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A possible quasinuclear state near the ΛΛ threshold
NUCLEAR PHYSICS A
Nuclear Physics A558 (1993) 353c-3% North-Holland, Amsterdam
A possible quasinuclear state near the h;i threshold Jaume “Institut
Carbonell”,
Konstantin
V. Protasov”
and Oleg D. Dalkarovb
des Sciences Nucldaires, 53 Av. des Martyrs,
“Lebedev Physical
Institute,
38026 Grenoble,
France
53 Leninsky pr., 117924 Moscow, Russia
Abstract Within the frame of an hermitian coupled-channels model we provide a natural explanation for the main properties of pfl --+ AA experimental data, In particular, the nearthreshold structure is shown to be produced by a narrow AA subthreshold state of quasinuclear nature. This resonance, produced in the 3SD1 partial wave, has quantum numbers Jpc = l--. The reason for the smallness of its width (few MeV) is explainend. Some experimental possibilities to find this resonance are proposed.
1. INTRODUCTION The first experimental results on the reaction p@ + Aii near the Aii threshold [l] manifested two very interesting features. First, an important P-wave contribution in all the observabies (reaction and differential cross sections, polarization). Second, although in a very preliminary stage, the reaction cross section cr(p$ --t Ali) suggested the existence of a narrow structure less than 1 MeV far from threshold. Both features have been recently confirmed in the new PS185 run [a]. The results of these two measurements are shown in Fig. 1. Several theoretical works have been devoted to this problem. They successfully describe the general behaviour of the cross sections and polarisation observables 13-81. However, up to now, none of them reproduce the nearthreshold narrow structure. Some of these works [4, 6, 71 use an optical potential to account for the annihilation process. This approach, though fruitful for fitting the scattering observables, cannot properly describe the singularities of the amplitude, namely the bound and resonant states. The reason for that lies in its non unitarity which leads to anomalous spectral properties and suppres the wavefunction in the interaction region [a, 91. In the Nijmegen calculations [5], the dynamics of the short distances is simply parametrised by a complex boundary condition at b=1.2 fm. A different approach is provided by the hermitian coupled channels models (CCM) [3, 81. The annihilation is here treated by introducing additional effective channels in a way that preserves the unitarity. In these framework the main properties of the baryonantibaryon system can be explained in terms of the singularities produced by the strong nuclear attraction [S]. In particular, the observed big P-wave contribution appears as a consequence of AI% nearthreshold P-states. Yet, these works did not account for the nearthreshold structure, which was not clearly seen in the first LEAR measurements [I]. 03759474/93/$06.00 0 1993 - Elsevier Science Publishers B.V.
All rights reserved.
354c
J. Carbonell et al. 1 Quasinuclear state near the AA threshold
-1
0
1
2
3
4
5
6
E (MeV) Figure
1. Experimental
reaction
cross section
compared
to the CCM calculations.
We will show in what follows that the hermitian CCM provides a natural of the nearthreshold structure in terms of a resonance in the AA system.
explanation
2. THE MODEL The model we have used is a small variant of that described in [S]. It consists in two interacting baryon-antibaryon (BB) c h annels, pp and AA, coupled by a I< and K* exchange potential. Each BB system is additionally coupled to an efective meson-meson annihilation channel. The masses of these effective mesons are respectively ml=760 MeV for pji and m2=890 MeV for AA. The transition potential has a Yukawa form with a dimensionless strength X and a range equal to the baryon Compton wavelength. This results into a four coupled channels problem and eigth for the tensor mixed states. The BE interaction is given by a realistic One Boson Exchange Potential regularized below some cut-off radius T,. In the pp case the potential as well as the annihilation coupling constants and cut-off radii were taken from [lo]. For the AA and pp + AA transition potentials we used-the coupling constants of (111. The coupling to others BB channels, like CC, has no influence in the considered phenomena and have been neglected. The model described has an important number of parameters. For instance, the potential in a partial wave without tensor coupling requires three cut-off radii, corresponding to the BB and transition potentials, plus two annihilation constants. Although the parameters assosciated to the pp sector have been fixed elsewhere [lo] there is a big uncertainty concerning the AA system. Accordingly, the quantitative results (differential cross sections, polarization, etc.) obtained by this and similar models cannot be considered as
1. Carbonell
et al. I Quasinuclear
state near the Ax threshold
355c
predictions but as possible a postetiori explanations of some empirical facts. Despite of that we should stress that the strong nuclear attraction is a general feacreates deeply bound states or ture of all baryon-antibaryon systems. This attraction nearthreshold resonances which manifest themselves either directly as in the AX(1515) case for pp [12], or as P-wave enhancement in the baryon-antibaryon scattering [8].
3.
RESULTS
In Fig. I _are shown the results obtained in the CCM for the reaction cross section ~(pp --+ AA). They are compared to the experimental results of PS185 group [l, 21. The full curve contains all the pjj states with L < 2 and the doted lines correspond to the separated contributions of the more relevant partial waves. The theoretical curve is in close agreement with the experimental data and reproduces the observed nearthreshold strucure. The origin of this structure is the existence of a quasinuclear state in the AA system. By switching off the different couplings, i.e. to the annihilation and pp channels, we have found a loosely bound state (E = -2.1 MeV) in the 3SD1 partial wave. The study of the wave function shows a clear dominance of its D-wave component. The couplings slightly shift and broaden this state. However, in spite of the strength of the annihilation and pp + AA transition potentials, it remains in the threshold vicinity and creates the bump in the 3SD1 partial cross section shown in Figure 1. We can get more information about this resonance below the AA threshold by studying its inlluence in the annihilation channel. In particular, through the coupling pp - K*I<* realized via the Ah potential. 1
0.8 0.6 0.4 0.2 0 -4
-3
-2
-1
0
1
2
3
4
E (MeV)
Figure 2. Resonant units)
behaviour
of the pjj -+ K*k*
annihilation
cross section
(arbitrary
In Fig, 2 we have ploted the annihilation cross section g(pjj --+ li”lr’“) in arbitrary units. The resonate is clearly manifested in this observable, displaying the classical BreitWigner form. The corresponding parameters are Eo = -‘?. MeV and lY=l.S MeV.
356~
J. Carbonell et al. I Quasinuclear state near the Ax threshold
Some preliminary investigations on the differential cross section show a small sensitivity to this resonance. The shape of u(6) was found rather stable with respect to the energy and essentially driven by P waves. A possible explanation for that is the fact that the singularity in the amplitude is located below the AA threshold and hence give no any zero in the denominator E - Eo, From a partial analysis of experimental data plotted in Figure 1, most of the theoretical works devoted to this question stressed the dominant role of P waves. Our results actually confirm this conclusion as far as the threshold vicinity is excluded. The slope of the 3PFz partial cross section is clearly in agreement wih the experimental one.
4. CONCLUSIONS The preceding results showthat it is possible to explain the nearthreshold structure by the existence of a narrow AA subthreshold state of quasinuclear nature. This resonance, produced in the 3SD1 partial wave, has quantum numbers Jpc = l--. The reason for the smallness of its width is the D-wave dominance of its wave function and the proximity of the AA threshold. Our calculations are very sensitive to the parameters of the model, specially the cut-off radius rC that determines the short range part of the potential and therefore the resonance position. However some model independent conclusions are whorthwhile. From one hand it is very difficult to reproduce such a narrow structure in a partial wave with L<2. From another hand the singlet potentials are to small in any model to create a bound state. This let no place for a big number of candidates, but the cases of 3D2 , 3Ds and higher angular momenta should be taken into account. Some experimental possibilities to find this resonance are suggested: (i) A high precision measurement of the pji 4 AA cross section and polarization observables in the region c 5 2MeV. (ii) The reaction pp -+ K*1i;* + nx below the Ah threshold, displaying the structure seen in Figure 2. (iii) If the quantum numbers are Jpc = l--, the reaction e+e- + AA should give a big value of the A electromagnetic form factor in the time-like region. (iv) The same conclusion holds for the proton form factor in the reaction e+e- + pp at AA threshold [14]. There are concret proposals to perform somez of these measurements [13]. We hope that in a near future the LEAR and ADONE (Frascati) facilities will be able to bring new lights into this challenging problem.
Acknowledgements We thank N. Hamann for its disponibility in the scientific discussions a helpful communication regarding the experimental results.
5. REFERENCES 1 R. v Frankenberg, PhD Thesis, Erlangen 1988 P.D. Barnes et al, Phys. Lett. B229 (1989) 432
and F. Stinzing
for
J. Carbonell
2
357c
F. Stinzing, PhD Thesis, Erlangen 1991 E. Klempt, Workshop on Low energy antiproton physics (Moscow, July 1991),
3 F. Tabakin,R. 4
et al. I Quasinuclear state near the AK threshold
A. Eiseinstein, Phys. Rev. C 31,5 (1985) 1857
M. Kohno and W. Weise, Phys. Rev. D 256 (1987) 659
5 R.G.E. Timmermans,Th.A.
Rijken, J.J. de Swart, Phys. Rev. D 45 (1992) 2288
6 J. Haidenbauer et al. Phys. Rev. 45 (1992) 931 7 P. La France, B. Loiseau, Nucl. Phys. A 528 (1991) 557 8 O.D. Dalkarov, K.V. Protasov, Sov. JETP Lett. 46,7 (1987) 329 O.D. Dalkarov,K.V. Protasov,I.S.Shapiro,Int. J. Mod. Phys. A 5,ll 9 J.Carbonell,O.D.Dalkarov,K.V.Protasov,I.S.Shapiro,
(1990) 2155
Nucl. Phys. A 535 (1991) 651
10 0. Dalkarov, J. Carbonell, K. V. Protasov, Sov J. Nucl. Phys. 52,6 (1990) 1052 11 M. M. Nagels,T. A. Rijken, J. J. de Swart, Phys. Rev. D 12 (1975) 744 M. M. Nagels,T. A. Rijken, J. J. de Swart, Phys. Rev. D 15 (1977) 2547 12 Asterix Collaboration, Phys. Lett. B 226,4 (1989) 450 D. Bridges et al., Phys. Rev. Lett. 57 (1986) 1534 13 Proposal to the CERN SPSLC, Preprint CERN/SPSLC
92-6
14 O.D. Dalkarov, K.V. Protasov, Phys. Lett. B 280 (1992) 117
Nuclear Physics A558 (1993) 353c-3% North-Holland, Amsterdam
A possible quasinuclear state near the h;i threshold Jaume “Institut
Carbonell”,
Konstantin
V. Protasov”
and Oleg D. Dalkarovb
des Sciences Nucldaires, 53 Av. des Martyrs,
“Lebedev Physical
Institute,
38026 Grenoble,
France
53 Leninsky pr., 117924 Moscow, Russia
Abstract Within the frame of an hermitian coupled-channels model we provide a natural explanation for the main properties of pfl --+ AA experimental data, In particular, the nearthreshold structure is shown to be produced by a narrow AA subthreshold state of quasinuclear nature. This resonance, produced in the 3SD1 partial wave, has quantum numbers Jpc = l--. The reason for the smallness of its width (few MeV) is explainend. Some experimental possibilities to find this resonance are proposed.
1. INTRODUCTION The first experimental results on the reaction p@ + Aii near the Aii threshold [l] manifested two very interesting features. First, an important P-wave contribution in all the observabies (reaction and differential cross sections, polarization). Second, although in a very preliminary stage, the reaction cross section cr(p$ --t Ali) suggested the existence of a narrow structure less than 1 MeV far from threshold. Both features have been recently confirmed in the new PS185 run [a]. The results of these two measurements are shown in Fig. 1. Several theoretical works have been devoted to this problem. They successfully describe the general behaviour of the cross sections and polarisation observables 13-81. However, up to now, none of them reproduce the nearthreshold narrow structure. Some of these works [4, 6, 71 use an optical potential to account for the annihilation process. This approach, though fruitful for fitting the scattering observables, cannot properly describe the singularities of the amplitude, namely the bound and resonant states. The reason for that lies in its non unitarity which leads to anomalous spectral properties and suppres the wavefunction in the interaction region [a, 91. In the Nijmegen calculations [5], the dynamics of the short distances is simply parametrised by a complex boundary condition at b=1.2 fm. A different approach is provided by the hermitian coupled channels models (CCM) [3, 81. The annihilation is here treated by introducing additional effective channels in a way that preserves the unitarity. In these framework the main properties of the baryonantibaryon system can be explained in terms of the singularities produced by the strong nuclear attraction [S]. In particular, the observed big P-wave contribution appears as a consequence of AI% nearthreshold P-states. Yet, these works did not account for the nearthreshold structure, which was not clearly seen in the first LEAR measurements [I]. 03759474/93/$06.00 0 1993 - Elsevier Science Publishers B.V.
All rights reserved.
354c
J. Carbonell et al. 1 Quasinuclear state near the AA threshold
-1
0
1
2
3
4
5
6
E (MeV) Figure
1. Experimental
reaction
cross section
compared
to the CCM calculations.
We will show in what follows that the hermitian CCM provides a natural of the nearthreshold structure in terms of a resonance in the AA system.
explanation
2. THE MODEL The model we have used is a small variant of that described in [S]. It consists in two interacting baryon-antibaryon (BB) c h annels, pp and AA, coupled by a I< and K* exchange potential. Each BB system is additionally coupled to an efective meson-meson annihilation channel. The masses of these effective mesons are respectively ml=760 MeV for pji and m2=890 MeV for AA. The transition potential has a Yukawa form with a dimensionless strength X and a range equal to the baryon Compton wavelength. This results into a four coupled channels problem and eigth for the tensor mixed states. The BE interaction is given by a realistic One Boson Exchange Potential regularized below some cut-off radius T,. In the pp case the potential as well as the annihilation coupling constants and cut-off radii were taken from [lo]. For the AA and pp + AA transition potentials we used-the coupling constants of (111. The coupling to others BB channels, like CC, has no influence in the considered phenomena and have been neglected. The model described has an important number of parameters. For instance, the potential in a partial wave without tensor coupling requires three cut-off radii, corresponding to the BB and transition potentials, plus two annihilation constants. Although the parameters assosciated to the pp sector have been fixed elsewhere [lo] there is a big uncertainty concerning the AA system. Accordingly, the quantitative results (differential cross sections, polarization, etc.) obtained by this and similar models cannot be considered as
1. Carbonell
et al. I Quasinuclear
state near the Ax threshold
355c
predictions but as possible a postetiori explanations of some empirical facts. Despite of that we should stress that the strong nuclear attraction is a general feacreates deeply bound states or ture of all baryon-antibaryon systems. This attraction nearthreshold resonances which manifest themselves either directly as in the AX(1515) case for pp [12], or as P-wave enhancement in the baryon-antibaryon scattering [8].
3.
RESULTS
In Fig. I _are shown the results obtained in the CCM for the reaction cross section ~(pp --+ AA). They are compared to the experimental results of PS185 group [l, 21. The full curve contains all the pjj states with L < 2 and the doted lines correspond to the separated contributions of the more relevant partial waves. The theoretical curve is in close agreement with the experimental data and reproduces the observed nearthreshold strucure. The origin of this structure is the existence of a quasinuclear state in the AA system. By switching off the different couplings, i.e. to the annihilation and pp channels, we have found a loosely bound state (E = -2.1 MeV) in the 3SD1 partial wave. The study of the wave function shows a clear dominance of its D-wave component. The couplings slightly shift and broaden this state. However, in spite of the strength of the annihilation and pp + AA transition potentials, it remains in the threshold vicinity and creates the bump in the 3SD1 partial cross section shown in Figure 1. We can get more information about this resonance below the AA threshold by studying its inlluence in the annihilation channel. In particular, through the coupling pp - K*I<* realized via the Ah potential. 1
0.8 0.6 0.4 0.2 0 -4
-3
-2
-1
0
1
2
3
4
E (MeV)
Figure 2. Resonant units)
behaviour
of the pjj -+ K*k*
annihilation
cross section
(arbitrary
In Fig, 2 we have ploted the annihilation cross section g(pjj --+ li”lr’“) in arbitrary units. The resonate is clearly manifested in this observable, displaying the classical BreitWigner form. The corresponding parameters are Eo = -‘?. MeV and lY=l.S MeV.
356~
J. Carbonell et al. I Quasinuclear state near the Ax threshold
Some preliminary investigations on the differential cross section show a small sensitivity to this resonance. The shape of u(6) was found rather stable with respect to the energy and essentially driven by P waves. A possible explanation for that is the fact that the singularity in the amplitude is located below the AA threshold and hence give no any zero in the denominator E - Eo, From a partial analysis of experimental data plotted in Figure 1, most of the theoretical works devoted to this question stressed the dominant role of P waves. Our results actually confirm this conclusion as far as the threshold vicinity is excluded. The slope of the 3PFz partial cross section is clearly in agreement wih the experimental one.
4. CONCLUSIONS The preceding results showthat it is possible to explain the nearthreshold structure by the existence of a narrow AA subthreshold state of quasinuclear nature. This resonance, produced in the 3SD1 partial wave, has quantum numbers Jpc = l--. The reason for the smallness of its width is the D-wave dominance of its wave function and the proximity of the AA threshold. Our calculations are very sensitive to the parameters of the model, specially the cut-off radius rC that determines the short range part of the potential and therefore the resonance position. However some model independent conclusions are whorthwhile. From one hand it is very difficult to reproduce such a narrow structure in a partial wave with L<2. From another hand the singlet potentials are to small in any model to create a bound state. This let no place for a big number of candidates, but the cases of 3D2 , 3Ds and higher angular momenta should be taken into account. Some experimental possibilities to find this resonance are suggested: (i) A high precision measurement of the pji 4 AA cross section and polarization observables in the region c 5 2MeV. (ii) The reaction pp -+ K*1i;* + nx below the Ah threshold, displaying the structure seen in Figure 2. (iii) If the quantum numbers are Jpc = l--, the reaction e+e- + AA should give a big value of the A electromagnetic form factor in the time-like region. (iv) The same conclusion holds for the proton form factor in the reaction e+e- + pp at AA threshold [14]. There are concret proposals to perform somez of these measurements [13]. We hope that in a near future the LEAR and ADONE (Frascati) facilities will be able to bring new lights into this challenging problem.
Acknowledgements We thank N. Hamann for its disponibility in the scientific discussions a helpful communication regarding the experimental results.
5. REFERENCES 1 R. v Frankenberg, PhD Thesis, Erlangen 1988 P.D. Barnes et al, Phys. Lett. B229 (1989) 432
and F. Stinzing
for
J. Carbonell
2
357c
F. Stinzing, PhD Thesis, Erlangen 1991 E. Klempt, Workshop on Low energy antiproton physics (Moscow, July 1991),
3 F. Tabakin,R. 4
et al. I Quasinuclear state near the AK threshold
A. Eiseinstein, Phys. Rev. C 31,5 (1985) 1857
M. Kohno and W. Weise, Phys. Rev. D 256 (1987) 659
5 R.G.E. Timmermans,Th.A.
Rijken, J.J. de Swart, Phys. Rev. D 45 (1992) 2288
6 J. Haidenbauer et al. Phys. Rev. 45 (1992) 931 7 P. La France, B. Loiseau, Nucl. Phys. A 528 (1991) 557 8 O.D. Dalkarov, K.V. Protasov, Sov. JETP Lett. 46,7 (1987) 329 O.D. Dalkarov,K.V. Protasov,I.S.Shapiro,Int. J. Mod. Phys. A 5,ll 9 J.Carbonell,O.D.Dalkarov,K.V.Protasov,I.S.Shapiro,
(1990) 2155
Nucl. Phys. A 535 (1991) 651
10 0. Dalkarov, J. Carbonell, K. V. Protasov, Sov J. Nucl. Phys. 52,6 (1990) 1052 11 M. M. Nagels,T. A. Rijken, J. J. de Swart, Phys. Rev. D 12 (1975) 744 M. M. Nagels,T. A. Rijken, J. J. de Swart, Phys. Rev. D 15 (1977) 2547 12 Asterix Collaboration, Phys. Lett. B 226,4 (1989) 450 D. Bridges et al., Phys. Rev. Lett. 57 (1986) 1534 13 Proposal to the CERN SPSLC, Preprint CERN/SPSLC
92-6
14 O.D. Dalkarov, K.V. Protasov, Phys. Lett. B 280 (1992) 117