On a possible nearthreshold ΛΛ state

Physics Letters B 306 (1993) 407-410 North-Holland

PHYSICS LETTERS B

On a possible nearthreshold AA state J. C a r b o n e l l , K . V . P r o t a s o v Instttut des Sciences Nuclkatres, 53 Av. des Martyrs, 38026 Grenoble, France

and O.D. Dalkarov Lebedev Physical Instltute, 53 Lemnsky pr., 117924 Moscow, Russtan Federation

Received 27 March 1993 Editor: L. Montanet

The behavaour of the pff ~ AA reaction cross section near the AA threshold 1s described within a hermitian coupledchannels approach. The observed structure is shown to be caused by a narrow AN subthreshold state of quasinuclear nature. This resonance with quantum numbers j P c = 1 - - is produced in the 3SD1 partial wave and has a width of a few MeV. The physical reasons for the smallness of its w~dth are explmned. Other experimental poss~bihties to find this resonance are proposed.

1. Introduction

The first experimental data on the reaction p ~ A A near the A A threshold [ 1 ] manifested two very interesting features. First, an important P-wave contribution in all the observables which manifests itself as a r a p i d growth of the reaction cross section, big angular anisotropy and large polarization signals. Second, although in a very preliminary stage, the reaction cross section a (pp ~ A A ) suggested the existence of a narrow structure less than 1 MeV from threshold. Both features have been recently confirmed in the new PS185 run [2,3]. Several theoretical works were devoted to the description o f these experimental data. They successfully reproduce the general behavlour o f the observables [4-11 ], but none o f them account for the nearthreshold narrow structure in question. Some o f these works [5,7,8] used an optical potential to take into account the annihilation processes. This approach, though frmtful for fitting the scattermg observables, cannot properly describe the singularities o f the amplitude. Its non-unitarlty leads to anomalous spectral properties, namely b o u n d and res-

onant states, and suppresses the wavefunction in the interaction region [ 11,12 ]. A different approach is given by the hermitian coupled channels models (CCM) [4,11 ], where the annihilation is treated by introducing additional effective channels in a way that preserves the unitarity. In this approach, the main properties o f the b a r y o n antibaryon system are shown to be governed by the b o u n d and resonant states produced by the strong nuclear attraction [ 11 ]. In particular, the observed big P-wave contribution appears as a consequence of A A nearthreshold P-resonances. Yet, these works did not account for the nearthreshold structure, which was not clearly seen in the first LEAR measurements [ 1 ]. The aim of this article is to show that the hermitlan CCM describes the p ~ -+ A A cross section and provides a natural interpretation o f the nearthreshold structure in terms o f a AA resonant state.

2. The model

The model used here is a variant o f that described in [11 ]. It consists o f two b a r y o n - a n t i b a r y o n ( B B )

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m

channels, p ~ and A A , coupled by a K and K* exchange potential. Each B B system is additionally coupled to an effective m e s o n - m e s o n annihilation channel. The transition annihilation potential has a Yukawa form with a dimensionless strength 2 and a range equal to the baryon C o m p t o n wavelength. This results into a four coupled channels problem and an eight coupled channel for the states with tensor mixing. The B B interaction is given by a realistic One Boson Exchange Potential regularized below some cutoff radius rc by a smooth function. The meson contents and coupling constants for the p g nuclear potential were taken from [ 13 ], whereas for the AN and p-fi ~ A A potentials we used those given in [ 14 ]. We d i d not consider here the coupling to others B B channels, like S S [ 15 ], for its influence in the considered kinematical region is supposed to be negligible. Our model contains two kinds o f unavoidable parameters: cut-off radii o f the OBE potentials (re) and annihilation strengths (2). These quantities are considered as fitting parameters. F o r the p g system they were determined in [16], where the low energy p ~ data was described. F o r the A A and p-ff --, A A potentials the existing experimental data are not enough to fix them. Thus, the set o f parameters chosen in our calculations is not unique. The only exception is the cut-off radius in the A A 3D 1 potential, which determines the spectral properties o f this partial amplitude and is responsible for the structure in the cross section. We should emphasize however that the existence o f this kind o f states is a consequence of the strong nuclear attraction, a general feature of all b a r y o n - a n t i b a r y o n systems. This attraction creates deeply botind and nearthreshold resonant states which manifest themselves either directly as in the case o f A X ( 1 5 6 5 ) (also cited as J~(1520)) or ~(1480) for a n t i p r o t o n - n u c l e o n [ 17 ], or as P-wave enhancement in the b a r y o n - a n t i b a r y o n nearthreshold interaction [11].

3. Results In fig. 1 the results obtained with the CCM for the reaction cross section a (PP -~ AA) are shown. They are compared to the experimental results o f PS185 group [ 1,21. 408

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e [MeV) Fig. 1. Experimental reaction cross section compared to the CCM calculations. The dashed-dotted line show the partial contribution of 3SDI and P states.

F r o m a partial analysis of experimental data plotted in fig. 1, most o f the theoretical works devoted to this question stressed the d o m i n a n t role of P waves. Our results actually confirm this conclusion as far as the threshold vicinity is excluded. The full curve contains the contribution of all the pfi states with L ~< 2. The dotted line corresponds to the separated contribution of the P and 3SD1 partial waves. The theoretical curve IS in close agreement with the experimental data and reproduces the observed nearthreshold structure. The origin o f this structure is the presence o f a quaslnuclear state in the A A system. By switching off the annihilation and the coupling to p ~ system, we have found a loosely b o u n d state (e = - 2 . 1 MeV) in the 3SD1 partial wave. The excess energy is defined as usual by e = x/s - 2mA, where s is the CMS energy and mA the A-mass. The S- and D- components o f its radial wave function, together with the probability density (p) are presented in fig. 2. The dominance of the D-wave component (96% o f the total n o r m ) is clearly seen. The RMS radius of this state is 1.3 fm, a large value compared to the interaction range in the AA system. The reasons for this are the importance of the centrifugal barrier in the d o m i n a n t D-wave contribution and, as in the deuteron case, the small binding energy. The couplings to other channels shift and broaden

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PHYSICS LETTERS B

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3 June 1993

of d a / d O appears to be rather stable with respect to the energy and essentially driven by P waves. A possible explanation for this is the fact that the singularity in the amplitude is located below the A A threshold and hence gives no any zero In the Brelt-Wigner denominator e - e0.

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Fig. 2. S and D wavefunction components and total probability density (p) of the nearthreshold 3SD1 bound state (e = -2.1 MeV). this state. However, in spite of the strength of the annihilation and p ~ -+ AA transition potentials, it remains in the threshold vicinity and creates the b u m p in the 3SD1 partial cross section shown in fig. 1. Additional information about this resonance below the AA threshold is obtained by looking at the AA annihilahon channels There, the state displays a classical Brelt-Wigner behavlou'r with parameters e0 = - 2.0 MeV and F = 1.8 MeV [18]. The smallness of the width as well as the negligible shift of the position are a consequence of its large RMS radius. We can estimate the contribution of this resonance into the p-fi --+ K K n n cross section. Our calculations give 0.2 m b for the cross section p ~ --+ AA(3SD1resonance) ~ all A A annihilation channels. If the AA annihilation is analogous to ,the N N one, i.e. BR(AA ~ K K n n ) ~ B R ( N N -+ n n n n ) , one obtains for the p ~ ~ AA(3SDl-resonance) -+ K-K2n cross section a value of ten microbarns. The A A annihilation modes with three or four plons (in addition to two kaons) being dominant, the cross section should be of a few tens microbarns. With the uncertainties of the model it is difficult to make unambiguous predictions for differential cross sections and polarisatlon observables. Our model actually reproduces the observed large anisotropy but show a small sensitivity to this resonance. The shape

The preceding results show the possibility 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 q u a n t u m numbers j e c = 1 - - . The reasons for the smallness of ItS width are the D-wave dominance of its wavefunction (96%) and the proximity to the A A threshold, which results into a large RMS radius. The model contains some fitting parameters, namely the cut-off radix and annihilation constants, which cannot be unambiguously fixed by the existing experimental data. The coupling constants are not firmly fixed as well, reflecting our poor knowledge of the AA, to which only a few works have been devoted [ 15,19 ]. In spite of this, some model independent conclusions are worthwhile. First, it is hardly possible to reproduce such a narrow structure in S- or P-partial waves. Second, in any one boson exchange model, the singlet potentials are too small to create a b o u n d state. This leaves no place for a big n u m b e r of candidates, but the cases of 3D2, aD3 should be taken into account. Some experimental posslbilmes to find this resonance are proposed: (i) A high precision measurement of the p-fi ~ A A cross section and polarization observables in the region e ~< 2 MeV. (ii) The measurement of the reaction PP -+ K K + nn (n = 2, 3, 4) near the AA threshold. (iii) If the q u a n t u m numbers are j e c = 1 - - , the reaction e+e - ~ A A 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 - ~ p g at A A threshold [20]. Concrete proposals to perform some of these measurements have already been submitted [3 ]. The conjugated efforts of LEAR and Frascatl facilities should 409

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be able to provide a definite conclusion about this possible new quasinuclear state.

Acknowledgement We thank I.S. Shapiro for the scaentlfic discussions and comments on the manuscript, N. H a m a n n and F. Stinzing for a helpful communication of the experimental results.

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[7] J. Haldenbauer et al., Phys. Rev. C 45 (1992) 931. [8] P. La France and B. Lolseau, Nucl. Phys. A 528 (1991) 557. [9] S. Furul and A. Faessler, Nucl. Phys. A 468 (1987) 669. [ 10] P. Kroll and W. Schweiger, Nucl. Phys. A 474 ( 1988 ) 608. [ 11 ] O.D. Dalkarov and K.V. Protasov, Sov. JETP Lett. 46 (1987) 329; I.S. Shaparo, Antiproton-nucleon and antiprotonnucleus interactions, eds. F. Bradamante et al. (Plenum Press, 1990) p. 81; O.D. Dalkarov, K.V. Protasov and I.S. Shapiro, Int. J. Mod. Phys. A 5 (1990) 2155. [12]J. Carbonell, O. Dalkarov, K. Protasov and I.S. Shapiro, Nucl. Phys A 535 (1991) 651. [13] R.A. Bryan and R.J.N Phillips, Nucl. Phys. B (1968) 201. [14] M.M. Nagels, T.A. Rljken and J.J. de Swart, Phys. Rev. D 12 (1975) 744, D 15 (1977) 2547. [15] R.T. Tyapaev and I.S Shapiro, Soy Phys. JETP 59 (1984) 21. [ 16] O. Dalkarov, J. Carbonell and K.V. Protasov, Soy. J. Nucl. Phys. 52 (1990) 1052. [17] B. Mayer al, Phys. Lett. B 225 (1989) 450, Z Phys. C 46 (1990) 203; D. Bridges et al., Phys. Rev. Lett. 57 (1986) 1534; C.B. Dover, T. Gutsche and A. Faessler, Phys Rev. C 43 (1991) 379. [18]J. Carbonell, K. Protasov and O. Dalkarov, Contributionto Second Biennial Conference on Lowenergy antlproton physics (Courmayeur, 1992). [19] C.B. Dover and M. Goldhaber, Phys. Rev. D 15 (1977) 1997. [20] O.D. Dalkarov and K.V. Protasov, Phys. Lett. B 280 (1992) 117.