Electromagnetic production of on the nucleon near threshold
Photo- and electroproduction of have been investigated near their production thresholds by using an effective Lagrangian approach. For this purpose, the background amplitude is constructed from suitable Feynman diagrams, whereas the resonance terms are calculated by means of the Breit-Wigner form of multipoles. Experimental data available in the proton channels ( and ) with energies up to 50 MeV above the thresholds have been utilized to extract the unknown parameters. In these proton channels the calculated observables fit nicely the experimental data, whereas in the neutron channels ( and ) the predicted observables contain some uncertainties due to the the uncertainties in the values of helicity photon couplings. To this end, new photoproduction data are urgently required. The present analysis indicates the validity of the relation derived a long time ago. In the electroproduction sector the present analysis confirms the smooth transition between photoproduction and low electroproduction data. The effect of new Crystall Ball data is shown to be mild at the backward angles. It is also found that the electroproductions of and are practically not the suitable reactions for investigating the charge form factor, since the effect is small.
pacs:13.60.Le, 25.20.Lj, 14.20.Gk
Meson photoproduction near its production threshold plays a crucial role in improving our knowledge on the strong interaction involving strangeness degree of freedom, since fewer parameters are involved and, therefore, only fewer uncertainties should be overcome at this kinematics. It is widely known that at energies where the new and precise experimental data points mostly exist there are more than 20 nucleon and 20 delta resonances listed by Particle Data Group (PDG) olive in the -channel of the reaction. There is also a number of hyperon and kaon resonances, in the - and -channel, respectively, which should be taken into account for a proper description of the kaon photoproduction process. Unfortunately, almost all of their coupling constants are hardly known and, therefore, must be treated as free parameters fitted to experimental data. As the energy increases the complexity of the problem also increases. For example, at a total center of momentum (c.m.) energy just above 2 GeV the necessity to include hadronic form factors Haberzettl:1998eq ; Davidson:2001rk ; Mart:2013yka and the phenomenon of Regge behavior seems to be inexorable Guidal:1997hy ; Mart:2003yb ; Corthals:2006nz ; DeCruz:2012bv . Clearly, such problems can be efficiently avoided by lowering the considered energy.
In the previous works I have analyzed the electromagnetic production of and off a proton for energies up to 50 MeV above the thresholds mart_thr ; mart_k0lambda . For this purpose I made use of an effective Lagrangian approach for the background terms and the Breit-Wigner form of multipoles for the resonance terms. Since the excitation energy was limited up to 50 MeV above threshold, only the state could exist in the resonance terms. However, despite this substantial simplification, there have been very few studies of kaon photoproduction devoted to the threshold region mart_thr ; mart_k0lambda ; Steininger:1996xw ; Cheoun:1996kn . This is understandable, since the corresponding theoretical analysis requires support from accurate experimental data, whereas near the threshold region the cross section tends to be significantly small. Therefore, such a study seemed to be irrelevant in the past. This situation of course changes with the operation of precise hadron detectors in modern accelerators such as CEBAF in Newport News and MAMI in Mainz.
In this paper I extend my previous analysis mart_thr ; mart_k0lambda to the four isospin channels of photoproduction, i.e. the , , , and productions. This analysis becomes part of the program for upgrading the phenomenological kaon photo- and electroproduction model, i.e. the Kaon-Maid kaon-maid . I also believe that it is important to study the processes in details, especially near the production thresholds, where a number of unknown parameters can be easily fixed and many related but important aspects can be also studied. As an example, the electromagnetic form factor of kaon has been shown to produce significant effects near the thresholds of the and channel mart_thr ; mart_k0lambda . Considering fewer uncertainties at this kinematics, my previous analyses obviously encourage investigation of the kaon charge form factors at thresholds. Furthermore, by using the method developed in igor ; arndt:2009 , small structure appearing at GeV in the polarization observable provides an important evidence of a new missing resonance or a narrow resonance mart-narrow predicted by the chiral quark soliton model diakonov .
The four isospin channels of photoproduction along with their threshold energies are given in Table 1. It is apparent that photoproduction of is similar to the photoproduction of pion-nucleon (), because it involves the production of isospin 1 and isospin 1/2 hadrons. However, the difference is also obvious, i.e. in the case of kaon (pion) the -hyperon (-meson) has isospin 1, whereas the -meson (nucleon) has isospin 1/2. Besides that, the presence of explicit strangeness in the case of kaon makes kaon photoproduction more unique than pion photoproduction.
There have been extensive discussions in the literature Kiswandhi:2011cq ; Saghai:2006ra ; Janssen:2001wk ; DeCruz:2012bv ; Ireland:2004kp ; Borasoy:2007ku ; Klempt:2009pi ; Nikonov:2007br ; anisovich_EPJA_2011 ; anisovich_EPJA_2012 ; missing-d13 ; Maxwell:2012 ; DeCruz:2011xi about strangeness photoproduction which provides a new mechanism to investigate the so-called missing resonances, i.e. the resonances predicted by quark models but not listed by the PDG olive , since it does not appear in the pion-nucleon scattering process. This is due to the fact that their decay widths are only sizable to the strangeness channels, rather than to the channels capstick94 . An example of such efforts has been performed for the channel, where a as a candidate of the missing nucleon resonance missing-d13 was concluded from an analysis of the second peak in the cross section of the photoproduction data from SAPHIR 1998 saphir98 . Note that different conclusion, however, could be drawn by using recent experimental data Janssen:2001wk . Recently, it is found that the peak originates mostly from the contribution of the , instead of the Nikonov:2007br ; mart_p13 .
Furthermore, there is an intrinsic difference between photoproductions of and , which comes from the consequence of the hyperon isospin in the final states. Since is an isovector particle, photoproduction of yields a total isospin 3/2 in the final state and, as a consequence, allows for isospin 3/2 () intermediate states in the -channel. Thus, photoproduction of would provide more information not available from photoproduction of . Although the number of resonances increases with the inclusion of resonances, the total number of resonances used in the present investigation is only four, in which only one resonance is relevant, i.e. the .
Photoproduction of was first considered more than 50 years ago in the lowest order perturbation theory by exploiting very modest information on the spin, parity, and coupling constants of both kaon and hyperon Kawaguchi . By normalizing the leading coupling constants ( and ) to unity a number of cross sections for different photon energies were calculated. At the same time, a similar calculation was also made with variation of coupling constants fujii . However, investigation of channels began more attractive only after the finding of Ref. Mart:1995wu , which showed that the available phenomenological models for the process over predict the cross section by almost two orders of magnitude. Only after including very few data in the fit, this problem can be partly alleviated. Unfortunately, the extracted leading coupling constants are too small and cannot be reconciled with the prediction of SU(3) and those extracted from the kaon scattering processes Mart:1995wu . Since most of the contributions come from the Born terms, introducing hadronic form factors in hadronic vertices of the scattering amplitude might become the suitable choice. There is a number of recipes proposed in the literature for including these form factors without destroying gauge invariance of the process Haberzettl:1998eq . In spite of significant improvements in the model, the inclusion of hadronic form factors simultaneously over-suppresses the cross section at very forward angles bydzovsky . Furthermore, different methods to suppress the excessively large Born terms also exist in the literature. For instance, Ref. janssen-sigma proposed the use of hyperon resonances, instead of hadronic form factors, to overcome the large contribution of background terms. Meanwhile, within the framework of chiral quark model (CQM), Ref. zhenping-sigma showed that the inclusion of higher-mass and spin resonances could also overcome the problem of the cross section over prediction, since the , , , and resonances have been shown to yield a minimum at GeV zhenping-sigma .
In contrast to the channel, where the problem of data consistency has been severely plagued phenomenological analyses for years Mart:2006dk ; Mart:2009nj , experimental data of the channel from SAPHIR 2004 Glander:2003jw , CLAS 2006 Bradford:2005pt , and CLAS 2010 biblap seem to be consistent. Thus, the number of available experimental data near threshold in this channel is relatively large, improving the accuracy of the present analysis.
The organization of this paper is as follows. In Sec. II I briefly present the formalism used in my analysis. In Sec. II I discuss the numerical result obtained for the photoproduction. Result for the electroproduction case is given in Sec. V. Section VI is exclusively devoted to discuss the recent MAMI electroproduction data at very low . Section IV presents the effect of the new Crystal Ball data on my calculation. In Sec. VII I briefly discuss the effect of the charge form factor on the cross sections of the and channels. I will summarize my present analysis and conclude my finding in Sec. VIII. A small portion of the result obtained in the present analysis, that uses the older PDG information pdg2010 , has been presented in conferences mart:conferences ; mart:conferences1 . In this paper I present the comprehensive result of my analysis. Furthermore, here I use the information of nucleon resonances obtained from the latest PDG report olive , which leads to a slightly different result in the extracted nucleon resonance properties as well as the calculated observables.
A complete formalism of the background and resonance amplitudes for the channel has been written in my previous paper mart_thr . For use in the four channels photoproduction, a number of modifications is needed. This includes the the isospin relation of hadronic coupling constants in the background terms Mart:1995wu , i.e.,
as well as the isospin factor
of the multipoles hanstein99 in the resonance terms, i.e.,
In the case of resonance contribution I adopt the convention of pion photo- and electroproduction hanstein99 for the physical amplitudes of the kaon photo- and electroproduction,
where and are the proton and neutron amplitudes with total isospin 1/2, respectively, whereas is the amplitude for the isospin 3/2 contribution. The formalism given by Eqs. (5)–(8) can be implemented in the calculation of CGLN amplitudes hanstein99 from the multipoles before calculating the cross section or polarization observables. Note that by limiting the energy up to 50 MeV above the production thresholds the number of electric, magnetic, and scalar multipoles are significantly limited. As a consequence, the relation between CGLN amplitudes and the multipoles can be simplified to
Since both proton and neutron channels exist in photoproduction, I obviously need the ratios between charged and neutral kaon transition moments and . The first ratio can be fixed by using the PDG values olive , whereas the second ratio can be considered as a free parameter during the fit process, because, fortunately, one of the proton channels that produces neutral kaon () has experimental data, though very limited. More detailed discussion about this topic will be given when I discuss the result of the channel in Sect. III.
Note that the electromagnetic vertices of hyperon resonances in the charged hyperon productions ( and ) are different from those in the neutral hyperon productions ( and ). Figure 1 exhibits the corresponding coupling constants for all channels. The hadronic part of coupling constants are obviously related by using Eq. (1), whereas the electromagnetic coupling depends on the charge of the hyperon. Obviously, the neutral hyperon () productions use the same coupling, while the charged hyperon () productions use the same coupling. Thus, in the fitting process one can use the ratio as a free parameter in order to distinguish the charged hyperon resonance from the neutral one.
Note that the above formalism is also valid in the case of electroproduction. To this end I use the standard electromagnetic form factors as in my previous work mart_thr ; mart_k0lambda for extension of my model to the finite region, where is the virtual photon momentum squared. As in the previous work mart_thr I do not use the hadronic form factor in the present work, because the considered energy is sufficiently low and, as a consequence, the agreement between model calculation and experimental data can be easily achieved.
|Status seen in||*||*||*||*|
As in the previous study I consider the energies from the production threshold ( MeV) up to 50 MeV above the threshold ( MeV). In this energy range there are three nucleon and one resonances in the PDG listing, i.e. the , , , and resonances. Their properties relevant to the present study are listed in Table 2. Properties of the particles as well as other parameters used in the background terms can be found in my previous work mart_thr . Due to the nature of resonance formalism used in the present study hanstein99 , the nucleon resonances with masses below the thresholds energy cannot be included as in the case of covariant formalism Mart:coupl_strength .
There are 331 experimental data points in the database, dominated by the photoproduction differential cross section biblap ; Glander:2003jw ; Bradford:2005pt ; McNabb2004 . In addition, there are also data for the electroproduction differential cross section Ambrozewicz:2006zj , photoproduction differential cross section lawall , recoil polarization biblap ; Glander:2003jw . Other data, such as from the and photoproduction measurement by LEPS collaboration sumihama06 ; kohri06 , have photon energies beyond the upper limit. Note that the number of data points in the production near threshold is larger than that in the case mart_thr (139 data points). Thus, a better statistics obtained from the present analysis could be expected.
Iii Results and Discussion
The extracted parameters from fit to 331 data points are displayed in Tables 3 and 4, where the background and resonance parameters are separated in different Tables for the sake of convenience. Note that the effect of the resonance, which was found to play important role in the photoproduction near threshold mart_thr as well as at higher photon energies Mart:2013hia , have also been investigated. In the present work it is found that the effect is almost negligible, i.e. the is reduced from 1.07 to 1.05, whereas other extracted parameters do not dramatically change after including the resonance (see Table 3). Therefore, in the following discussion the hyperon resonance will be excluded.
Table 3 indicates that contributions of the and vector mesons are relatively small, which is in contrast to the case of production mart_thr . The extracted ratio is obviously larger than that obtained in Kaon-Maid, i.e., . The extracted decreases when the hyperon resonance is included in the model (see Table 3). This issue will be discussed later in this Section.
The achieved per number of degrees of freedom is close to one, indicating that the omission of hadronic form factors in the present analysis does not lead to a serious problem as in the analyses beyond the threshold region. The extracted resonance properties shown in Table 4 do not show any dramatic deviations from the PDG values, since during the fit they were varied within the error bars given by the PDG olive .
Comparison between contributions of the background and resonance terms is displayed in Fig. 2. It is obvious from this figure that contribution of the background terms is dominant in the and channels, which can be understood as the isospin effects in the background amplitudes given by Eqs. (1) and (2). In contrast to this, the effect of resonances clearly shows up in both and channels. This phenomenon is also understood from the isospin factors in the resonances given by Eqs. (6) and (7).
Comparison between the predicted total cross sections and those from previous works Steininger:1996xw ; kaon-maid as well as experimental data Glander:2003jw ; Bradford:2005pt ; lawall is shown in Fig. 3. It is obvious that the present analysis provides a more accurate prediction in both proton channels ( and ). In the neutron channels ( and ) the cross section uncertainties are found to be relatively large as shown by the shaded area in the right panels of Fig. 3, especially at MeV, where most of the involved resonances are located. Note that all uncertainties shown in the right panels of Fig. 3 originates from the uncertainties in the neutron helicity amplitudes and given by PDG (see Table 2) olive . Thus, experimental data in both neutron channels are urgently required to reduce this uncertainty. Such experimental data could be expected from the photoproduction experiment performed by the Tohoku group which uses deuteron as a target tsukada . Nevertheless, for this purpose, higher statistics data are more recommended in order to reduce some uncertainties coming from Fermi motion in the deuteron as well as from the final-state interaction induced by the spectator nucleon. For the photoproduction off a deuteron experimental data have been available from the CLAS collaboration with photon lab energies from 1.1 GeV (almost 50 MeV above the threshold, see Table 1) up to 3.6 GeV pereira . Although the lowest energy is very close to the upper limit of the present analysis, the challenging task now is to remove the effects of initial- and final-state interactions from the data.
Comparison between the calculated differential cross section of the channel with the prediction of Kaon-Maid kaon-maid and experimental data Glander:2003jw ; Bradford:2005pt ; biblap is shown in Fig. 4. Within the existing experimental error bars the present work also provides a significant improvement to the result of Kaon-Maid, especially at and 1745 MeV. Further improvement can be also observed in the forward directions. Note that in Kaon-Maid the problem in this kinematics originates from the inclusion of hadronic form factors, that over suppresses the cross sections at forward angles bydzovsky . Therefore, the present study also emphasizes the need for a thorough investigation of the effects of including hadronic form factors on differential cross sections at forward kinematics.
Differential cross sections of the process display an interesting result. Unlike the prediction of Kaon-Maid, which is almost similar to the case, here the cross sections rise sharply in the backward directions and reach the minima at . The cross section enhancement is also detected at forward angles. The result indicates a strong -channel contribution which is solely mediated by the (since the resonances do not significantly contribute and therefore are not included in the model) as well as important contributions from the -channel intermediate states obtained from the and meson resonances.
Photoproduction of is especially important for the extraction of the ratio between the transition moments in and productions, i.e.
since there is no information available for the decay width. This is in contrast to the lower mass vector meson, the , since PDG provides the values of both and decay widths olive , which can be related to their transition strengths by means of thom
whereas its sign can be constrained by using the cloudy bag model computation by Singer and Miller sing .
In the present work the value of is found to be (see Table 3). In Kaon-Maid this value was obtained to be mart_k0lambda . The presently extracted is larger probably because the contribution of would be different for different models. The discrepancy between the two values could originate from the small number of data used in the database. In the present work the available data for the channel near threshold are merely 10 points as shown in Fig. 5, whereas Kaon-Maid used only 29 data points in its database. As shown in Ref. mart_k0lambda this ratio is required for extending the photoproduction model to include the channel. In the pseudoscalar theory it was found that variation of this ratio changes the cross section only at higher energies. However, the effect is substantially large in the case of pseudovector coupling. It is also apparent that by including the new Crystal Ball data (will be discussed in Sect. IV) a smaller ratio, i.e., , would be obtained, which is in principle approaching the value of Kaon-Maid. This happens presumably because the new Crystal Ball data are closer to the SAPHIR data, instead of the CLAS ones (See Sect. IV), whereas Kaon-Maid was fitted to the the SAPHIR data saphir98 .
In order to investigate the sensitivity of the calculated cross sections depicted in Fig. 5 to the ratio, the calculated cross sections are replotted in Fig. 6. Figure 6 shows that the cross section changes if the ratio is varied within . Obviously, sizable variations can be observed at the forward and backward angles. Nevertheless, the presently available data cannot resolve this variation. Therefore, it is urgent to measure this channel in order to improve our understanding on the photoproduction. With about error bars the experimental data would be able to constrain this ratio to vary within less than of its value. Meanwhile, photoproduction experiment has been performed off a proton target by the CLAS collaboration at JLab. Data with very high statistics have been collected and will be analyzed in the near future schumacher1 . Precise data on the channel would allow us to extract not only the ratio, but also the corresponding ratio for the vector meson. Therefore, a more stringent constraint could be also applied to both and decay widths.
Figures 7 and 8 display the predicted differential cross section of the and channels, respectively, where the prediction of Kaon-Maid is also shown for comparison. In the channel, except for the lowest energy, the predictions of both Kaon-Maid and the present work are in agreement with each other, whereas in the case of the both predictions look very different in the whole energy range. In both cases, however, the present work indicates smaller uncertainties can be obtained at energies very close to the threshold. Therefore, in both channels measurement of the cross section close to the threshold is strongly recommended to further constrain the present model. The energy dependent uncertainty exhibited by the total cross section given in Fig. 3 can be understood from the uncertainties shown in Fig. 7 and 8.
The hyperon decays to a photon and a hyperon. By analyzing the corresponding magnetic dipole () transition matrix element, which is proportional to , where and are the Pauli matrix and photon polarization vector, respectively, it can be shown that the polarization of () is related to the polarization of () through schumacher
Experimental data on and photoproduction seem to obey this relation.
As shown in the previous paper mart_thr , exhibits an inverted sine function, i.e. it has negative values near the forward angle, but changes the sign near the backward angle. Therefore, in the case of the expected polarization should display a sine function which is shown in Fig. 9, where it is obvious that the relation nicely works. The agreement of experimental data with the present work is probably not so surprising, because the data shown in Fig. 9 are included in the fitting data base. However, comparing this result with the prediction of Kaon-Maid demonstrates that the present work obeys the relation given by Eq. (17) and provides a substantial improvement in the case of recoil polarization observable .
As is pointed out in Ref. biblap , the relation between and given above seems to hold only at higher . Indeed, it is found that in certain kinematics region the relation fails to reproduce experimental data. In the present work, by comparing the solid curves in Fig. 9 and the result of my previous work (Fig. 6 of Ref. mart_thr ), I find that this relation seems to work very well near the threshold region.
In spite of the nice agreement between experimental data and the present result, Fig. 9 also indicates that more data at backward and very forward angles are desired to support the present conclusion, especially that on the relation between the and polarizations near threshold.
The polarization of in the process has been also measured with a similar technique, because decays to and lawall . However, since the energy of measurement has been averaged between threshold and GeV, the corresponding energy is obviously beyond the present interest.
Iv New Crystal Ball Data
Recently, a new measurement of the differential cross section has been performed by the Crystal Ball collaboration at MAMI with finer energy bins Jude:2013jzs . For the present work the result of this measurement increases the number of experimental data by 229 points. Since the number of data points in the database is almost doubled, the inclusion of these new data might have a significant influence on the previous result. To this end, I have refitted my previous model by including the new data. The relevant parameters obtained in this case, i.e. the photoproduction parameters, are shown in Table 5, where the result from the previous model (see Table 4) along with the corresponding PDG estimate are also displayed for comparison. Obviously, there are no dramatic changes in the parameters. Furthermore in both fits (with and without the new Crystal Ball data) the fitted parameters are still consistent with the PDG values. Since the new measurement has been performed mostly in the backward direction, the corresponding effect is clearly more apparent in this kinematics, as shown in Fig. 10. Note that the new Crystal Ball data seem to be more consistent with the SAPHIR data Glander:2003jw and, consequently, the result of including the new data at the corresponding kinematics is lowering the predicted differential cross section, approaching the prediction of Kaon-Maid kaon-maid .
V Result for Electroproduction
Experimental data for low energy kaon electroproduction were unavailable until the CLAS Ambrozewicz:2006zj and MAMI A1 collaborations patrick_EPJA published their recent measurements. Note that in the old database the lowest energy available is 1.930 GeV old-data and, therefore, they are irrelevant for the present study. Since the discussion on MAMI data will be given in details in the next section, I will only focus on the CLAS data in this section.
In the present work the dependence of the resonance multipoles is given by Mart:2007mp
where and are fitting parameters given in Table 4. Note that this parameterization is used in Maid for the higher resonances (see Eq. (47) of Ref. Drechsel:2007if ). The values of and given in Table 4 are certainly not comparable to those of Maid, because in Maid the and amplitudes have different parameterization, whereas in the present work they are the same. Nevertheless, the same trend can be observed, e.g., in the case of , where the value of tends to be large, while the value of is moderately low. In general, except for the it is found that the value of is not zero, so that the amplitudes increase from at low and monotonically decrease at higher values. This behavior for the four nucleon resonances used in the present analysis is exhibited in Fig. 11.
Unlike the old data, the latest CLAS data have been already separated in terms of the unpolarized differential cross section , the transverse one , and the longitudinal-transverse interference one . Comparison of these data with the results of present work and Kaon-Maid is shown in Fig. 12. In contrast to the prediction of Kaon-Maid, the CLAS data are remarkably much smaller, almost one order of magnitude. The over prediction of Kaon-Maid in the finite region will be discussed in the next Section, when the result of the present work is compared with the new MAMI data. The agreement of the result of the present work with the CLAS data is clearly not surprising, because the data are fitted. However, I would like to notice here that in the case of unpolarized differential cross section (top panels) the cross section shows a certain structure in the angular distribution, i.e., a peak at and a tendency to increase at backward direction. This indicates that the and channels should contain a significant longitudinal coupling in the case of electroproduction, which seems to disappear in the photoproduction case as displayed in Fig. 4. Figure 12 also exhibits that the virtual photoproduction cross section is in fact very small, much smaller than the predictions of isobar models as well as old data. Nevertheless, this is consistent with the photoproduction cross section, provided that there is no dramatic increase of the cross section in the distribution, which will be discussed in the next section.
Finally, it should also be noted that the longitudinal-transverse (LT) separation of the cross section has been also performed in Ref. Ambrozewicz:2006zj . The lowest energy available for this separation is 1.75 GeV, which is slightly beyond the upper limit of the present calculation. Nevertheless, for the sake of completeness and future separation technique the prediction of the present work along with the experimental data is exhibited in Fig. 13, where the prediction of Kaon-Maid is also shown for comparison. In general, the prediction of the present work provides a fair agreement with experimental data. Interestingly, Kaon-Maid predicts a large and forward peaking longitudinal cross section, whereas in the case of transverse cross section it shows very different behavior. It can obviously be seen that the shape of unpolarized cross section of both models shown in the upper panel of Fig. 12 clearly originates from the separated ones as reflected by Fig. 13. It is also apparent that the result of the present calculation over estimates the data near forward angles. This happens presumably because the corresponding energy is already beyond the upper limit of current study. However, at this kinematics the longitudinal cross section data have negative values, which is certainly difficult to be reproduced by the model, since by definition , where and are functions of the longitudinal CGLN amplitudes and germar . Therefore, the present calculation recommends a new analysis on the separation by imposing a new constraint on the longitudinal cross section, i.e. . Such a constraint could be expected to reduce some uncertainties in the separation technique given in Ref. Ambrozewicz:2006zj .
Vi New MAMI Data at Low
Recently, the A1 Collaboration at MAMI, Mainz, has measured the kaon electroproduction process close to the production threshold and at very low virtual photon momentum transfers, i.e. GeV patrick_EPJA . These new data is obviously of interest, because they can be expected to shed new information on the transition between photo- and electroproduction process. This transition corresponds to the longitudinal coupling in the process and therefore is very crucial for investigation of the electromagnetic form factors, especially those of kaons and hyperons for which no stable target exists.
More than a decade ago, Niculescu et al. gabi98 have measured the process and found that the longitudinal cross section at GeV is significantly large, almost as large as the transverse one . In order to reproduce these data an isobar model must dramatically increases both cross sections from photon point up to a certain value of (see Fig. 5 of Ref. triest99 ). The revised analysis mohring_2003 of the same data found that the longitudinal cross section is much smaller than the previous ones. Recent result from Jefferson Lab improves these data significantly Ambrozewicz:2006zj . However, in spite of this substantial improvement, extrapolation of the combined cross section to the photon point overshoots the experimental photoproduction data Ambrozewicz:2006zj . Furthermore, due to the detector properties, there were no data points available in the range of GeV. Thus, the problem of dramatic increase in the cross sections remained unsolved.
Although fitted to the different electroproduction data old-data , the evolution of the cross section for the channel of Kaon-Maid exhibits the same behavior. However, this situation seems to be improved after the A1 Collaboration published its result patrick_EPJA . As shown in Figs. 14 and 15 the transition between photo- and electroproduction is found to be very smooth. In fact, within their error bars the data seem to be consistent. Nevertheless, unlike the prediction of Kaon-Maid, the present calculation predicts an excellent agreement with the new MAMI data, as shown clearly in Fig. 14.
Figure 15 shows that the differential cross section just monotonically falls off as the virtual photon momentum increases from zero, in contrast to the prediction of Kaon-Maid. The latter is understandable, since it was fitted to the old data, which are scarce, have large error bars and scattered in a wide range of kinematics old-data . Thus, Fig. 15 indicates that for low energy case the longitudinal coupling in the channel is relatively small and the shape of the electroproduction cross section is practically driven by the conventional electromagnetic form factors. Obviously, more electroproduction data with the same kinematics but within the range of GeV are needed to support the present conclusion. Such experimental data will be available in the near future from MAMI collaboration patrick-private .
Vii Electromagnetic Form Factor of the Neutral Kaon
In the previous paper mart_k0lambda I have investigated the effect of charge (electromagnetic) form factor on the longitudinal differential cross section of the process. By using the the light-cone quark (LCQ) model ito1 it is found that the form factor can raise the longitudinal cross section up to 50%. In view of this promising result, it could be expected that experimental data with about 10% error-bars would be able to experimentally prove the existence of this form factor in the process and, simultaneously, to select the appropriate form factor.
Given the large effect of charge form factor on the longitudinal cross section, it is clearly of interest to investigate the effect on both and channels studied in the present work, where the neutral kaon can directly interact with the virtual photon in the -channel. For this purpose I use the same form factor models as in my previous study mart_k0lambda , i.e., the light-cone quark (LCQ) model ito1 and the quark-meson vertex (QMV) model buck ; buck1 .
The result for both and isospin channels is shown in Fig. 16. Obviously, the effect found in both cases is milder than that found in the channel mart_k0lambda , which is understandable, since the form factor in the present case is multiplied with the coupling constant. As shown in Table 3, the value of the in the present case is about 60% smaller than that of the . Furthermore, I also note that in the case of channel contribution from the background terms is significantly larger than that of the resonance terms (see Fig. 1 of Ref. mart_k0lambda ). This is not the case in both and channels (see Fig. 2). Nevertheless, it is worth to mention that in both channels there is moderate sensitivity to these form factors in the range of GeV, where the largest one (up to about 10%) originates from the LCQ model. The latter corroborates the finding of my previous work mart_k0lambda .
From the above result I could conclude that in kaon electroproduction process only the channel seems to be the most promising process for investigating the neutral kaon charge form factor. However, due to the lack of free neutron target, the channel shown in the upper panel of Fig. 16 could become another alternative for this purpose, provided that more precise experimental measurements with about 5% error bars along with a more accurate separation technique were available. Such a measurement is presumably suitable for future experiment at MAMI in Mainz.
Viii Summary and Conclusions
I have analyzed the elementary photo- and electroproduction of for all four possible isospin channels near their production thresholds. To this end I have used an isobar model based on suitable Feynman diagrams for the background terms, for which all unknown parameters such as hadronic coupling constants and electromagnetic form factor cut offs were extracted from experimental data. For the resonance terms I used the Breit-Wigner form of multipoles, in which the values of photon couplings were taken from the PDG. It is found that near the thresholds the four isospin channels of photoproduction are mostly driven by their background terms, instead of the resonance terms as in the case of photoproduction. Furthermore, in contrast to the channel, the present study indicates that the hyperon resonances do not play an important role in channels.
Whereas the result of the present calculation for the proton channels provides a nice agreement with experimental data as well as a substantial improvement of my previous work, the prediction of the present analysis for the neutron channels are plagued with large uncertainties that originate from the uncertainties in the values of helicity photon couplings given by the PDG. The present study also proves the validity of the relation between and polarizations, i.e., , at energies near thresholds.
The extracted longitudinal differential cross section from the CLAS experiment is found to be too small. This finding suggests the necessity for a new extraction method that imposes the condition that the cross section values are always positive. The new MAMI electroproduction data at very low can be nicely reproduced, although they were not included in the present analysis. These new data support the smooth transition behavior from photo- to electroproduction, which is exhibited by the present work, but not Kaon-Maid. Therefore, the large longitudinal term coming from the resonance in Kaon-Maid is not proved.
Finally, the effect of neutral kaon charge form factor on the longitudinal cross sections of and channels is found to be smaller than that obtained in the channel. Nevertheless, the channel could become an alternative process for investigation of this form factor, provided that the corresponding longitudinal cross section can be accurately extracted.
The author thanks Tom Jude and Daniel Watts for providing him with the new Crystal Ball data. Useful discussion with Igor I. Strakovsky and Reinhard Schumacher is gratefully acknowledged. This work has been partly supported by the Research-Cluster-Grant-Program of the University of Indonesia, under contract No. 1709/H2.R12/HKP.05.00/2014.
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