Photoproduction of η mesons off neutrons from a deuteron target
A.V.Anisovich, I.Jaegle, E.Klempt, B.Krusche, V.A.Nikonov, A.V.Sarantsev, U.Thoma
aa r X i v : . [ h e p - ph ] O c t EPJ manuscript No. (will be inserted by the editor)
Photoproduction of η mesons off neutrons from a deuterontarget A.V. Anisovich , , I. Jaegle , E. Klempt , B. Krusche , V.A. Nikonov , , A.V. Sarantsev , , and U. Thoma Helmholtz–Institut f¨ur Strahlen– und Kernphysik der Universit¨at Bonn, Nußallee 14-16, 53115 Bonn, Germany Petersburg Nuclear Physics Institute, Gatchina, 188300 Russia Institut f¨ur Physik der Universit¨at Basel, Klingelbergstrasse 82, CH-4056 Basel, SwitzerlandReceived: November 5, 2018/
Abstract.
A formalism is developed for the partial wave analysis of data on meson photoproduction offdeuterons and applied to photoproduction of η and π mesons. Different interpretations of a dip-bumpstructure of the η photoproduction cross section in the 1670 MeV region are presented and discussed.Helicity amplitudes for two low-mass S states are determined. PACS.
The cross section for photoproduction of η mesons off pro-tons is dominated by the N (1535) S resonance, other res-onances make only minor contributions. In particular the N (1650) S resonance, which one would naively expect tocontribute to η photoproduction in a similar strength as N (1535) S , is hardly visible in the total cross section.There are two explanations why N (1650) S is so muchsuppressed compared to N (1535) S : the N (1650) S → N η decay branching fraction is much smaller than thatfor N (1535) S decays, and the N (1650) S photopro-duction cross section seems to be suppressed comparedto N (1535) S photoproduction.The large N (1535) S → N η coupling found differentinterpretations by Isgur and Karl [1], by Weise and col-laborators [2] and by Glozman and Riska [3]. In [1], thetwo quark-model S states with s = 1 / s = 3 / − ◦ ). A phenomenological fit to baryon decayshad given precisely this value [4]. For this mixing angle, N (1650) S decouples from N η decays while N (1535) S has a strong coupling to N η . In [2],
N η and ΣK photo-production were described by the dynamics of the cou-pled ΣK − p η -system; no genuine 3-quark resonance wasrequired in their model. In [3], the N (1535) S is a con-ventional 3-quark state; one-pion exchange was assumedto make an essential contribution to quark-quark inter-actions. Clustering of the baryonic wave functions intoquarks and diquarks then led to the strong selectivity ofthe N (1535) S → N η coupling.
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The Moorhouse rule [5] gives a second reason for thesmall η photoproduction cross section off protons. Thisselection rule forbids photo-excitations off protons of spin3/2 members of the lowest-mass [70 , − ] super-multipletof nucleon resonances. The Moorhouse rule forbids onlytransitions to the [70 ,
8] component of the N(1650)S .Burkert et al. [6] analyzed the existing photo- and electro-production data and extracted transition amplitudes fortransitions from the nucleon ground state to the [70 , − ]super-multiplet. The - scarce - data on electro-productionoff neutrons were not used; due to their large errors, thedata at the photo-point hardly constrained their analysis.Recently, photoproduction of η mesons off neutronshas attracted additional interest. A narrow structure at1.67 GeV was observed which was not easily understoodin terms of known nucleon excitations. It was first reportedby the GRAAL collaboration at NSTAR2004 [7] and in-terpreted as narrow resonance by part of the authors [8,9].The bump-like structure in the nη invariant mass distri-bution is not seen in the cross section on the proton eventhough a reanalysis of the GRAAL data [10] indicated thepossibility of a bump structure at 1.69 GeV also for pro-ton data. This structure was suggested to signal the exis-tence of a relatively narrow ( M ≈ .
68 GeV, Γ ≤
30 MeV)baryon state. In particular the possibility that the stateis the non-strange member of an anti-decuplet of pen-taquarks [11,12,13] is an attractive possibility. The bumpstructure in the nη invariant mass spectrum was confirmedby the CB-ELSA/TAPS [14] and LEPS [15] collabora-tions.Different interpretations have been offered as origin ofthis structure. Choi et al. [16] use three known nucleon res-onances, N (1535) S , N (1650) S N (1710) P , and a nar- A.V. Anisovich et al. : Photoproduction of η meson off neutron row state at 1675 MeV which they discuss as pentaquark N (1675) P . Vector meson exchange in the t channel wasused as a background amplitude.The Giessen group arrives at different conclusions [17].Within their unitary coupled-channels effective Lagrangianapproach, the cross section of η photoproduction on theneutron was fully described. The peak at √ s =1.66 GeVwas explained as coupled-channel effect due to N (1650) S and N (1710) P resonance excitations. No narrow reso-nance was required.The analysis of Fix et al. [18] required, in addition tothe conventional ingredients of the MAID model, a narrowstate which was assumed to have P quantum numbers.In this paper, we present a partial wave analysis of therecent data of the CB-ELSA/TAPS collaboration [19] on γd → p spectator nη . In view of the long-standing discrep-ancies between the photo-production amplitude A n / for N (1535) S production ( A n / = − . ± .
035 GeV − / from γn → nπ [20]; A n / = − . ± .
030 GeV − / from γn → nη [21]), it seems adequate to include some olderdata on γn → nπ , but we also include recent data fromGRAAL on the beam asymmetry for γn → nη [22] and γn → nπ [23]. In addition, we use data on photoproduc-tion of 2 π , π η and of hyperons as well as some partial-wave amplitudes from elastic πN scattering and data on π − p → p π . A survey of the data used in the fits, of thepartial wave analysis method and of recent results can befound elsewhere [24,25,26,27,28].The paper is organized as follows: after this introduc-tion we present, in section 2, how the Fermi motion ofthe neutron in the deuteron is treated. Reasonable consis-tency is found for the γp → pη cross sections for protonsbound in deuterons - folded with the Fermi momentumdistribution - with the cross sections measured on freeprotons. The success encouraged us to perform a partialwave analysis for the part of the data where the protonacts as a spectator. The fits and the results are presentedin section 3. The paper ends with a short summary andour conclusions (section 4). Experimentally, the cross section for η meson photopro-duction off deuterons is measured. The deuteron is at restin the laboratory system, the neutron not. It has had, atthe moment of the interaction, the same (but opposite)momentum as the proton. A cut in the missing momen-tum of the (undetected) proton selects events in which theproton acted as spectator.There are two approaches to fit data. First, one couldunfold the experimentally observed cross section to deter-mine the cross section for a neutron target. This data canthen be fitted. Alternatively, the calculated cross sectioncan be folded with the neutron momentum. In this way,adopted here, the fitted cross section can be compareddirectly to the measured quantities. The differential cross section for production of n par-ticles in the photon nucleon interaction has the form dσ γN = (2 π ) | A | p ( k k ) − m m dΦ n ( P, q , . . . , q n ) (1)where k i and m i are the four–momenta and masses of theinitial particles, P is the total momentum ( P = k + k )and q i are the four–momenta of final state particles. The dΦ n ( P, q , . . . , q n ) is the n-body phase volume dΦ n ( P, q , . . . , q n ) = δ ( P − n X i =1 q i ) n Y i =1 d q i (2 π ) q i (2)where q i are the energy components.In the case of meson photoproduction off nucleons boundin a deuteron, the cross section (1) should be integratedover its momentum: dσ γD = Z d | p N | | p N | f ( | p N | ) dz N dφ N π (2 π ) | A | p ( k p N ) × dΦ n ( k + p N , q , . . . , q n ) , (3)where p N is the momentum of the nucleon, z N = cos Θ N ,and where dz N dφ N forms the solid angle element of thenucleon in the laboratory system. The function f ( P N ) de-scribes the momentum distribution of the nucleon insidethe deuteron. It can be chosen in the form of the Paris[29] or Gatchina wave function [30].The spectator nucleon in the γd interaction has themomentum p s = − p N in the lab system (deuteron at rest)and is on shell. Therefore the energy of the interactingparticle is given by E N = M d − q m s + p N (4)where M d is the deuteron mass and m s is the mass of thespectator nucleon. The off shell mass squared ( t ) of theinteracting nucleon and the total energy squared in the γN interaction s tot ( t ) are equal to t = E N − m N s tot ( t ) = t + 2 E γ (cid:0)q p N + t − | p N | z N (cid:1) . A major problem in this approach is to relate the off-shell amplitude of the interacting particles with measur-able on-shell distributions. It can be shown [21] that thebest description is achieved under the assumption σ ( s tot ( t ) , t ) = σ ( s tot ( m N ) , m N ) σ ( s tot ( t ) , t ) = 0 for s tot ( t ) < ( m N + m η ) . (5)Due to relation (5), all further calculations can be per-formed for an on-shell nucleon. The components of theinitial 4-vectors in the lab system are defined as p N = ( p N , p xN , p yN , p zN ) k = ( E γ , , , E γ ) p xN = | p N | sin Θ N cos φ N , p zN = | p N | z N p yN = | p N | sin Θ N sin φ N , p N = q m N + p N (6) .V. Anisovich et al. : Photoproduction of η meson off neutron 3 where m N is nucleon mass and momentum of the photon k is directed along z -axis.In the case of single-meson photoproduction, the am-plitude depends on the total energy of the γN system andthe angle between the initial photon and the final mesoncalculated in the center of mass system (cms) of the re-action. Differential cross sections are usually given in thecenter of mass system of the photon and the hit nucleon.We will call this system as “data” system. Let us calculatethe momentum of the particles and scattering angles in thelaboratory system, in the cms and the “data” system.The total energy squared (which is an invariant value)can be calculated, for example, in the laboratory system: s tot = ( k + p N ) = m N + 2 E γ ( p N − | p N | z N ) . (7)Then in cms of the reaction: z cms = q cms k cms | q cms || k cms | = q cms k cms − ( q k ) | q cms || k cms | ,q cms = s tot + m − m N √ s tot , k cms = s tot − m N √ s tot , | q cms | = q ( q cms ) − m , | k cms | = k cms . (8)Here, q is the 4-momentum of the final meson with mass m . The invariant quantity ( q k ) can be calculated in anysystem (e.g. the “data” system).To define the photon 4-vector in the “data” system letus calculate the invariant ( k P eff ), where P eff is the sumof photon and nucleon momenta, in both the laboratorysystem and in the “data” system. P labeff = ( m N + E γ , , , E γ ) , k lab = ( E γ , , , E γ ) P dataeff = ( √ s eff , , , , k data = ( E mγ , , , E mγ ) . (9)Comparing this invariant in the two systems we obtain E mγ = m N E γ √ s eff , s eff = m N + 2 m N E γ (10)Then the invariant ( k q ) in the “data” system is equal to q k = m N E γ √ s eff ( q m + | q | − | q | z ) . (11)In this equation, q is the laboratory momentum of themeson. As a result, we can express all variables in termsof measured values; needed are - in the “data” system - thephoton energy E γ and z , the cosine of the angle betweenmeson and photon.Our next task is to define the initial nucleon momen-tum in the “data” system. Then: p mN = ( p m N , p xN , p yN , p mzN ) p m N = p N m N + E γ ( p N − p zN ) √ s eff ,p mzN = p m N − ( p N − p zN ) √ s eff m N (12) The transition from the lab system to the “data” systemis performed via a boost along the z -axis, so ” x ” and ” y ”components of 4-vector are not changed. The equationsfor p m N and p mzN can be obtained from the invariance ofthe scalar products ( p N P eff ) and ( p N k ) calculated in thelab and “data” systems.Now one can calculate the phase volume for the meson-nucleon final state in the “data” system: dΦ n ( k m + p mN , q , q ) = δ ( P m − q − q ) d q π ) q q (13)where q = q m + | q | q = q m N + | P m − q | P m = ( p m N + E mγ , p xN , p yN , p mzN + E mγ ) (14)and m is the mass of the final meson.From energy conservation, the absolute value of themeson momentum in the “data” system is calculated to | q | = Σξ | P m | + P m p Σ − m [( P m ) − | P m | ξ ]( P m ) − | P m | ξ (15)where Σ = 12 ( s tot + m − m N ) (16)and ξ is the cosine of the angle between P m and q : ξ = zP mz + | p N | p − z N √ − z cos ( φ N − φ ) | P m | (17)and where φ is the azimuthal angle of the final meson.Then the phase volume is given by dΦ n ( P m , q , q ) = 14(2 π ) | q | dzdφ | q | P m − | P m | ξ p m + | q | . (18)All variables now depend only on the relative angle φ N − φ . In the evaluation of the cross section (3), oneintegration can be performed trivially and eq. (3) can berewritten in the form dσ γD = Z d | p N | | p N | f ( | p N | ) dz N dφ N π ×| A ( s tot , z cms ) | π ( k p N ) | q | dz | q | P m − | P m | ξ p m + | q | (19)where ξ = zP mz + | p N | p − z N √ − z cos ( φ N ) | P m | P m = ( p N + E γ ) m N + E γ ( p N − p Nz ) √ s eff | P m | = m N ( p zN + E γ ) − E γ ( p N − p zN ) √ s eff + E γ (20)and | q | is defined by eq.(15).At low energies, the phase volume given by eq.(18)decreases for forward angles leading to a correspondingbehavior of the cross section in the region where the S wave is the dominant contribution. A.V. Anisovich et al. : Photoproduction of η meson off neutron η -mesons off deuterons η photoproduction off protons As a first step, we describe η photoproduction off protonsbound in a deuteron. This allows us to test the reliabilityof the folding procedure accounting for the Fermi motion.The total cross section and the angular distributions arepresented in Figs.1 and 2 for the case of the Paris wavefunction. The error bars on these figures represent statis-tical errors only.For the fits, we use alternatively the Paris wave func-tion [29] or a deuteron wave function obtained from a dis-persion N/D -method [30]. The fit uses no new parame-ters: all masses, widths, partial decay widths, and helicityamplitudes are determined by the data from γp → pη [31] and the fits described in [26]. The χ was found tobe 2396 for 380 points using the Paris wave function and2410 with the N/D -based wave function. The χ ’s aresimilar demonstrating that the extraction of cross sectionfrom deuteron data is insensitive to details of the deuteronwave function. This observation is confirmed when crosssections for γn → nη are extracted. Hence we show hereonly figures obtained by using the Paris wave function.The χ ’s are large; inspecting the differential cross sec-tions and the deviations between data and fit suggeststhat systematic errors in the extraction of the cross sec-tions may be responsible for a significant fraction of thelarge χ ’s. M( g p) [ MeV ] s tot [m b ] CB-ELSA
Fig. 1.
The total cross section for γ p → η p from the deuterontarget. The description of the data (solid line) is obtained fromthe solution on the free proton smeared with the Paris wavefunction. The dashed line is the S , the dash-dotted line the P , and the dotted line the D contribution. d s /d W [m b/sr ] cos q h Fig. 2.
The differential cross section for γ p → η p from thedeuteron target in the 1505-2340 MeV mass range. The solidcurves represent a fit to free-proton data smeared with theParis wave function. The dashed curves show the contributionof the S wave. η and π photoproduction off neutrons In the present analysis, the following data sets are addedto our data base used in our fits: η photoproduction off theneutron from the CB-ELSA experiment [19], beam asym-metry for η [22] and π [23] photoproduction off the neu-tron from the GRAAL experiment and π photoproductionoff the neutron from the SAID database [32]. These datawere fitted together with other photo- and pion-inducedsingle and double photoproduction data as listed in theIntroduction. All our fits produced a very similar χ forthe Paris and N/D -based wave function. Hence we dis-cuss only the investigations which had been done usingthe Paris wave functions. .V. Anisovich et al. : Photoproduction of η meson off neutron 5 d s /d W [m b/sr ] cos q h Fig. 3.
The differential cross section for γ n → η n off deuterons[19]. The PWA description is shown as solid line (solution 1),dashed line (solution 2) and dotted line (solution 3). -0.400.40.8 -0.400.40.8 cos q h S Fig. 4.
Beam asymmetry for γ n → η n for neutrons boundin a deuteron [22]. The PWA description is shown as solid line(solutions 1), dashed line (solution 2), and dotted line (solution3). The differential cross section for γn → nη is shown inFig. 3, the beam asymmetry in Fig. 4. The correspondingdata for γn → π n are shown in Fig. 5 and 6. The data arefitted using three different scenarios. In all cases, the mostsignificant contributions came from the S , P , and P partial waves, with S providing the largest contribution. d s /d W [m b/sr ] cos q p Fig. 5.
The differential cross section for γ n → π n using adeuteron target [32]. The PWA description is shown as solidline (solutions 1) , dashed line (solution 2), and dotted line(solution 3). These three partial waves, and for the waves P and D which are irrelevant here, were described using K-matrices. For the other less important waves, relativisticmulti-channel Breit-Wigner amplitudes were used. For theimportant waves, the elastic scattering amplitudes from[33] were included in the fit using the same K-matrix asfor the photoproduction data.In the first solution, the low-energy region is describedmainly by the interference between N (1535) S and N (1650) S . In the second solution we enforce a large con-tribution from a standard N (1710) P resonance. In thethird solution, we test the possibility of a narrow (lessthan 10 MeV) state at about 1650 MeV. The resulting fitcurves are also shown in Figs. 3-6. In Table 1 we give a A.V. Anisovich et al. : Photoproduction of η meson off neutron -0.4-0.200.20.40.60.8 1560 1617-0.4-0.200.20.40.60.8 1687 0 0.5-0.5 1734 0 0.5-0.5 cos q p S Fig. 6.
Beam asymmetry for the reaction γ n → π n fromthe deuteron target [23]. The PWA description is shown assolid line (solutions 1), dashed line (solution 2), and dottedline (solution 3). breakdown of the χ contributions of the four data setsin the three scenarios. All three scenarios provide an ad-equate description of the dip-bump structure observed inthe γn → nη total cross section.A first analysis [38] of the preliminary CB-ELSA data[14] presented at NSTAR 2007 did not include t and u -exchanges due to the fact that in the low energy regionthese contributions are difficult to separate from othernon-resonant terms. The present analysis is extended upto 2.1 GeV, first without contributions from t and u chan-nel exchanges and second with these contributions included.The fits with t and u exchanges result in a slightly betterdescription of the high energy tail but qualitatively do notchange the solutions in the region below 1.75 GeV. How-ever, both, the inclusion of t and u channel exchanges andthe use of the final data decreased the helicity amplitudes.The new values reported here supersede those reported atNSTAR 2007. The contributions of high mass states areambiguous and cannot be identified reliably. More dataand further systematical investigations are needed. Theseuncertainties do not affect our conclusions concerning thelow-mass region which is the prime issue of the study. Table 1.
Single meson photoproduction off neutron data usedin the partial wave analysis and χ for solutions 1 (interferencein S wave), 2 ( N (1710) P ), and 3 (narrow P ).Observable N data χ N data χ N data χ N data Ref.Sol. 1 Sol. 2 Sol. 3 σ ( γ n → n η ) 280 1.32 1.26 1.31 [19]Σ( γ n → n η ) 88 1.75 1.85 1.79 [22] σ ( γ n → n π ) 147 2.01 2.35 2.03 [32]Σ( γ n → n π ) 28 1.02 1.07 0.90 [23] S wave Following our previous analyses [31],[24] the S wave wasparameterized as two pole, 5 channel K-matrix amplitude: K ab = X α =1 g ( α ) a g ( α ) b M α − s + f ab , (21)where a, b = pπ , pη , KΛ , KΣ , ∆π , and M α and g ( α ) a aremasses and coupling constants of the K-matrix poles.In [34] the non-resonant contributions were parame-terized as linear mass dependent functions. We also foundthat such mass dependence introduced for the πN → πN and πN → ηN and ηN → ηN non-resonant terms im-proves notably the description of the pion induced andphotoproduction reactions. However, in our parameteriza-tion we introduced in addition a factor which suppressesthe divergency of the non-resonant terms at large energies.Thus f ab = ( f (1) ab + f (2) ab √ s ) 2 + s ab s + s ab a, b = πN, ηN (22)and s ab >
0. The non-resonant transitions between πN → KΛ , πN → KΣ and πN → ∆π channels also improve thecombined description. However these terms can be param-eterized as constants. All other transitions contribute verylittle to the data description and were fixed to zero.The amplitude for the transition between K-matrixchannels can be written as: A ab = ˆ K ac ( ˆ I − i ˆ ρ ˆ K ) − cb . (23)The phase space ˆ ρ is a diagonal matrix ρ ab = δ ab ρ a with ρ a ( s ) = 2 | k B |√ s m aB + p ( m aB ) + | k B | m aB (24)for the two body final states. Here m aB is the mass and k B is the momentum (calculated in the c.m.s. of the reaction)of the baryon in the channel (a) (see [35]). The parame-terization of the ∆π phase volume is given in details in[35].The K-matrix parameters for the πN and ηN channelsare constrained from the fit of the elastic πN → πN data(extracted by [33]) and the fit of the π − p → ηn differen-tial cross section [36],[37]. The description of these data isshown in Figs. 7 and 8.The photoproduction amplitude is parameterized inthe P –vector approach since the γ N couplings are weakand do not contribute to rescattering. The amplitude isthen given by A a = ˆ P b ( ˆ I − i ˆ ρ ˆ K ) − ba . (25)with P -vector parameterized as: P b = X α g ( α ) γ N g ( α ) b M α − s + ˜ f b (26)Here g ( α ) γ N are γN couplings of the K-matrix poles and ˜ f b are non–resonant production terms, parameterized in thefit as real constants. .V. Anisovich et al. : Photoproduction of η meson off neutron 7 -0.3-0.2-0.100.10.20.30.40.50.6 1.2 1.4 1.6 1.8 2 Re T a) M( p N), GeV -0.200.20.40.60.8 1.2 1.4 1.6 1.8 2
Im T b) M( p N), GeV
Fig. 7.
The description of the πN → πN S amplitude ob-tained in the combined solution. The data are taken from en-ergy independent solution [33]. cos q h d s /d W [m b/sr ] Fig. 8.
The description of the πp → ηn differential cross sec-tion obtained in the combined solution. The data are takenfrom [36] (open circles) and [37] (full squares). S wave The first solution with a strong interference in the S wave provides a very good description of the fitted data(see Table 1). In particular the bump in the 1650 MeVregion is well described. This solution gives the followinghelicity couplings for S resonances calculated at the polepositions of the S amplitude: S (1535) : A n / = − . ± . , φ = 12 ◦ ± ◦ S (1650) : A n / = − . ± . , φ = 40 ◦ ± ◦ (27)The bump in the region of 1650 MeV appears due toan interference between S (1535), S (1650) and a non-resonant background. In our combined solution of the sin-gle photoproduction data S (1650) has the rather small( 15%) branching ratio into the ηN channel. Therefore anappreciable large coupling of this state to the γn chan-nel is needed to describe the bump structure. Here weare in contradiction with the Giessen result [17] where thebump appears with decreasing of the S (1650) γn helicitycoupling. The two S states have very close (apart fromoverall sign) couplings into γp and γn channels. However M( g n) [ MeV ] s tot [m b ] CB-ELSA
Fig. 9.
The total cross section for the reaction γ n → η n fromthe deuteron target [19]. The PWA description from Solution 1(Paris wave function) is shown as the solid line. The dashed lineis the S contribution, dash-dotted line is P contribution anddotted line is P contribution The grey (online: green) curvesshow the corresponding cross sections on the free neutron (noFermi motion) there is an important correlation: the phase difference be-tween the couplings is fixed more precise than the absolutenumbers. We found the phase difference 5 ± γp channel and 28 ± γn channel. The bumpstructure in the 1650-1700 MeV region becomes much lesspronounced in the case of a smaller phase difference (seesolutions discussed below).The K-matrix parameters of the S wave are ratherfirmly fixed from the fit of the elastic data and photo-production reactions off the proton. The only mandatoryparameters to fit γn reactions are two P-vector γn polecouplings and five non-resonant production constants. The γn → πn and γn → ηn can be fixed directly from the com-bined analysis of the differential cross sections and beamasymmetry data from the neutron target. Fixing these pa-rameters to zero leads to a large deterioration of the com-bined description.Among other non-resonant contributions the most im-portant one is the direct production of the KΛ channel.It can notably influence the structure at 1650-1700 MeVwhich is situated in vicinity of the KΛ threshold. The KΣ production only slightly improves the description at highenergies and ∆π can be put to zero.To check the influence of the γn → KΛ and γn → KΣ direct production terms we performed the fit fixing theseparameters to zero value. To reproduce the description ofthe γn → ηn data we increase the weight of this data setby a factor of 2. In this fit we could reproduce the un-polarized ηn cross section and beam asymmetries for π n A.V. Anisovich et al. : Photoproduction of η meson off neutron M( g n) [ MeV ] s tot [m b ] CB-ELSA
Fig. 10.
The total cross section for the reaction γ n → η n fromthe deuteron target [19]. The PWA description from Solution 2(Paris wave function) is shown as the solid line. The dashed lineis the S contribution, dash-dotted line is P contribution anddotted line is P contribution The grey (online: green) curvesshow the corresponding cross sections on the free neutron (noFermi motion) and ηn . However the fit failed to reproduce the unpolar-ized γn → π n differential cross section: the χ changedfrom 2.11 to 2.71. The residue for the S (1535) state didnot change within errors (27). The helicity coupling ofthe S (1650) is slightly bigger in this solution: ∼ . − and the phase difference with the first pole cou-pling reached 120 degrees.A simplified parameterization provides a simplified pic-ture: the difference in phases of helicity couplings in the γp and γn reactions is clearly seen. However it failed to de-scribe simultaneously all reactions. This is one of the mainreasons why analyses of different sets of photoproductiondata results in incompatible helicity couplings.The P and P waves provide contributions of similarstrengths to nη . In the 1700 MeV region, the N (1710) P resonance is weak while N (1720) P makes a small con-tribution. The P wave becomes stronger at 1900 MeV. N (1710) P contributions We have investigated other mechanisms for an explana-tion of the bump-like structure in the region 1670 MeV.To prevent a strong interference in the S wave we for-bid a direct photoproduction of the second K-matrix poleby setting its γn coupling to zero. We still observed somesmall interference effect in the S wave on the free neu-tron but it is too small to describe the bump-like structurein the data (see dashed lines in Fig. 10). In some analyses, N (1710) P has a sizable coupling to N η , the Review of Particle Properties calculates a branch-ing ratio Br ( N (1710) → N η ) = (6 . ± . S wave and absence of anexotic state, this is the only mechanism which can explainthe data. The χ of the fit is very similar to the solution 1.The contributions are depicted in Fig. 10. The helicitycouplings for the S resonances calculated as residues inthe pole position are determined to S (1535) : A n / = − . ± . , φ = 10 ◦ ± ◦ S (1650) : A n / = − . ± . , φ = 25 ◦ ± ◦ (28)This solution differs from the solution 1 by a differentpartial wave decomposition: it has a significant contribu-tion from P in the region around 1.7 GeV which comesfrom the N (1710) P resonance. The description of thetotal cross section for the Paris wave function is shown inFig. 10. This analysis shows that there is a second possi-ble mechanism to describe the existing experimental dataand the structure around 1.67 GeV in η photoproduction.As before, the dominant contribution stems from the S wave but in the 1700 MeV region, the P wave pro-vides an appreciable contribution, too. In this solution,interference between N (1535) S and N (1650) S makesa visible but small effect. M( g n) [ MeV ] s tot [m b ] CB-ELSA
Fig. 11.
The total cross section for the reaction γ n → η nfrom the deuteron target. The PWA description from Solution3 (Paris wave function) is shown as the black solid line andthe contributions as the colored solid lines. The dashed curvesshow the corresponding cross sections on the free neutron (noFermi motion).V. Anisovich et al. : Photoproduction of η meson off neutron 9 P state? A narrow P state in the region of 1670 MeV is discussedas a candidate for the pentaquark [41] and is one of themain motivations behind this analysis. In a third fit, wefollowed the procedure for the solution 2 but introduced anarrow state in the region 1670 MeV. Its mass optimizedat 1670 ± N (1710) P resonance. The fits became unstable and aseries of solutions were obtained in which a relatively nar-row state and the broader N (1710) P interfered. Solu-tion 3, presented in the Fig. 11, shows the extreme wherethe broad N (1710) P wave is absent. In this solution,the helicity coupling for the narrow P state is equal to0.016 GeV − / , assuming a ηp branching to be 50%. It isinteresting to note that Azimov et al. [42,41] derived avalue 0.021 GeV − / using the GRAAL data on η photo-production off neutrons.For the two S resonances the following helicity cou-plings are calculated: S (1535) : A n / = − . ± . , φ = 25 ◦ ± ◦ S (1650) : A n / = − . ± . , φ = 20 ◦ ± ◦ (29) η photoproduction on the free proton Finally we consider the recent conjecture of Kuznetsov etal. [10] that the beam asymmetry for η photoproductionon free protons may reveal a structure in the 1.69 GeVregion. Here, we check the compatibility of this data withsolution 1 (interference in S wave) and/or with solution3 (narrow P ). In addition to [10]we include also the beamasymmetry data for η photoproduction from GRAAL [43]. o S o o
900 1000 1100900 1000 1100 E g o
900 1000 1100900 1000 11000.60.40.20-0.2 140 o
900 1000 1100900 1000 1100
Fig. 12.
Beam asymmetry for the reaction γ p → η p [10]. ThePWA description is shown as solid line (solutions 1) and dottedline (solution 3). The data on γp → pη and fit are shown on Figs. 12and 13. The data are described by the solution 1 with χ /N data = 1 .
35 (new data [10]) and χ /N data = 1 . P state (so-lution 3) results in a χ /N data = 0 .
95 (new data [10]) and S cos q h Fig. 13.
Beam asymmetry for the reaction γ p → η p [43]. ThePWA description is shown as solid line (solutions 1) and dottedline (solution 3). χ /N data = 1 .
90 (GRAAL data [43]). Although the solu-tion with a narrow P gives a better description of thenew data [10], the fit faces some problems. While all in-dividual pictures in Fig. 13 exhibit a peak-like structures,they cannot be described consistently by one resonancewith one unique mass position. Hence new high precisiondata on this reactions are urgently needed if this idea isto be pursued further. Main parameters for the two S states are given in Table2. Pole positions and photoproduction couplings off pro-tons are in good agreement with a previous analysis [24].The main change was found in the imaginary part of thepole positions: the first pole of the S amplitude becamea bit narrower and the second pole a bit broader. Bothresonances have a Flatte like structure, the first one dueto the ηN threshold and the second one due to KΛ . InTable 2, the position of the poles closest to the physicalregion are listed. The behavior of the Flatte amplitude isdefined by an interplay of two poles on two sheets definedby the cut; small instabilities in pole positions are hencenot surprising.The helicity couplings given in Table 2 are calculatedas the residues at the pole position and have phases. Forprotons, our N (1535) S helicity amplitude coincides withthe PDG estimate, for neutrons the two errors just coverthe difference [44]. The discrepancy is due to the results re-ported in [20,45] while most analyses [21,46,47,48] quotevalues which are fully compatible with our finding.For the N (1650) S , we found stronger photon cou-plings than the average value given in [44], with the dif-ferences being at the 2 σ level. We point out that our values et al. : Photoproduction of η meson off neutron provide a consistent description of almost all existing datasets. Our γn coupling is, for the first time, derived from η photoproduction off neutrons (and constrained by π photoproduction off neutrons).The values in Table 2 are averaged using the first andthird solution. In the solution proposing a large P (1710)contribution, the γn coupling of the N (1650) S was found ∼ . D (1675)is ruled out by our analysis. The combined fit to the π , η photoproduction off free protons and the deuteron andthe results from the elastic πN scattering fixes well thebranching ratio to the ηN channel (which is < γn coupling of the D (1675) resonance, we couldonly reach a contribution of 0.5 µ b from this state to the γn → ηn total cross section which is far from the valueneeded for a good description of the data.Finally, we note that we do not use different helicityamplitudes for π and η photoproduction. Discrepancies, asfound in the literature for both S resonances, betweenhelicity amplitudes derived from different data cannot oc-cur.In the so-called “Single Quark Transition Model”, Burk-ert el al. [6] extracted amplitudes for electromagnetic tran-sitions from proton and neutron to excited states. The ex-trapolation to the photon point (read off their diagrams)are listed in Table 3. The agreement is excellent.Finally we also compare our photocouplings with modelcalculations [50,51,52,53]. In all models, the signs are rightand the magnitudes agree with the experimental values atthe 30% level. On the basis of this data, no preference canbe given to one particular model calculation. We have presented an analysis of data on photoproduc-tion of η (and π ) mesons off neutrons. The analysis was Table 2.
Masses and widths (in GeV) and helicity amplitudesof S (1535) and S (1650). S (1535) S (1650)Pole position (mass) 1 . ± .
020 1 . ± . . ± .
025 0 . ± . . ± .
020 1 . ± . . ± .
080 0 . ± . A p / (GeV − / ) 0 . ± .
025 0 . ± . . ± .
030 0 . ± . ± ◦ (25 ± ◦ A n / (GeV − / ) − . ± . − . ± . − . ± . − . ± . ± ◦ (30 ± ◦ Table 3.
Model predictions of S (1535) and S (1650) helicityamplitudes for protons and neutrons (in 10 − GeV − / ).This work [6] [50] [51] [52] [53] N p ±
25 97 +147 +142 +127 +76 n − ±
20 -53 -119 -77 -103 -63 N p ±
35 90 +88 +78 +91 +54 n − ±
20 -32 -35 -47 -41 -35 motivated by a bump structure at 1670 MeV observed inthe total cross section for γn → nη in several experiments.There is a hot discussion in the literature if the structuresignals a resonance. Often, it is interpreted as evidence fora pentaquark with hidden strangeness.We find that the data can naturally be interpreted byinterference within the S wave. This is the most naturalinterpretation and does not require any ad-hoc assump-tion. Other interpretations can, however, not be ruled out.The N (1650) S may have a small coupling to nγ . Then,the P amplitude plays a more significant role. For anappropriate choice of parameters, a narrow P can be in-troduced and the data are well described. Hence the datado not support the need to introduce a narrow resonancebut, for a suited set of parameters, the existence of a nar-row resonance is also not ruled out. Fluctuations in recentbeam asymmetry data for γp → pη may serve as an indi-cation for a narrow structure at 1670 MeV but fits withoutit provide a reasonable description of the data as well.A second aspect of the data is the determination of he-licity amplitudes. Our values are mostly consistent withthose listed by the Particle Data Group. Comparison withmodel calculations show reasonable agreement but none ofthe models gives strikingly better results than the othermodels. Our values agree very well with a fit to electropro-duction data using the “Single Quark Transition Model”,Burkert el al. [6]. Acknowledgements
We would like to thank the CBELSA collaboration formany useful discussion and the GRAAL collaboration forallowing us to use their data prior to publication. We ac-knowledge financial support from the Deutsche Forschungs-gemeinschaft (DFG-TR16) and the Schweizerische Nation-alfond. The collaboration with St. Petersburg receivedfunds from DFG and RFBR.
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