 87 , no. 5, 054502 (2013).[8] S. Capstick and W. Roberts, Prog. Part. Nucl. Phys. , 241 (2000).[9] A. V. Sarantsev, A. V. Anisovich, V. A. Nikonov, H. Schmieden, Eur.Phys. J. A 39 , 61 (2008).[10] J. Ajaka et al. , Phys. Rev. Lett. , 132003 (2006).[11] F. Klein et al. , Phys. Rev. D 78 , 117101 (2008).[12] F. Dietz, V. Metag et al. , Eur. Phys. J.
A 51 , 6 (2015).[13] M. Williams et al. , Phys. Rev.
C 80 , 065208 (2009).[14] M. Williams et al. , Phys. Rev.
C 80 , 065209 (2009).[15] Ch. Bradtke and H. Dutz et al. , Nucl. Instr. Meth.
A 436 , 430 (1999).[16] H. Dutz, Nucl. Instrum. Meth.
A 526 , 117 (2004).[17] W. Hillert, Eur. Phys. J.
A 28 , s01, 139 (2006).[18] J. Ballam et al. , Phys. Rev.
A 7 , 3150 (1973).[19] B. Friman and M. Soyeur, Nucl. Phys.
A 600 , 477 (1996). [20] J. Barth et al. , Eur. Phys. J.
A 18 , 117 (2003).[21] H. Schmieden, Ch. Phys.
C 33 , 1146 (2009).[22] A. Wilson et al. , submitted to Physics Letters.[23] K. Fornet-Ponse, doctoral thesis, University of Bonn (2009).[24] S. Kammer, doctoral thesis, University of Bonn (2009).[25] H. Olsen and L.C. Maximon, Phys. Rev. , 887 (1959).[26] U. Timm, Fortschritte der Physik , 765 (1969).[27] F. A. Natter et al. , Nucl. Instr. Meth. B 211 , 465 (2003).[28] D. Elsner et al. , Eur. Phys. J.
A 39 , 373 (2009).[29] G. Suft et al. , Nucl. Instr. Meth.
A 538 , 416 (2005).[30] E. Aker et al. , Nucl. Instr. Meth.
A 321 , 69 (1992).[31] Ch. Funke, doctoral thesis, University of Bonn (2008).[32] Ch. Wendel, doctoral thesis, University of Bonn (2008).[33] A. Thiel et al. , Phys. Rev. Lett. , 102001 (2012).[34] H. Eberhardt, doctoral thesis, University of Bonn (2012).[35] A. V. Sarantsev, private communication (2015).[36] I. Denissenko et al. , in preparation.[37] R. Ewald et al. , Phys. Lett.
B 713 , 180 (2012).[38] R. Ewald et al. , Phys. Lett.
B 738 , 268 (2014).[39] A. Ramos and E. Oset, Phys. Lett.
B 727 , 287 (2013).[40] B. Bantes et al. , Int. J. Mod. Phys: Conf. Ser. , 1460093 (2014).[41] H. Schmieden, Int. J. Mod. Phys. E 19 , 1043 (2010)., 1043 (2010).