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the first evidence for the pentaquark hadron @xmath7 , discovered by the leps collaboration at spring-8 @xcite , was subsequently confirmed in some other experiments @xcite . however , many other experiments failed to find the @xmath7 signal ( for surveys see  @xcite ) . most of them came from the data analysis of high - statistics high - energy experiments . these null results at high energies were not so much surprising because it is natural to expect a sizable suppression in the production of the more complicated five - quark system compared to the conventional three - quark hyperons @xcite . but the state of affairs became dramatic after the recent publication of the high statistics results of the clas collaboration @xcite . the first experiment is designed to search for the @xmath0 signal in @xmath9 in direct @xmath10 interactions at relatively low photon energy , @xmath11  gev . the second one aimed to search for the @xmath0 signal in @xmath12 and @xmath13 reactions . within the experimental significance , no @xmath0 signal was observed . note however , that recently the diana collaboration confirmed a former result for @xmath0 production in @xmath14 interaction with xe nuclei @xcite . another positive , but low statistics result on @xmath0 production in @xmath15 interaction was obtained in kek  @xcite . therefore , the situation concerning the existence of the pentaquark state remains controversial . coming back to the high statistics clas experiments , one can conclude that if the @xmath0 exists , then the null result means that we do not understand the mechanism of @xmath0 photoproduction in elementary @xmath16 reactions . indeed , in all theoretical studies ( for references , see the recent review paper @xcite ) the cross section of this reaction is defined by the @xmath17 and @xmath18 exchange dynamics . in the first case , the amplitudes are proportional to the product of the @xmath0-nucleon - kaon coupling constant @xmath19 and the form factor @xmath20 , where @xmath21 are the four momenta of the baryon ( nucleon or @xmath0 ) and the kaon , respectively . one of the hadrons is far off - shell . if one uses the @xmath22 decay width ( @xmath23 ) as an input parameter , then the @xmath19 coupling is fixed , but unfortunately , there are no guiding rules for the off - shell form factors which bring some ambiguity into the theoretical predictions . for @xmath18 exchange processes the situation is even worse . in this case we do not know the @xmath24 coupling constant ( the ambiguity of its estimate is rather large @xcite ) and the `` off - shellness '' in the @xmath0- nucleon-@xmath18 vertex is much greater because of the large mass difference between @xmath18 and @xmath17 mesons . the clas null result for a finite @xmath0 decay width means large off - shell suppression of the corresponding amplitudes and small @xmath24 coupling constant . therefore , the best way to check whether the @xmath0 exists or not is to study the @xmath1 fusion reaction with a quasi - free kaon and a nucleon in the initial state . in this case the @xmath19 coupling is fixed ( for given @xmath23 ) , and there is no ambiguity with the off - shell form factor because all hadrons are on the mass shell . this situation may be realized in the reaction @xmath25 ( @xmath6 ) with the @xmath0 showing up as a peak in the @xmath26 invariant mass distribution as shown in ref . there are several conditions which can enhance this effect . first , the @xmath4 invariant mass must be close to the mass of @xmath5 . in this case , the total amplitude is the coherent sum of two amplitudes with charged and neutral kaon exchange shown in fig . [ fig:1 ] . tree level diagrams for the reaction @xmath27 . the exchange of charged and neutral kaons is shown in ( a ) and ( b ) , respectively . ] the dominance of the @xmath18 meson exchange in @xmath5 photoproduction @xcite results in a constructive interference between the two amplitudes which enhances the @xmath0 signal . second , the deuteron wave function greatly suppresses the processes with a fast moving recoil nucleon , therefore , the experiment must be able to measure an extremely slowly moving recoil ( spectator ) nucleon which participates in the @xmath28 reaction . and third , the @xmath4 pair must be knocked out in the forward direction . in this case , the momentum of the recoil kaon is small , and it can merge with the slowly moving spectator nucleon to produce a @xmath0 . the clas experiment  @xcite to search for @xmath0 was designed to study the direct @xmath29 reaction and , in principle , it does not satisfy the above conditions . thus , the @xmath0 and the outgoing neutron have finite momenta , and , therefore , the experiment has a neutron momentum cut of @xmath30  gev / c . in order to reduce the contribution of @xmath31 mesons coming from @xmath5 excitation the data analysis makes a cut on the @xmath5 mass , i.e. the @xmath4 invariant mass is outside the @xmath5 mass . it has cuts for the kaon momenta , @xmath32  ( gev / c ) , and cuts for the angles for positive and negative particles , @xmath33 and @xmath34 degrees , respectively . all these experimental conditions ( the @xmath4invariant mass , momenta and the angle cuts ) while being quite acceptable for studying the @xmath35 reaction result in a large suppression of the @xmath36 formation process in the @xmath9 reaction and reduce the ratio of @xmath0 resonance contribution ( signal ) to background ( noise ) - s / n .    in order to avoid the obvious difficulty in measuring the slowly moving recoil nucleon one has to analyze the @xmath8 $ ] missing mass distribution  @xcite . in this case , all momenta , allowed by the conservation laws participate in the process and , of course , the dominant contribution would come from slowly moving nucleons . as a result , the total cross section strongly increases . unfortunately , in this case the background processes increase roughly by a factor of two compared to the exclusive @xmath9 reaction , because both the @xmath26 and @xmath37 final states now contribute . nevertheless , even under this circumstance such experimental conditions can give a better chance to see the @xmath0 signal , in case it exists . the aim of the present paper is to extend the results of ref . @xcite for the inclusive reaction @xmath38 , where @xmath3 , towards finding favorable kinematical conditions for a manifestation of the @xmath0 signal . we are going to show that this signal is independent of the mechanism of the elementary @xmath39 reaction if the @xmath4 pair is produced in the forward hemisphere . our paper is organized as follows . in sec . ii we consider the kinematics of a @xmath40 reaction and define the observables . in sec . iii we briefly discuss the elementary @xmath41 reaction which will be used later on for estimating the resonant effect and background . sec . iv is devoted to a description of the associated @xmath42 photoproduction in @xmath43 interactions , where we discuss the most favorable kinematics for the coherent effect and the dependence of the cross section on @xmath0 spin and parity . in sec . v we discuss two dominant components of the non - resonant background : spectator and rescattering channels . in sec . vi we present our main results and give a comparison of a possible @xmath0 signal for the inclusive reaction @xmath38 with favorable kinematics and the exclusive reaction @xmath9 under the clas conditions . we show that in latter case the @xmath0 signal is weak due to the experimental conditions . the summary is given in sec . vii . in appendices a and b we show some details for the kinematics considered and the amplitudes of the elementary rescattering processes . the differential cross section of the reaction @xmath44 , where @xmath45 or @xmath37 , shown in fig .  [ fig:2 ] , reads     reaction @xmath46 . ] @xmath47}\equiv   \frac{d\sigma}{dm_x dm_y d\omega\,d\omega_{x}\,d\omega_{y } }   = \frac{1}{64\pi^2s_d}\frac{p_f}{p_i }   \frac{1}{6}\sum\limits_{nk,\lambda , m_d , m_p , m_n }   |t_{fi}^{nk}|^2\ ,   \frac{{\tilde{q}}\ , }   { 16\pi^3}\ ,   \frac{{\tilde{\bar q } } }   { 16\pi^3}.    \label{e1}\ ] ]    hereafter , we use the following notations : @xmath48 is the @xmath49 pair with mass @xmath50 , @xmath51 is the @xmath4 pair with mass @xmath52 , @xmath53 is the absolute value of the three - momentum of @xmath51 in the @xmath43 center of mass system ( c.m.s . ) , @xmath54 is the absolute value of the photon momentum in the c.m.s . , @xmath55 denotes the square of the total energy in this system , @xmath56 and @xmath57 stand for the absolute values of the @xmath17 and @xmath31 mesons momenta in the rest frames of the @xmath48 and @xmath51 systems , respectively . the indices @xmath58 correspond to the spin projections of the deuteron , outgoing proton and nucleon , respectively , @xmath59 is the photon helicity ; @xmath60 and @xmath61 are the solid angles of the directions of flight of @xmath17 and @xmath31 mesons in the rest frames of the @xmath48 , and @xmath51 systems , respectively ; @xmath62 is the solid angle of the @xmath51 system in the c.m.s . the quantization axis @xmath63 is chosen along the photon momentum , and the @xmath64 axis is perpendicular to the production plane of @xmath48 and @xmath51 pairs : @xmath65 , where @xmath66 is the three momentum of the @xmath51 system in the c.m.s . @xmath67 represents sum of the amplitudes of the resonant ( @xmath68 ) , semi - resonant ( @xmath69 ) , and non - resonant ( @xmath38 ) processes .    the invariant mass distribution @xmath70 is defined as a 6-dimensional integral @xmath71 }    \,d m_y\,d\cos\theta\,d\omega_{x }    d\omega_{y}.    \label{e2}\ ] ] in order to define the four momenta of all particles involved in the process appearing as arguments of the corresponding elementary amplitudes , we use the following incoming kinematical variables : photon 4-momentum ( laboratory system ) : @xmath72 ; deuteron 4-momentum ( laboratory system ) : @xmath73 ; invariant masses @xmath50 and @xmath52 ; the polar angle of @xmath4 pair photoproduction in the c.m.s . @xmath74 ; and the solid angles @xmath60 and @xmath61 . using these variables we now calculate all momenta in the @xmath75 c.m.s . ( for details see appendix  a ) and then , transform them to the laboratory system . that is because the deuteron wave function is only well defined in the laboratory system .    in our study we analyze the missing mass distribution in the range @xmath76 , where @xmath77 and @xmath78 in several selected regions of the invariant mass @xmath79  mev . the @xmath80 transition leads to a @xmath0 signal in the missing mass distribution . associated @xmath81 photoproduction manifests itself most clearly for @xmath82 and @xmath83 . the coherent signal must be suppressed outside of the resonance position . to analyze this situation we choose @xmath84 at the resonance position with @xmath82 and at a larger value ( @xmath85  gev ) . we also analyze the sensitivity of the @xmath0 signal to the @xmath4 pair photoproduction angle to get a maximum value for the s / n ratio . this gives the conditions for the range of integration over @xmath74 . integration over @xmath86 in eq . ( [ e2 ] ) is performed in all regions . the mechanism of @xmath88 photoproduction in @xmath89 interaction is quite complicated because many processes can contribute . in our consideration we select the channel with an intermediate excitation of @xmath5 , @xmath90 , and denote it hereafter as the `` resonant '' channel . as we will demonstrate , this process is dominant in the associated @xmath91 photoproduction at @xmath92  gev . we denote all other channels as `` non - resonant '' background . of course , this notation is rather conventional , because the @xmath88 pairs can also be produced from the virtual vector mesons , hyperon resonances other than @xmath5 , and so on . in this case the notation `` resonant '' selects just the @xmath5 resonance excitation . in this work we do not put emphasis on @xmath0 photoproduction in @xmath89 interactions because , at the considered kinematics when @xmath4 is produced in the forward direction with a fast moving proton , this channel is strongly suppressed by the deuteron wave function .    in this section all variables are given in the @xmath89 c.m.s . in this part we follow closely our previous paper @xcite and recall the main aspects of our considerations for the sake of completeness . we assume , that at low photon energies , close to threshold , the amplitude of @xmath5 excitation in the @xmath41 reaction may be described by the effective lagrangian formalism , whereas at high energies , the regge model with the @xmath18 exchange as a leading trajectory can be used . the value @xmath94  gev is chosen as the matching point between these two regimes . the tree level diagrams for @xmath95 reaction at low energies are shown in fig . [ fig:3 ] . the diagrams ( a ) , ( b ) , ( c ) and ( d ) correspond to the @xmath96 , @xmath97 , @xmath98 exchange amplitudes and the contact term , respectively , and are denoted as the born terms . the diagram ( e ) describes the @xmath96-channel @xmath18 exchange amplitude . we neglect the photon interaction within the decay vertex and restore the gauge invariance by the proper choice of the contact term . tree level diagrams for the reaction @xmath99 . ] the amplitudes of the @xmath100 and @xmath101 reactions at low energy read    [ res_ampll ] @xmath102   u_p(p)\,\varepsilon^\mu~,\\   & & { a^{\lambda^*}}_{fi}(\gamma n)=\bar u_{\lambda^*}^\sigma(p_\lambda^ * )    \left [   { { { \cal m}^s}}_{\sigma\mu } +    { { { \cal m}^t}}_{\sigma\mu}(k^ * )    \right ]   u_n(p)\ , \varepsilon^\mu~,\end{aligned}\ ] ]     the total cross section of the reaction @xmath103 as a function of the photon energy . the experimental data are taken from ref . the dot - dashed curve is a fit to this data by @xmath104b)@xmath105^{2.1}$ ] . the long - dashed curve represents the cross section for a constant amplitude . the solid curve corresponds to a solution in the low and high energy regimes . the dashed curve describes the extrapolation of the effective lagrangian model to the high energy region . see  @xcite for more details . ]    where @xmath106 , @xmath107 are the @xmath5 and nucleon spinors , respectively , and @xmath108 is the photon polarization vector . at high  energy ( @xmath109  gev ) they are replaced by the @xmath96-channel @xmath18 meson exchange amplitude with reggeized @xmath18 meson propagator . the explicit form of the transition operators @xmath110 as well as the choice of parameters are given in @xcite .    the total cross section of the reaction @xmath103 as a function of the photon energy from ref . @xcite together with available experimental data @xcite is exhibited in fig . [ fig:4 ] . similar results are obtained in refs . @xcite using slightly different approaches . the differential cross section of the reactions @xmath103 ( a ) and @xmath111 ( b ) as a function of the kaon photoproduction angle in @xmath89 c.m.s . at @xmath112 , and 2.3  gev . , title="fig : " ]   the differential cross section of the reactions @xmath103 ( a ) and @xmath111 ( b ) as a function of the kaon photoproduction angle in @xmath89 c.m.s . at @xmath112 , and 2.3  gev . , title="fig : " ]     the differential cross section for the @xmath103 @xmath113 and 3.8  gev . experimental data from ref .  @xcite . ] figure  [ fig:5 ] shows the differential cross sections for @xmath100 and @xmath101 as a function of the kaon production angle in the @xmath89 c.m.s . at different @xmath114 in the near - threshold region . the difference in shape for these two reactions at forward photoproduction angles is explained by the sizeable contribution of the born amplitudes in the @xmath115 reaction . in the @xmath10 reaction the born term ( @xmath97-channel ) is small , and the main contribution comes from the @xmath18 exchange process . at backward photoproduction the shapes and the absolute values of the cross sections for @xmath115 and @xmath10 are similar to each other , but the total cross sections for @xmath115 is larger . at @xmath116  gev it varies from 0.59 to 1.14 @xmath117b as compared with 0.27 to 1.08 @xmath117b for @xmath10 . as we will see in the next section , the dominant contribution to the associated @xmath91 photoproduction comes from the backward angle of the @xmath17 photoproduction in @xmath95 reaction . in fig . [ fig:6 ] we show the differential cross section at @xmath1182.1 and 3.8 gev together with available experimental data  @xcite . one can see that for increasing initial photon energy the cross section decreases at backward angles for the @xmath17 photoproduction . therefore , we expect that the threshold region with @xmath119  gev is most favorable for studying associated @xmath91 photoproduction which reflects the @xmath0 formation . note that a similar approach for the @xmath120 photoproduction based on the effective lagrangian formalism was recently developed by nam , hosaka , and kim @xcite . the difference to our approach consists in ( i ) a different choice of the form factors and ( ii ) a different @xmath121 coupling constant , which results in an enhancement of the born terms . in this case one gets a large constructive interference in the @xmath115 reaction and essentially a destructive interference in the @xmath10 reaction which leads to a strong suppression of the latter one . the difference in the different parameter sets may be resolved experimentally . finally , let us mention that in our approach the total sign of the @xmath5 photoproduction amplitude follows the sign of the @xmath18 exchange amplitude . thus , in the @xmath115 reaction the interference between @xmath18 exchange and born terms is constructive , i.e. their total sign coincide with the sign of the @xmath18 exchange amplitude . in the @xmath10 reaction the @xmath18 exchange is the dominant channel . but su(3 ) symmetry predicts opposite signs for the @xmath122 and @xmath123 couplings which results in opposite signs of the total amplitudes in @xmath115 and @xmath10 reactions .      in ref . @xcite we assumed that the dominant contribution to the non - resonant @xmath125 reaction comes from the virtual vector meson production ( @xmath126 ) and intermediate @xmath127 excitation ( @xmath128 ) . we believe that the vector meson contribution is under control because the mechanism of real vector meson photoproduction is well known .     the differential cross section of @xmath129 meson photoproduction based on the model of ref . data from refs . @xcite . ]    as an example , in fig . [ fig:7 ] we show the differential cross sections for @xmath129 meson photoproduction at @xmath130  gev calculated using the model of ref . @xcite together with the available experimental data . one can see that the description of this reaction is quite reasonable . next , the coupling constant of @xmath131 can be extracted from the @xmath132 decay , and the @xmath133 and @xmath134 couplings can be found from su(3 ) symmetry relations . then , the contribution to @xmath135 photoproduction from the virtual vector meson excitation may be easily evaluated . but at this moment , we have to make two comments . first , in the @xmath124 reaction the virtual vector mesons are off mass shell and , therefore , one has to introduce the corresponding form factors @xcite . the form factors , together with the vector meson propagators , strongly suppress contributions of the virtual @xmath136 and @xmath137 mesons leaving only a noticeable contribution from the @xmath129 meson which is almost on - shell because of the small decay width of the @xmath129 meson . second , in the data analysis for @xmath0 photoproduction the contribution of the @xmath129 meson can be excluded by making a corresponding `` @xmath129-meson cut '' @xcite . nevertheless , we discuss it here in order to fix other sources of @xmath135 photoproduction , having in hand only the total cross section @xmath138 of the @xmath139 reaction  @xcite . the situation with the contribution from the @xmath127 is not so transparent . at @xmath140  gev , there is some difference ( @xmath141 ) on the level of @xmath142% between the total cross section @xmath138 and the total contribution from @xmath5 and vector meson excitations . this difference increases at higher energies , because @xmath138 increases with energy , whereas the contribution from @xmath5 decreases with energy and the contribution from the @xmath129 mesons stays constant . at low energies , @xmath141 may be identified with the virtual excitation and decay of hyperons other than @xmath5 . thus for example , oh , nakayama , and lee considered contributions from @xmath143 , and @xmath144  @xcite , roberts included additionally contributions from @xmath145 and @xmath146  @xcite . in principle , one can also add contributions from @xmath147 and @xmath148 hyperons , listed in pdg  @xcite . another source of @xmath88 pair photoproduction in @xmath89 reaction is the so - called drell process @xcite where the incoming photon virtually decays into a @xmath135 pair with subsequent quasi - elastic or charge - exchange @xmath149 re - scattering . also a @xmath88 pair may be produced from the virtual decay @xmath150 with a subsequent inelastic @xmath151 transition . the total cross section of the @xmath152 reaction as a function of the photon energy . thin solid curve is the contribution of @xmath5 excitation , the dashed curve depicts the contribution of the vector mesons decay , all other sources denoted as @xmath153 are shown by the short - dashed curve . the solid curve is the sum of all processes . experimental data from ref .  @xcite . ] it is quite clear that a consistent description of all the listed background sources is well beyond the present state - of - the - art because one needs a fairly large number of poorly known strength parameters , form factors , phases etc . moreover , we need a proper description of the high energy behavior of these processes . on the other hand , in case of a large number of background sources we can assume random relative phases between them which leads to cancellations of the interference terms . also , as a first approximation one can choose the incoherent sum of the squares of the amplitudes to be a constant . this means that the energy dependence at low energies of this source of @xmath135 pairs is defined essentially by the phase space factor . our analysis of the @xmath5 photoproduction shows that this approximation works well ( see the solid and long dashed curves in fig . [ fig:4 ] at low energy ) . the value of the constant matrix element can be obtained from a comparison with experimental data for the @xmath154 reaction . in our further analysis we parameterize the amplitude of the additional contribution @xmath141 ( for the sake of a concise notation , we denote it as @xmath153 ) by the constant matrix element with @xmath155  gev@xmath156 . this parameterization , being quite reasonable at low energy with @xmath157  gev , results in a somewhat larger rise of the cross section and overestimates the data by @xmath158 at @xmath159  gev . to fit the data , we multiply @xmath160 by a correction factor @xmath161 @xmath162 with the matching point @xmath163  gev . in fig . [ fig:8 ] we show the total cross section of the @xmath152 reaction together with available experimental data  @xcite . to summarize this section we conclude , that for the elementary @xmath152 process which will be used in our analysis of the @xmath38 reaction we have selected and described explicitly the @xmath5 and vector meson ( @xmath129 meson ) excitation channels . the sum of all other possible processes is parameterized effectively by a constant matrix element . the energy dependence of this channel follows the phase space . at higher energies , @xmath164  gev , this dependence is slightly corrected . in case of @xmath165 we use the corresponding expressions for @xmath5 photoproduction in the @xmath10 reaction , keeping the @xmath166 contribution the same as in the @xmath115 reaction . now we turn to the associated @xmath81 photoproduction off the deuteron . basically , our consideration of @xmath168 is similar to that in ref . @xcite , however , we make several modifications . therefore , for completeness , we recall the main aspects of our model to fix the new points . we assume that main contribution comes from the charge and neutral @xmath17 meson exchange , shown in fig . [ fig:1 ]  ( a ) and ( b ) , respectively , and we do not discuss the diagrams with direct @xmath0 photoproduction being important at backward angles of @xmath4 pair photoproduction . in calculating the @xmath36 vertices we consider the @xmath0 decay width as an input parameter , taking @xmath169  mev  @xcite . the amplitudes of the associated @xmath170 photoproduction are expressed through the transition operators of the `` elementary '' process @xmath171 as @xmath172 where the transition operator @xmath173 defines the amplitude of @xmath5 photoproduction and uses the sum of transition operators in eqs . ( [ res_ampll]a ) and ( [ res_ampll]b ) ; @xmath174 and @xmath175 stand for the deuteron @xmath176 coupling vertex and the deuteron spinor , respectively , @xmath177 , and @xmath178 is the momentum of the exchanged kaon . we begin our consideration for the case of @xmath0 spin - parity @xmath179 . generalization and discussion of our results for another @xmath0 spin - parity is relegated to the end of this section . following refs . @xcite we assume that the dominant contribution to the loop integrals comes from their pole terms . the consideration of the regular parts with off - shell kaons needs incorporation of the corresponding off - shell form factors which brings an additional ambiguity into the model . thus , our estimate may be considered as a lower bound of the coherence effect . the pole part may be evaluated by summing all possible cuttings of the loops , as shown in fig . [ fig:9 ] . diagrammatic representation of cutting ( indicated by crosses ) the loop diagrams . ]    calculating the imaginary parts we use the following substitutions for the propagators of the on - shell particles ( cutkovsky rules  @xcite ) , shown by crosses in fig . [ fig:9 ] , @xmath180 and the identity @xmath181 with @xmath182 . we also use the standard representation of the product of the deuteron vertex function and the attached nucleon propagator through the non - relativistic deuteron wave function @xmath183 where @xmath177 , and @xmath184 is the deuteron wave function with the spin projection @xmath185 and the nucleon spin projections @xmath186 and @xmath187 . by using eqs . ( [ cut1 ] ) - ( [ cut3 ] ) , one can express the principal parts of the invariant amplitudes in eq . ( [ gamma - d1 ] ) as @xmath188 where @xmath189 is the spatial component of the corresponding 4-vectors , defined as @xmath190 and @xmath191 . indices @xmath192 and @xmath193 refer to the left and right cutting diagrams in fig . [ fig:9 ] , respectively . the function @xmath194 is the cosine of the polar angle of the internal nucleon momentum @xmath195 in a deuteron when the @xmath196 axis is along the momentum @xmath189 . @xmath197 with @xmath198 and @xmath199 . the @xmath5 photoproduction and @xmath0 decay amplitudes read @xmath200 now we have an additional cut @xmath201 , compared to ref . @xcite which suppresses the integrals in eq . ( [ gamma - d2 ] ) and reduces the values of the corresponding cross sections . the effective deuteron vertex reads @xmath202 where @xmath203 is the cosine of the polar angle of @xmath195 , @xmath204 denotes the deuteron wave function in momentum space @xmath205 normalized as @xmath206 in our calculation we use the deuteron wave function derived from the `` realistic '' paris potential . we checked that the final result does not depend on the fine details of the deuteron wave function and practically does not depend on the choice of the potential . calculating the loop integrals in eq . ( [ gamma - d2 ] ) , one has to be careful with the proper determination of the 3-momentum of @xmath195 which is the argument of the corresponding elementary amplitudes in the integrals . the azimuthal angle of @xmath195 is chosen to be zero because all momenta are in the production plane . in order to get the internal momentum @xmath195 in the laboratory system with the @xmath196 axis along the beam direction , we make the following transformation @xmath207 where @xmath208 is the polar angle of momentum @xmath209 . the differential cross section of the associated @xmath4 and @xmath49 photoproduction , integrated over the @xmath4 invariant mass in the range @xmath210  mev at @xmath211 is related to the differential cross section of the associated @xmath91 photoproduction as @xmath212 where @xmath213 is the integral over the breit - wigner @xmath214 decay distribution @xmath215 with @xmath216  mev and the branching ratio @xmath217 . the differential cross section of the coherent @xmath170 photoproduction reads @xmath218 where @xmath219 and @xmath220 are the amplitudes of the charge and neutral current exchange , respectively , depicted in fig . [ fig:1 ] . in this equation , averaging and summing over the spin projections in the initial and the final states are performed . the difference between @xmath219 and @xmath220 consists of different elementary amplitudes for the @xmath221 and @xmath222 reactions , and in an opposite sign of the @xmath223 and @xmath224 couplings which is a consequence of the zero isospin of @xmath0 . the relative sign of the amplitudes of @xmath221 and @xmath222 follows the relative sign of the @xmath225 and @xmath226 coupling constants and , according to su(3 ) predictions , is opposite . therefore , the sum of the charged and neutral @xmath17 meson exchange diagrams leads to a constructive interference between @xmath219 and @xmath220 , and an enhancement of the cross section of the associated @xmath91 photoproduction . the average momenta @xmath227 and @xmath228 in the loop diagrams shown in figs .  [ fig:9 ] ( @xmath192 ) and ( @xmath193 ) , respectively , as a function of the @xmath4 photoproduction angle . ]    in fig . [ fig:10 ] we show the average momenta @xmath229 and @xmath228 in the loop diagrams depicted in figs .  [ fig:9 ] ( @xmath192 ) and ( @xmath193 ) , respectively , as a function of the @xmath4 photoproduction angle in the c.m.s . this example corresponds to @xmath113  gev and @xmath230  gev . the definition of this averaging is given as usual , @xmath231 with @xmath232 where @xmath233 is the integrand in the loop integrals . one can see that the average momenta have a minimum at @xmath234 . near this position the corresponding amplitudes have a maximum . at large angles , mean values of @xmath235 are large and as a result , the corresponding amplitudes are very small because of the exponentially small value of the deuteron wave function at large  @xmath235 .    in fig . [ fig:11 ] we show the angular distribution of the differential cross section @xmath236 of the @xmath237 reaction at @xmath113  gev , and the missing mass @xmath238 $ ] , @xmath239  gev , and at @xmath240 and 1.62  gev in ( a ) and ( b ) , respectively .     the angular distribution of the differential cross section @xmath236 at @xmath239  gev , @xmath113  gev and @xmath240 and 1.62 ( gev ) , shown in ( a ) and ( b ) , respectively . the solid and dashed curves correspond to resonant and coherent background contributions.,title="fig : " ]   the angular distribution of the differential cross section @xmath236 at @xmath239  gev , @xmath113  gev and @xmath240 and 1.62 ( gev ) , shown in ( a ) and ( b ) , respectively . the solid and dashed curves correspond to resonant and coherent background contributions.,title="fig : " ]    the solid curves correspond to the resonance contribution , i.e. @xmath241 , while the dashed curves shows the contribution from the non - resonant @xmath242 processes depicted schematically in fig . [ fig:12 ] . +     diagrammatic representation of the associated non - resonant @xmath243 photoproduction . ]     the same as in fig . [ fig:11 ] , but for different @xmath114 . ( a ) and ( b ) correspond to the dependence on the @xmath5 photoproduction angle in the c.m.s . and the laboratory frame , respectively.,title="fig : " ]   the same as in fig . [ fig:11 ] , but for different @xmath114 . ( a ) and ( b ) correspond to the dependence on the @xmath5 photoproduction angle in the c.m.s . and the laboratory frame , respectively.,title="fig : " ] one can see , that in the @xmath5 region , where @xmath244 , the resonant cross section is about one order of magnitude larger than the contribution of the non - resonant channels discussed in the previous section . outside the resonance position , say for @xmath245  mev , the result is opposite , namely , the resonant contribution is strongly suppressed because of a small @xmath5 total decay width , and the processes with non - resonant @xmath246 transitions become dominant . in fig . [ fig:13 ] ( a ) and ( b ) we show the resonant cross section as a function of the @xmath5 photoproduction angle in the c.m.s . and the laboratory system , respectively , for several values of the photon energy . the value of the cross section at maximum and the position of the maximum depends on the energy . one can see that the @xmath0 formation in associated @xmath91 photoproduction is hardly measurable if the detector acceptance does not allow measuring the @xmath4 pairs at small angles @xmath247 . finally , let us discuss the dependence of the associated @xmath91 photoproduction on the spin and parity of the @xmath0 . the case of @xmath248 is especially attractive because the small @xmath0 decay width  @xcite has a natural explanation for this assignment of the @xmath0 spin and parity  @xcite . the effective lagrangians of the @xmath249 interactions are expressed usually in the following form  @xcite @xmath250 where @xmath251 and @xmath17 are the @xmath0 , nucleon and kaon fields , @xmath252 , and @xmath253 . for the fixed @xmath22 decay width the coupling constant @xmath19 depends on the spin and parity of @xmath0 as @xmath254}~,\end{aligned}\ ] ] where @xmath255 is the @xmath0 decay momentum . these equations result in the following relation @xmath256 where , for example for @xmath169  mev , @xmath257 . using this estimate one can expect naively that in case of @xmath258 ( @xmath259 ) the coherent @xmath91 photoproduction would be enhanced ( suppressed ) roughly by two orders of magnitude compared to the case of @xmath260 . but the real situation is far from this expectation . the matrix elements defining the @xmath0 formation are proportional to the products @xmath261 with @xmath262 where @xmath178 is the kaon momentum , @xmath263 and @xmath264 denote the spin projections of @xmath0 and nucleon , respectively . as a result , the large ( small ) value of @xmath265 is compensated by the corresponding small ( large ) value of @xmath266 . for a qualitative estimate of such a compensation let us consider the combination @xmath267 where the nucleon may be off - shell and express @xmath268 through the @xmath0 decay width @xmath269 where @xmath270 is the square of the nucleon momentum in the @xmath271 vertex . from these equations one can conclude that in case of an on - shell nucleon with @xmath272 : ( i ) @xmath268 does not depend on parity , and ( ii ) @xmath273 . the latter is the consequence of the spin factor @xmath274 in the expression for the decay width . the dependence on parity arises only for off - shell nucleons . @xmath268 increases ( decreases ) for @xmath260 and @xmath275 ( @xmath276 ) at the off - shell region with @xmath277 . the increase for @xmath278 and @xmath279 is different , because in the former case @xmath268 is defined by the interplay of suppression and enhancement factors . on average , the ratio of @xmath280 would be slightly larger than 2 .     the same as in fig . [ fig:13 ]  ( a ) , but for different @xmath0 spin and parities . @xmath113  gev and @xmath230   gev . ]    in some sense , the dependence of the amplitude of the associated @xmath91 photoproduction on spin and parity of the @xmath0 is rather similar to that of @xmath281 in our example . the diagrams with the on - shell hadrons in the @xmath0 formation vertex ( see fig .  [ fig:9 ] ( @xmath192 ) ) do not depend on @xmath0 parity , and for @xmath282 their contribution is roughly two times greater than for @xmath283 . the amplitudes with the off - shell nucleon in the @xmath0 formation vertex ( fig . [ fig:9 ] ( @xmath193 ) ) are enhanced for @xmath284 and suppressed for @xmath285 . but this off - shell modification is not so large , because the contribution of the nucleons which are far off - shell are suppressed by the deuteron wave function .    in fig . [ fig:14 ] we show the angular distribution of the differential cross section @xmath236 at @xmath239  gev , and @xmath113  gev , @xmath240 and different @xmath0 spin and parities , @xmath286 and @xmath287 . the ratio of the cross section at their maximum position for different @xmath288 reads @xmath289 this result is in agreement with our qualitative analysis , namely , the cross section for @xmath282 on average is 2.4 times greater than for @xmath283 . for @xmath260 and @xmath279 the cross sections are enhanced compared to the cases of @xmath290 and @xmath291 , respectively . now two questions arise . first , whether the associated @xmath81 photoproduction may be seen against other non - resonant processes in the resonance region with @xmath244 , and second , whether this signal is suppressed outside the resonance region and why ? to answer these questions we have to analyze the background processes . the spectator channels are depicted in fig .  [ fig:15 ] . diagrammatic representation of background spectator channels . ( a , b ) : quasi - free @xmath292 photoproduction , ( c , d ) : quasi - free non - resonant @xmath293 photoproduction . ]    contributions of these channels to the invariant mass distribution are defined by eqs . ( [ e1 ] ) and ( [ e2 ] ) , where the amplitudes are expressed via products of the amplitude of the elementary @xmath294 reactions @xmath295 and the deuteron wave function @xmath129 as @xmath296 where the deuteron wave function is defined in eq . ( [ gamma - d4 ] ) , and the index @xmath297 corresponds to the different elementary sub - processes discussed in sec . background contributions to the missing - mass distribution in the @xmath38 reaction at @xmath113  gev for quasi - free @xmath5 photoproduction , vector meson and hyperon excitations ( spectator mechanism ) , and rescattering channels shown by solid , dot - dashed , long - dashed , and dashed curves , respectively . ( a ) and ( b ) correspond to @xmath230 and 1.62 gev , respectively.,title="fig : " ] background contributions to the missing - mass distribution in the @xmath38 reaction at @xmath113  gev for quasi - free @xmath5 photoproduction , vector meson and hyperon excitations ( spectator mechanism ) , and rescattering channels shown by solid , dot - dashed , long - dashed , and dashed curves , respectively . ( a ) and ( b ) correspond to @xmath230 and 1.62 gev , respectively.,title="fig : " ]    the background contributions for the quasi - free @xmath5 photoproduction , vector meson and hyperon excitation are shown in fig . [ fig:16 ] by solid , dot - dashed , and long - dashed curves , respectively . if the @xmath4 invariant mass is close to the @xmath5 mass ( cf . [ fig:16](a ) ) the quasi - free @xmath5 photoproduction gives the dominant contribution to the background . the next important contribution comes from the @xmath153 channel , parameterized by the constant matrix element . the contribution of the vector mesons in the region where the @xmath298 $ ] missing mass is around the @xmath0 mass is rather small . indeed , it does not contribute to the @xmath10 reaction and , moreover , it is suppressed dynamically . thus , the kinematics of the associated @xmath91 photoproduction in the forward direction requires a fast @xmath31 and slow @xmath14 . in this case , the @xmath135 invariant mass is far from the @xmath129 meson mass . but the situation changes at large values of the @xmath298 $ ] missing mass . in this case the available values of @xmath135 invariant mass cover the @xmath129 meson mass region , and the contribution of the @xmath129 meson excitation becomes essential . the case when the @xmath4 invariant mass is far from the @xmath5 mass is shown in fig .  [ fig:16 ]  ( b ) . now , the quasi - free @xmath5 photoproduction is suppressed , whereas the other channels have the same order of magnitude . let us consider proton and @xmath31 meson rescattering when a @xmath4 pair is produced in the @xmath89 interaction as shown in fig . [ fig:17 ]  ( a , b ) and ( c , d ) , respectively . in principle , the @xmath299 and @xmath300 rescattering in quasi - free @xmath242 photoproduction from a deuteron must be taken into account too , but we skip them at the present stage , assuming first that such processes give a small correction to the spectator ( quasi - free photoproduction ) channels considered in the previous section and second , the cross section for elastic @xmath301 scattering is much smaller than for @xmath302 scattering  @xcite . moreover , as we will show , the dominant contribution here comes from proton rescattering and , therefore , kaon rescattering is a small part . rescattering of the proton ( a , b ) and @xmath31 meson ( c , d ) in the @xmath303 photoproduction from the deuteron . ] basically , the amplitudes of the rescattering processes are evaluated similarly to the amplitudes of the associated coherent @xmath42 or @xmath304 photoproduction considered in sect . iii , where we assumed the dominance of the imaginary part of the corresponding loop diagrams , calculated by cutting rules . but there are several new aspects : + first , the rescattered particles are outside of the production plane and , therefore now , in the loop integrals we have to integrate over the virtual nucleon momentum @xmath235 and the azimuthal angle @xmath305 . if the polar and azimuthal angles of the momentum @xmath189 are @xmath208 and @xmath306 , respectively , then the three dimensional vector of the virtual nucleon in the laboratory frame , with the @xmath196-axis along the beam direction , reads @xmath307 where @xmath308 the polar angle @xmath309 is fixed by the on - shell conditions ( cf . ( [ cosine ] ) ) @xmath310 where the four momenta @xmath311 are defined as follows . + @xmath235 rescattering : @xmath312 @xmath31 rescattering : @xmath313 were @xmath314 and @xmath53 refer to the momenta of the outgoing nucleon and the proton of the @xmath48 and @xmath51 systems , respectively . we remind the reader that the indices @xmath315 refer to the cut loops shown in fig . [ fig:9 ]  ( @xmath192 ) and ( @xmath193 ) , respectively . the @xmath316 and @xmath302 rescattering channels in @xmath38 reaction at @xmath113  gev for @xmath230 and 1.62 gev shown at ( a ) and ( b ) , respectively . , title="fig : " ] the @xmath316 and @xmath302 rescattering channels in @xmath38 reaction at @xmath113  gev for @xmath230 and 1.62 gev shown at ( a ) and ( b ) , respectively . , title="fig : " ]    to preserve the energy - momentum conservation in the loop vertices one has to be careful with the determination of the azimuthal angles @xmath306 . the corresponding expression reads @xmath317    next , one has to choose the effective amplitudes in the loop integrals . we take them as a product of the deuteron wave function , photoproduction of the @xmath318 pair in @xmath319 reaction and elastic scattering amplitudes . for the proton and @xmath31meson rescattering they read correspondingly @xmath320 where @xmath321 and @xmath264 are the spin projections of the outgoing proton and nucleon , respectively . in our calculations we use an on - shell approximation for the elastic scattering amplitudes @xmath322 and @xmath323 , taken from the experimentally measured cross sections of elastic scattering . details of the employed parameterizations are given in appendix  b.    an important point is related to the @xmath324 vertex . in our model it consists of three components : @xmath5 excitation , the vector meson contribution , and the remaining background contribution denoted above as @xmath153 . consider first the @xmath5 channel . due to the rescattering kinematics , the invariant mass of the virtual @xmath4 pair in the loop integrals covers the @xmath5 resonance region even when the invariant mass of the outgoing @xmath235 and @xmath31 meson is outside the resonance position . this results in increasing the background contribution at @xmath325 . but the situation is not so simple . since the @xmath5 has a small total decay width , @xmath326  mev , its decay length is large , @xmath327 at a @xmath5 velocity @xmath328 . in other words , the @xmath5 decays mostly outside of the deuteron . similar or even larger suppression is expected for the case of the @xmath129-meson contribution . therefore , we can simply neglect these two channels .    in fig . [ fig:18 ] we show the relative contributions of @xmath235 and @xmath31 rescattering for different channels . enhancement of the @xmath235-rescattering is explained by the difference between the cross sections for @xmath316 and @xmath302 elastic scattering .    the angular dependence of the missing mass distribution for the associated @xmath91 ( solid curve ) photoproduction and the background spectator processes ( dashed curve ) at @xmath329  gev , @xmath230  gev , and @xmath113  gev . ]    to summarize this section we conclude that at low energy , say @xmath330  gev , the dominant component of the non - resonant background comes from the quasi - free @xmath5 spectator channel , the next important contribution is composed of the @xmath153 spectator channel and @xmath316 rescattering , if the invariant mass of the @xmath4 pair is inside the @xmath5 resonance position with @xmath230  gev . outside of the @xmath5 resonance position the quasi - free @xmath5 spectator channel is strongly suppressed , whereas other channels remain on the same level    finally , let us examine the angular dependence of the spectator channel , similar to the associated @xmath91 photoproduction ( cf . figs . [ fig:13 ] and [ fig:14 ] ) . the corresponding result is shown in fig . [ fig:19 ] where we present simultaneously contributions from the associated @xmath91 photoproduction ( signal ) and from the background ( noise ) dominated by the spectator channels . the calculation is for the resonance region with @xmath329  gev , @xmath230  gev , and @xmath113  gev . we choose the case of @xmath331 . one can see that the spectator channel has a sharp peak caused by the deuteron wave function with a maximum close to the maximum for coherent @xmath91 photoproduction . at small angles the noise decreases much faster than the signal . therefore , we can conclude that the largest value for the s / n ratio is expected at extremely forward @xmath4 photoproduction angles , say @xmath332 . below , we discuss the prediction for the @xmath0 formation processes under two different conditions . the first is @xmath0 photoproduction at low energy ( @xmath330  gev ) in the inclusive @xmath38 reaction . it can be studied , for example , by leps at spring-8 and/or crystal - barrel at elsa ( bonn ) . the second is the formation @xmath0 photoproduction process in exclusive @xmath9 reaction in a wider energy interval ( @xmath11  gev ) with the experimental conditions of the clas collaboration measurement  @xcite . all calculations are made for a total @xmath0 decay width of @xmath169  mev . we calculate the missing mass distribution in the inclusive @xmath38 reaction with two cuts . the first one is the @xmath129-meson cut . we exclude all events with a @xmath135 invariant mass close to the mass of the @xmath129 meson : @xmath333  mev  @xcite . the second one is the angular cut : we keep only forward @xmath4 pair photoproduction with @xmath334 . this cut gives a maximum s / n ratio . hereafter , we define the corresponding missing mass distribution as @xmath335 , where the superscript @xmath336 indicates , conditionally , an alignment in the forward photoproduction of the @xmath4 pair . the @xmath8 $ ] missing mass distribution in the @xmath337 reaction together with the partial contributions of different background channels at @xmath230  gev and @xmath330  gev . the contributions from the @xmath0 signal , spectator and rescattering processes are shown by the thin , long dashed , and dashed curves , respectively . ( a ) and ( b ) correspond to calculations without and with the angular cut @xmath338 , respectively.,title="fig : " ]   the @xmath8 $ ] missing mass distribution in the @xmath337 reaction together with the partial contributions of different background channels at @xmath230  gev and @xmath330  gev . the contributions from the @xmath0 signal , spectator and rescattering processes are shown by the thin , long dashed , and dashed curves , respectively . ( a ) and ( b ) correspond to calculations without and with the angular cut @xmath338 , respectively.,title="fig : " ]    figure  [ fig:20 ] illustrates the effect of the angular cut in the missing mass distribution @xmath337 reaction at the @xmath5 resonance position with @xmath339 ( @xmath230  gev ) , averaging over the energy interval @xmath330  gev . here , we choose the case of @xmath331 . first of all , in the @xmath5 resonance region one can see a distinct effect of the associated @xmath91 photoproduction as a sharp @xmath0 peak against the flat non - resonant background with and without the angular cut . the angular cut increases the s / n ratio . [ fig:20 ]  ( a ) shows the missing mass distribution calculated for @xmath340 ( c.m.s . ) , whereas in fig . [ fig:20 ]  ( b ) the angular interval is limited to @xmath341 in accordance with the results in fig . [ fig:19 ] . the angular cut suppresses the cross sections of both the @xmath0 signal and the background ; it further modifies the shape of the background in such a way as to get the maximum s / n ratio at the resonance position @xmath342 . the shape modification is explained by the suppression of the quasi - free spectator channel at large invariant mass @xmath50 . when @xmath50 increases the maximum in the quasi - free background distribution , shown in fig . [ fig:19 ] ( dashed curve ) , moves towards large angles being outside of the integration region and , therefore , the contribution of this channel decreases . as a result , the angular cut creates an enhancement of the s / n ratio by about @xmath343 .     the same as in fig . [ fig:20 ]  ( b ) , but for @xmath85  gev . ] figure  [ fig:21 ] illustrates the case when the @xmath4 invariant mass is far from the @xmath5 resonance position , @xmath85  gev . now we also see some @xmath0 peak generated mainly by the associated non - resonant processes . the resonance channel is suppressed because of the small @xmath5 decay width . the background near the @xmath0 peak is dominated by the @xmath153 and rescattering channels . since now the charged and neutral @xmath17 meson exchange diagrams contribute incoherently , the ratio @xmath344 would be smaller compared to the ratio in the resonance region , @xmath345 . neglecting the rescattering channels and the background shape modification , one can get the following qualitative estimate @xmath346 the background shape modification and the rescattering channels result in decreasing @xmath344 . missing mass distribution in the @xmath337 reaction at @xmath330  gev and @xmath230  gev for different @xmath0 spin and parity : ( a ) , ( b ) , ( c ) and ( d ) correspond to the @xmath0 spin and parity @xmath347 , and @xmath348 , respectively . , title="fig : " ]   missing mass distribution in the @xmath337 reaction at @xmath330  gev and @xmath230  gev for different @xmath0 spin and parity : ( a ) , ( b ) , ( c ) and ( d ) correspond to the @xmath0 spin and parity @xmath347 , and @xmath348 , respectively . , title="fig : " ]   missing mass distribution in the @xmath337 reaction at @xmath330  gev and @xmath230  gev for different @xmath0 spin and parity : ( a ) , ( b ) , ( c ) and ( d ) correspond to the @xmath0 spin and parity @xmath347 , and @xmath348 , respectively . , title="fig : " ]   missing mass distribution in the @xmath337 reaction at @xmath330  gev and @xmath230  gev for different @xmath0 spin and parity : ( a ) , ( b ) , ( c ) and ( d ) correspond to the @xmath0 spin and parity @xmath347 , and @xmath348 , respectively . , title="fig : " ]    in fig . [ fig:22 ] we show the missing mass distribution for different @xmath0 spin and parity : @xmath349 . the signal - to - noise ratio for different @xmath288 reads @xmath350 this result is in qualitative agreement with the previous analysis of the differential invariant mass distributions ( cf . ( [ res11 ] ) ) . note that the value of the invariant mass distribution at the resonance is independent of the @xmath0 decay width . but since all experiments have a finite experimental resolution , the measured signal is smeared by the experimental resolution , and this smeared signal must depend on the value of @xmath23 .     the missing mass distribution for @xmath351 at @xmath330  gev and @xmath230  gev and for different @xmath0 spin and parity , folded with a gaussian resolution function . ]    in fig . [ fig:23 ] we show the missing mass distribution folded with a gaussian distribution function @xmath352~,\end{aligned}\ ] ] with @xmath353  mev , which imitates a finite experimental resolution . in this case , the height of the resonance peak ( s ) decreases proportional to the factor of @xmath354 therefore , in order to see this peak above the background , one needs rather good experimental resolution even assuming that the @xmath0 spin parity is @xmath279 . finally , let us estimate the total @xmath0 formation cross section in inclusive @xmath38 reactions with angle and @xmath129-meson cuts . for @xmath248 , the @xmath0 photoproduction cross section at maximum is equal to @xmath355 and this value is independent of the @xmath0 decay width . then , the total cross section for the @xmath0 signal reads @xmath356 results for other assignments of @xmath357 can be evaluated using eq . ( [ res111 ] ) . the reaction @xmath360 has been analyzed recently by the clas collaboration  @xcite . we note that this experiment was designed for studying the @xmath0 photoproduction in direct @xmath35 elementary processes . in order to enforce the @xmath0 signal the data analysis was performed with some specific cuts . for convenience , we denote those cuts together with acceptance of the clas detector as the clas experimental conditions . no sizable @xmath0 signal in the @xmath26 invariant mass distribution was observed . therefore , it seems to be interesting and important to estimate the cross section for @xmath0 formation for the condition of this experiment . if we find that the formation cross section is greater than the experimental accuracy of the clas experiment , then it indicates problems for the @xmath0 : either @xmath0 does not exist , or it does exist but the @xmath0 width is much smaller than 1  mev .     the non - resonant background structure of the @xmath26 invariant mass distribution in @xmath351 at @xmath11  gev and for clas conditions . ]    the acceptance of the clas detector allows to detect ( i ) proton and kaons with momenta greater than 0.35 and 0.25  ( gev / c ) , respectively ; ( ii ) the angles of the direction of flight of the positively and negatively charged particles are greater than 9@xmath361 and 15@xmath361 ( laboratory system ) , respectively . the data analysis was performed with + ( iii ) @xmath129-meson cut @xmath362  gev , + ( iv ) @xmath5 cut @xmath363 , + ( v ) neutron momentum cut @xmath364  gev / c . the @xmath5 cut almost kills the associated @xmath91 photoproduction shown in fig . [ fig:1 ] . `` almost '' means that at @xmath365  mev the @xmath5 signal is rather weak , but finite . nevertheless , the main contribution to the @xmath0 formation comes from the non - resonant channels shown in fig . [ fig:12 ] . the neutron momentum cut strongly reduces the spectator processes , shown in fig . [ fig:15 ] , making rescattering channels dominant . in fig . [ fig:24 ] we show the non - resonant background for @xmath26 invariant mass distribution accounting for the clas experimental conditions . one can see the dominance of the rescattering ( mainly @xmath366 rescattering ) channel . two other cuts are dangerous for the formation processes . as we have shown in sec . iv , the dominant contribution to the @xmath0 formation comes from the forward photoproduction of a @xmath4 pair with @xmath367 in laboratory system . in this case , the @xmath14 meson is a slowly moving particle . therefore , the acceptance restriction for momentum @xmath368  gev / c together with the angle limitation for the proton and @xmath31 meson reduce the cross section of @xmath0 formation . note that for the inclusive photoproduction discussed above the @xmath4 pairs are detected in the forward direction , i.e. , there are no such restrictions ( cuts ) , and any value of @xmath369 consistent with conservation laws is allowed .     the @xmath26 invariant mass distribution in @xmath351 at @xmath11  gev and for conditions ( i)-(v ) . ] [ fig:25 ] shows the @xmath26 invariant mass distribution in @xmath370 at @xmath11  gev and for clas conditions ( i ) -(v ) . for convenience , we denote this distribution as @xmath371 , where the superscript `` @xmath372 '' indicates the clas conditions . one can see some @xmath0 signal against the non - resonant background dominated by the rescattering channels . we have chosen the more favorable case of @xmath373 . however , even in this case the s / n ratio is about three times smaller compared to the case shown in fig . [ fig:20 ]  ( b ) .     left panel : missing mass distribution in inclusive @xmath337 at @xmath330  gev and the @xmath4 photoproduction angular cut ( @xmath374  ( c.m.s . ) ) and @xmath129-meson cut . right panel : @xmath26 invariant mass distribution in exclusive @xmath370 at @xmath11  gev and for clas experimental conditions(i)-(v ) . experimental data from ref .  @xcite . in both cases , @xmath375 and the @xmath0 signal is folded with a gaussian resolution function with a width of 3  mev.,title="fig : " ]   left panel : missing mass distribution in inclusive @xmath337 at @xmath330  gev and the @xmath4 photoproduction angular cut ( @xmath374  ( c.m.s . ) ) and @xmath129-meson cut . right panel : @xmath26 invariant mass distribution in exclusive @xmath370 at @xmath11  gev and for clas experimental conditions(i)-(v ) . experimental data from ref .  @xcite . in both cases , @xmath375 and the @xmath0 signal is folded with a gaussian resolution function with a width of 3  mev.,title="fig : " ]    the @xmath0 photoproduction cross section at maximum is equal to @xmath376 using this value we can evaluate the total @xmath0 formation cross section for conditions ( i)-(v ) @xmath377 in the latter case , the additional factor 2 means that only the @xmath378 decay channel is under consideration . our estimate of the @xmath0 formation cross section for the clas experiment is three times smaller than the upper bound for the @xmath0 signal ( 0.3  nb ) reported in  @xcite .    for illustration , in fig . [ fig:26 ] we exhibit simultaneously the missing mass distribution in the inclusive @xmath38 reaction , averaged over the interval @xmath330  gev with the @xmath4 photoproduction angular cut ( @xmath374  ( c.m.s . ) ) ( left panel ) and the @xmath26 invariant mass in the exclusive @xmath379 reaction for the clas experimental conditions ( i)-(v ) ( right panel ) together with the available experimental data @xcite . remember , that the @xmath26 invariant mass distribution shown in  @xcite is obtained after removing certain processes : contributions from @xmath129 meson and @xmath5 excitations , and the neutron spectator channels , because this experiment intends to search for direct @xmath0 production in the @xmath35 reaction . in our analysis of the @xmath0 formation process in the clas experiment we include all experimental conditions ( i)-(v ) . in order to be close to the conditions of the data analysis in ref . @xcite we include in the consideration the acceptance correction factor which restores the full 4-body phase space broken by the cuts ( i)-(v ) . our results with acceptance corrections are shown in fig . 26 .. ) to 0.15  nb . ] the model satisfactory describes the data at low @xmath380 and slightly underestimates them at higher invariant mass with @xmath381  gev . it is not surprising because our simple model does not pretend for detailed description of all aspects of the @xmath43 interaction in a wide interval of the photon energy . our main purpose is the analysis of @xmath0 signal - to - noise ratio at @xmath382 , where the model looks quite reasonable . for the left and right panels of fig .  26 the @xmath0 signal is folded with a gaussian resolution function with @xmath353  mev . notice , that utilizing the gaussian resolution function reduces the @xmath0 signal at the maximum position by a factor @xmath383 ( cf . ( [ res13 ] ) )  mev is rather illustrative . using eq . ( [ res13 ] ) one can easily re - estimate the amplitude of the @xmath0 signal for any value of @xmath384 . ] . from fig . [ fig:26 ]  ( right ) one can see that the effective @xmath0 signal predicted for the clas conditions ( i)-(v ) is comparable to the statistical fluctuations . therefore , absence of a bright @xmath0 signal in the clas data  @xcite does not exclude its possible manifestation under more favorable experimental conditions . in summary , we analyzed the possible manifestation of the @xmath0 formation process in inclusive @xmath38 reactions . if the @xmath0 exists , then in the @xmath8 $ ] missing mass distribution there must be a distinct @xmath0 peak . its strength depends on the @xmath0 spin and parity , and has a maximum value for @xmath331 . we found that at forward angles of the @xmath4 pair photoproduction the signal - to - noise ratio is most favorable . we also analyzed the recent results of the clas collaboration and found that the present experimental conditions are not favorable for studying the @xmath0 processes . the corresponding signal to noise ratio is small , and the @xmath0 signal is comparable to the statistical fluctuations due to the experimental acceptance .    in our model a distinct @xmath0 signal is caused by the constructive interference of the @xmath5 photoproduction from the proton and neutron in the associated @xmath91 photoproduction off the deuteron . in calculations we use relatively old data for @xmath5 photoproduction off the proton at photon energies greater than the most favorable ones for the associated @xmath91 photoproduction making a corresponding extrapolation . for a more detailed study of this effect , new high - statistics low - energy data both for @xmath385 and @xmath386 are greatly desired , especially for large kaon photoproduction angles . a similar problem concerns fixing the non - resonant background . the elementary @xmath152 cross section is very important here . in our analysis we used old data with low accuracy . it is clear that for understanding the @xmath0 formation processes one needs more accurate low - energy data for this elementary subprocess , too . however , our main results have a general character . thus , it seems more reliable to detect the @xmath0 signal in the @xmath387 fusion reaction realized in associated @xmath91 photoproduction , which may be seen in inclusive @xmath388 reaction for certain experimental conditions .    finally , we note that the @xmath0 formation reaction together with other accompanying processes considered in the present paper may be studied experimentally at the electron and photon facilities at leps of spring-8 , jlab , crystal - barrel of elsa , and graal of esrf . we appreciate many fruitful discussions with t.  nakano , and we thank d.  diakonov , h.  ejiri , m.  fujiwara , k.  hicks , a.  hosaka , t.  mibe , r.  mutou , m.  naruki , t.  sato , and k.  yazaki for useful comments . we appreciate b.  mecking for careful reading our manuscript and valuable suggestions . one of the authors ( a.i.t . ) thanks h.  enyo for offering the hospitality at riken . this work was supported by bmbf grant 06dr121 , gsi - fe . let us consider the determination of the momenta of all outgoing particles in the @xmath390 reaction at fixed input parameters defined in sec . ii in detail . the square of the total energy in the c.m.s . is @xmath391 where @xmath392 is the deuteron mass and @xmath114 is the photon energy in the laboratory system . the momenta @xmath393 and @xmath53 read @xmath394 where @xmath395 is the triangle kinematical function . the four momenta of proton and @xmath31 meson in the @xmath51 rest frame is defined by the mass @xmath52 and the solid angle @xmath61 . thus , the absolute value of the decay 3-momentum reads @xmath396 then the four momenta are defined as @xmath397 and @xmath398 respectively . note , that here the @xmath399 axis is taken along @xmath66 , and the @xmath400 axis coincides with @xmath401 . next , we boost these momenta to the c.m.s . along the @xmath402 axis as @xmath403 where @xmath404 and @xmath405 . then , we rotate the coordinate system around the @xmath64 axis by the angle @xmath74 to get the momenta in the c.m.s . with @xmath406 along the photon momentum @xmath407 @xmath408 similarly , we transform the momenta of the outgoing nucleon @xmath409 and @xmath17 meson of the @xmath48 system with obvious substitutions : @xmath410 , @xmath411 , @xmath412 , and @xmath413 . let us consider the elastic @xmath415 scattering . the amplitude is related to the differential cross section via @xmath416 where @xmath417 and @xmath418 are the three dimensional relative momenta and the proton spin projections in the initial and the final states , respectively , @xmath97 is the square of the total energy in the c.m.s . , and @xmath74 denotes the scattering angle . in our calculations we take the differential cross section from experiment @xcite , given as a function of the scattering angle in certain energy intervals . in rescattering processes , one of the incoming proton may be off - shell , and therefore , generally , @xmath419 . thus , the scattering angle is defined as @xmath420 with @xmath96 , @xmath421 and @xmath422 given as @xmath423 where @xmath178 and @xmath424 are the kaon four momenta in initial and final states , respectively , and @xmath425 is the square of the four momentum of the incoming off - shell nucleon . we use the following parameterization of the differential cross section ( in mb ) @xmath426 where @xmath427 is the kaon momentum in laboratory frame in gev / c and @xmath428 the spin dependence of the amplitude is chosen in the simplest form as @xmath429        for the differential cross section of the elastic @xmath433 scattering we use the parameterization of ref . @xcite : @xmath434 where @xmath435 , @xmath235 and @xmath436 are the proton momentum and energy in the c.m.s . , respectively . the parameters @xmath437 , and @xmath372 are listed in table . i.        99 t. nakano _ [ leps collaboration ] , phys . .  lett . * 91 * , 012002 ( 2003 ) . barmin _ et al . _ [ diana collaboration ] , phys .  atom . nucl . * 66 * , 1715 ( 2003 ) ; + s. stepanyan _ [ clas collaboration ] , phys . lett .  * 91 * , 252001 ( 2003 ) ; + v.  kubarovsky _ et al . _ [ clas collaboration ] , phys . lett .  * 92 * , 032001 ( 2004 ) ; ibid . * 92 * , 049902(e ) ( 2004 ) ; + j.  barth _ et al . _ [ saphir collaboration ] , phys . b * 572 * , 127 ( 2003 ) ; + a.e . asratyan , a.g . dolgolenko , and m.a . kubantsev , phys .  atom . nucl .  * 67 * , 682 ( 2004 ) ; + a.  airapetian _ et al . _ [ hermes collaboration ] , phys . b * 585 * , 213 ( 2004 ) ; + s.  chekanov _ et al . _ [ zeus collaboration ] , phys . b * 591 * , 7 ; + m.  abdel - 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we analyze the possibility to produce an intermediate @xmath0 via a @xmath1 formation process in @xmath2 ( @xmath3 ) reactions at some specific kinematical conditions , in which a @xmath4 pair is knocked out in the forward direction and its invariant mass is close to the mass of @xmath5 ( @xmath6 ) . 
 the @xmath7 signal may appear in the @xmath8 $ ] missing mass distribution . 
 the ratio of the signal ( cross section at the @xmath7 peak position ) to the smooth background processes varies from 0.7 to 2.5 depending on the spin and parity of @xmath0 , and it decreases correspondingly if the @xmath4 invariant mass is outside of the @xmath5-resonance region . 
 we analyze the recent clas search for the @xmath0 in the @xmath9 reaction and show that the conditions of this experiment greatly reduce the @xmath0 formation process making it difficult to extract a @xmath0 peak from the data .