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Production of η mesons in nucleon-nucleon collisions
ELSEVIER
Nuclear Physics A721 (2003) 727c-73Oc www.elsevietcom/locate/npe
Production
of q mesons in nucleon-nucleon collisions
V. Baru”, A.M. Gasparyana, J. Haidenbaue?, C. Hanharta, A.E. Kudryavtsevb and J. Spetha aInstituf fur Kernphysik, Forschungszentrum Jiihch GmbH, D-52425 Jiilich, Germany bInstitute of Theoretical and Experimentat Physics, 117259, B. Cheremushkinskaya 25, Moscow, Russia A model cahdation for the reaction NN + NNq near-threshold is presented. The 7 meson production is described by elementary rescattering processes via hlN --+ vN, with M = z, p, q and 0. Corresponding amplitudes are taken from a multi-channel mesonexchange modeI of the TN system developed by the Jiihch group. Effects of the NN interaction in the final as well as in the initial state are taken into account microscopically. I. Introduction Considerable attention has been paid to the study of meson production in nucleonnucieon (NN) collisions over the last decade or so. This developement was initiated by the arrivaal of a new accelerator generation (e.g., the IUCF Cooler at the Indiana University, CELSIUS in Uppsala or COSY at the Forschungszentrum Jfilich) which allowed not only to measure such reactions with much higher precision than before but also to carry out experiments very close to the production thresholds. Among those reactions the production of the v meson is certainIy rather interesting, especially, because the 7 production near threshold is closeIy linked with the properties of the Sii N*(1535) resonance. AIso, there is already a wealth of rather accurate data on 17meson production near threshold [l-6] providing a sensible testing ground for model eakdabions. In the present contribution we report rest&s of our investigation of 17production in NN collisions [7]. The goal is a combined theoreticaE analysis of all measured channels of the reaction NN -+ NN?, namefy pp + ppq, pn -+ pnq and pn + dv, by taking into account consistently the interaction between the nucleons in the final as well as in the initial state [S] and by utilizing a microscopic model of meson-nucleon (MN) scattering [9] for the description of the v-meson production process.
We study v-meson production in distorted wave Born approximation (DWBA). This means that the transition amplitude from the initial to the final state, Mz+s, is given by 0375-9474/@3/$ - see front matter 0 2003 Elsevier Science B.V doi:~O.l016/sO375-9474(03-)0~167-9
All rights reserved.
72%
K Bar-u et al. /Nuclear Physics A721 (2003) 727c-730~
Figure 1. Production mechanisms for the reaction NN + NNq taken into account in our model: (a) 17production via MN --+ VN rescattering; (b) direct 71production.
the expression
where AZ-+3 is the (elementary) production operator (cf. Fig. 1) and ThG and T{f are the NN reaction amplitudes in the initial and final states. The production amplitude A2+3 consists of re-scattering diagrams with 7r, p, n, and c meson exchanges (Fig. la) plus the direct 77emission (Fig. lb). One of the principal novelties of our study is the utilization of a realistic microscopic model for the elementary reaction amplitudes MN + nN entering in AZ-+3 (Fig. la), namely a coupled-channels model for TN scattering that has been developed recently by the Jiilich group [9]. The interactions in and between the various channels (TN, qN, pN, aN, and 7rA) are derived in the meson-exchange picture starting out from effective chiral Lagrangians. The model includes the N*(1535) resonance as essential contribution but in addition also various (t-channel) meson and (uchannel) baryon exchange diagrams. The parameters of the model are fixed by requiring a simultaneous description of the TN phase shifts and inelasticities as well as of the transition cross sections for the reactions TN + VN and TN --+ pN over an energy range that extends well beyond the 7N threshold. The reaction amplitudes are obtained from solving a coupled-channels relativistic scattering equation of Lippmann-Schwinger type. Clearly, in such a model not only the TN -+ VN amplitude is determined by empirical data, but also the transition amplitudes involving heavier mesons are to a large extend constrained by the phase shifts and inelasticity parameters of rrN scattering. This is also true for the relative phases between the various amplitudes. Another merit of our model study of 71production in NN collisions consists in the full and consistent treatment of effects from the NN FSI as well as IS1 by employing an NN model that describes the relevant NN phase shifts reasonably well up to energies around the 77production threshold [7,8]. We focus on the description of q-meson production in the near-threshold region, i.e. for excess energies Q up to around 50 MeV. Therefore, we restrict our investigation to S-wave contributions.
FTBaru et al. /Nuclear Physics A721 (2003) 727c-730~
729~
100
10
! -P D
_<-**----;-----I I ,I-_--. .C.lm m .cnhnB . .COSY.,, ccsvl, I_ --L._
10
B ci
0.1
0.01
0
IO
20
xl
40
50
1
0
0 [Mev]
Figure 2. Total cross sections of the reactions pp + ppr] (top), pn + pnn (middle) and pn + drl (bottom). The dashed lines represent the results of our calculation with the original MN model of Ref. [9], whereas the solid lines are based on the extended MN model described in the text. Data are taken from Refs. [l-6].
3. Results
Results for the reactions pp -+ ppq, pn -+ pnq and pn --t dq are presented in Fig. 2 and compared with empirical information from the Uppsala/Celsius [l-4] and Jiilich/COSY [5,6] accelerator facilities. The dashed curves correspond to the calculation based on the original Jiilich MN model [9] for the elementary v-production amplitude and the CCF NN model [g] for the IS1 and FSI. Evidently, the calculation based on the Jiilich MN model [9] yields a qualitative overall description of the experimental data. This has to be certainly considered as success because there are no adjustible parameters in our calculation of NN + NNv. As one can observe from Fig. 2, for the ppq case we overestimate the cross section by approximately 30% whereas for pn -+ pnq the model calculation underestimates the experimental data by about 50%. The situation for pn + dq is very similar to pn + pnq since both processes are governed by the I = 0 isospin channel. As is known from earlier investigations [lO,ll] for the latter reaction the contribution of the I = 1 channel is much smaller than the one
J! Barn et al. /Nuclear Physics A721 (2003) 727c-730~
73oc
for I = 0. It is interesting to investigate the sensitivity of our results to the MN amplitude and, in particular, to see whether the model predictions for NN -+ NNq can be improved by modifications in the MN model. Here specifically the pN + VN transition amplitude is of interest because (i) in the original model [9] no direct pN -+ QN transition potential at all was included and (ii) this particular transition amplitude plays a rather crucial role in the analysis of the reaction NN + NNq by FBldt and Wilkin [lo]. For this purpose we have created a variant of the MN model where we explicitly include a coupling of the pN channel to the VN channel via the Sri N*(1535) resonance, cf. Ref. [7] for details. Varying the bare coupling constants (gpNN., etc.) we explored the variation in the amplitude for pN + YIN while staying as close as possible to the experimental phase shift and inelasticity of the $1 RN partial wave and the TN -+ qN transition cross section produced by the original model. Thereby it turned out that there is not much room for variations within our MN model. Obviously, the requirement of reproducing the TN phase shifts as well as the TN --t 7N transition cross section constrains also other transition amplitudes of the various coupled channels to a large extent. In particular, the magnitude of the amplitudes is basically fixed. Only the relative phase between the T-matrices could be changed within certain limits. For the original MN model the amplitudes of the Rand pexchange contributions to 71 production turned out to be almost orthogonal to each other. Thus, there is practically no interference between these contributions. The additional diagrams which we introduced into the MN model allow a slight modification of the orientation of these amplitudes and, as a consequence, now interference effects do occur. Specifically, it is possible to generate a destructive interference in the isotriplet channel (I = 1) and a constructive interference in the I = 0 case. This leads to a slight reduction of the cross section in the reaction pp + ppn7and to a significant enhancement for pra -+ pn~, cf. the solid lines in Figs. 2, bringing now the results quite close to the experiment. Also the prediction for the reaction pn + dq is now in good agreement with the experimental data. Further details and results of our model calculation for NN + NNq can be found in Ref. [7] REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
H. C&n et al., Phys. Lett. B 366 (1996) 366. H. CalCn et al., Phys. Rev. Lett. 79 (1997) 2642. H. Cal& et al., Phys. Rev. Lett. 80 (1998) 2069. H. Calen et al., Phys. Rev. C 58 (1998) 2667. J. Smyrski et al., Phys. Lett. B474 2000) 182. P. Moskal et al., ?rN Newsletter 16 (2002) 367. V. Baru et al., in preparation. J. Haidenbauer, K. Holinde, and M.B. Johnson, Phys. Rev. C 48 (1993) 2190. 0. Krehl, C. Hanhart, S. Krewald, and,J. Speth, Phys. Rev. C 62 (2000) 025207. G. Fiildt and C. Wiikin, Phys. Ser. 84 (2001) 427. K. Nakayama, J. Speth, and T.-S. H. Lee, Phys. Rev. C 65 (2002) 045210.
Nuclear Physics A721 (2003) 727c-73Oc www.elsevietcom/locate/npe
Production
of q mesons in nucleon-nucleon collisions
V. Baru”, A.M. Gasparyana, J. Haidenbaue?, C. Hanharta, A.E. Kudryavtsevb and J. Spetha aInstituf fur Kernphysik, Forschungszentrum Jiihch GmbH, D-52425 Jiilich, Germany bInstitute of Theoretical and Experimentat Physics, 117259, B. Cheremushkinskaya 25, Moscow, Russia A model cahdation for the reaction NN + NNq near-threshold is presented. The 7 meson production is described by elementary rescattering processes via hlN --+ vN, with M = z, p, q and 0. Corresponding amplitudes are taken from a multi-channel mesonexchange modeI of the TN system developed by the Jiihch group. Effects of the NN interaction in the final as well as in the initial state are taken into account microscopically. I. Introduction Considerable attention has been paid to the study of meson production in nucleonnucieon (NN) collisions over the last decade or so. This developement was initiated by the arrivaal of a new accelerator generation (e.g., the IUCF Cooler at the Indiana University, CELSIUS in Uppsala or COSY at the Forschungszentrum Jfilich) which allowed not only to measure such reactions with much higher precision than before but also to carry out experiments very close to the production thresholds. Among those reactions the production of the v meson is certainIy rather interesting, especially, because the 7 production near threshold is closeIy linked with the properties of the Sii N*(1535) resonance. AIso, there is already a wealth of rather accurate data on 17meson production near threshold [l-6] providing a sensible testing ground for model eakdabions. In the present contribution we report rest&s of our investigation of 17production in NN collisions [7]. The goal is a combined theoreticaE analysis of all measured channels of the reaction NN -+ NN?, namefy pp + ppq, pn -+ pnq and pn + dv, by taking into account consistently the interaction between the nucleons in the final as well as in the initial state [S] and by utilizing a microscopic model of meson-nucleon (MN) scattering [9] for the description of the v-meson production process.
We study v-meson production in distorted wave Born approximation (DWBA). This means that the transition amplitude from the initial to the final state, Mz+s, is given by 0375-9474/@3/$ - see front matter 0 2003 Elsevier Science B.V doi:~O.l016/sO375-9474(03-)0~167-9
All rights reserved.
72%
K Bar-u et al. /Nuclear Physics A721 (2003) 727c-730~
Figure 1. Production mechanisms for the reaction NN + NNq taken into account in our model: (a) 17production via MN --+ VN rescattering; (b) direct 71production.
the expression
where AZ-+3 is the (elementary) production operator (cf. Fig. 1) and ThG and T{f are the NN reaction amplitudes in the initial and final states. The production amplitude A2+3 consists of re-scattering diagrams with 7r, p, n, and c meson exchanges (Fig. la) plus the direct 77emission (Fig. lb). One of the principal novelties of our study is the utilization of a realistic microscopic model for the elementary reaction amplitudes MN + nN entering in AZ-+3 (Fig. la), namely a coupled-channels model for TN scattering that has been developed recently by the Jiilich group [9]. The interactions in and between the various channels (TN, qN, pN, aN, and 7rA) are derived in the meson-exchange picture starting out from effective chiral Lagrangians. The model includes the N*(1535) resonance as essential contribution but in addition also various (t-channel) meson and (uchannel) baryon exchange diagrams. The parameters of the model are fixed by requiring a simultaneous description of the TN phase shifts and inelasticities as well as of the transition cross sections for the reactions TN + VN and TN --+ pN over an energy range that extends well beyond the 7N threshold. The reaction amplitudes are obtained from solving a coupled-channels relativistic scattering equation of Lippmann-Schwinger type. Clearly, in such a model not only the TN -+ VN amplitude is determined by empirical data, but also the transition amplitudes involving heavier mesons are to a large extend constrained by the phase shifts and inelasticity parameters of rrN scattering. This is also true for the relative phases between the various amplitudes. Another merit of our model study of 71production in NN collisions consists in the full and consistent treatment of effects from the NN FSI as well as IS1 by employing an NN model that describes the relevant NN phase shifts reasonably well up to energies around the 77production threshold [7,8]. We focus on the description of q-meson production in the near-threshold region, i.e. for excess energies Q up to around 50 MeV. Therefore, we restrict our investigation to S-wave contributions.
FTBaru et al. /Nuclear Physics A721 (2003) 727c-730~
729~
100
10
! -P D
_<-**----;-----I I ,I-_--. .C.lm m .cnhnB . .COSY.,, ccsvl, I_ --L._
10
B ci
0.1
0.01
0
IO
20
xl
40
50
1
0
0 [Mev]
Figure 2. Total cross sections of the reactions pp + ppr] (top), pn + pnn (middle) and pn + drl (bottom). The dashed lines represent the results of our calculation with the original MN model of Ref. [9], whereas the solid lines are based on the extended MN model described in the text. Data are taken from Refs. [l-6].
3. Results
Results for the reactions pp -+ ppq, pn -+ pnq and pn --t dq are presented in Fig. 2 and compared with empirical information from the Uppsala/Celsius [l-4] and Jiilich/COSY [5,6] accelerator facilities. The dashed curves correspond to the calculation based on the original Jiilich MN model [9] for the elementary v-production amplitude and the CCF NN model [g] for the IS1 and FSI. Evidently, the calculation based on the Jiilich MN model [9] yields a qualitative overall description of the experimental data. This has to be certainly considered as success because there are no adjustible parameters in our calculation of NN + NNv. As one can observe from Fig. 2, for the ppq case we overestimate the cross section by approximately 30% whereas for pn -+ pnq the model calculation underestimates the experimental data by about 50%. The situation for pn + dq is very similar to pn + pnq since both processes are governed by the I = 0 isospin channel. As is known from earlier investigations [lO,ll] for the latter reaction the contribution of the I = 1 channel is much smaller than the one
J! Barn et al. /Nuclear Physics A721 (2003) 727c-730~
73oc
for I = 0. It is interesting to investigate the sensitivity of our results to the MN amplitude and, in particular, to see whether the model predictions for NN -+ NNq can be improved by modifications in the MN model. Here specifically the pN + VN transition amplitude is of interest because (i) in the original model [9] no direct pN -+ QN transition potential at all was included and (ii) this particular transition amplitude plays a rather crucial role in the analysis of the reaction NN + NNq by FBldt and Wilkin [lo]. For this purpose we have created a variant of the MN model where we explicitly include a coupling of the pN channel to the VN channel via the Sri N*(1535) resonance, cf. Ref. [7] for details. Varying the bare coupling constants (gpNN., etc.) we explored the variation in the amplitude for pN + YIN while staying as close as possible to the experimental phase shift and inelasticity of the $1 RN partial wave and the TN -+ qN transition cross section produced by the original model. Thereby it turned out that there is not much room for variations within our MN model. Obviously, the requirement of reproducing the TN phase shifts as well as the TN --t 7N transition cross section constrains also other transition amplitudes of the various coupled channels to a large extent. In particular, the magnitude of the amplitudes is basically fixed. Only the relative phase between the T-matrices could be changed within certain limits. For the original MN model the amplitudes of the Rand pexchange contributions to 71 production turned out to be almost orthogonal to each other. Thus, there is practically no interference between these contributions. The additional diagrams which we introduced into the MN model allow a slight modification of the orientation of these amplitudes and, as a consequence, now interference effects do occur. Specifically, it is possible to generate a destructive interference in the isotriplet channel (I = 1) and a constructive interference in the I = 0 case. This leads to a slight reduction of the cross section in the reaction pp + ppn7and to a significant enhancement for pra -+ pn~, cf. the solid lines in Figs. 2, bringing now the results quite close to the experiment. Also the prediction for the reaction pn + dq is now in good agreement with the experimental data. Further details and results of our model calculation for NN + NNq can be found in Ref. [7] REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
H. C&n et al., Phys. Lett. B 366 (1996) 366. H. CalCn et al., Phys. Rev. Lett. 79 (1997) 2642. H. Cal& et al., Phys. Rev. Lett. 80 (1998) 2069. H. Calen et al., Phys. Rev. C 58 (1998) 2667. J. Smyrski et al., Phys. Lett. B474 2000) 182. P. Moskal et al., ?rN Newsletter 16 (2002) 367. V. Baru et al., in preparation. J. Haidenbauer, K. Holinde, and M.B. Johnson, Phys. Rev. C 48 (1993) 2190. 0. Krehl, C. Hanhart, S. Krewald, and,J. Speth, Phys. Rev. C 62 (2000) 025207. G. Fiildt and C. Wiikin, Phys. Ser. 84 (2001) 427. K. Nakayama, J. Speth, and T.-S. H. Lee, Phys. Rev. C 65 (2002) 045210.