1 S. Wycech (Warsaw, Poland), B. Loiseau Antiproton-proton resonant like channels in decays Beijing 09/2004  Scattering lengths for 2I+1,2S+1 L J states from low energy scattering experiments but clear separation of quantum state difficult. Introduction Existence of quasi-bound, virtual or resonant antinucleon-nucleon states ?  Complementary X rays transitions in -hydrogen if fine structure of level resolved e.g. 1S states : M. Augsburger et al., PLB461 (1999) 417, « Measurement of the strong interaction parameters in antiprotonic deuteriuim » and partly 2P states : M. Augsburger et al. NPA658 (1999) 149, « Measurements of the strong interaction parameters in antiprotonic hydrogen and probable evidence for an interface with inner bremsstrahlung »

2 Collaboration, J.Z. Bai et al. PRL91 (2003) , « Observation of a near-threshold enhancement in the mass spectrum from radiative decay ». On the other hand clear threshold suppression in. But fine structure resolution not achieved yet.  Possible understanding from subthreshold energy region like in low- or zero - energy reactions cf. atomic experiments : D. Gotta et al. NPA660 (1999) 283, « Balmer and transitions in antiprotonic hydrogen or deuterium ».  Formation experiments : resonant-like behaviour in BES

3 Physics of slow pairs produced in J/  decay : J PC conservation  several final states possible  Close to threshold different behavior Some recent approaches to interpret BES Collaboration results  B. S. Zou, H. C. Chiang, PRD69 (2004) , « One-pion- exchange final state interaction and the near threshold enhancement in decays »,  B. Kerbikov, A. Stavinsky, V. Fedotov, nucl-th/ , « Low- mass proton-antiproton enhancement : Belle and BES results, premises of LEAR and expectations from CLAS »,  Chong-Shou Gao and Shi-Liu Zhu, hep-ph/ , « Understanding the Possible Proton Antiproton Bound State Observed by BES Collaboration ».

4  Use of Paris potential model. r > 1 fm from G-parity transformation from Paris NN potential based on dispersion theoretic treatment of 2  exchange. r < 1 fm fit to data. State dependent optical potential : phenomenological short range with a form suggested by calculation of mesons or resonances. Paris model : parameters of short range readjusted by fitting to new data. We here shall rely on elastic and inelastic NN scattering experiment.

5 Paris 82 : J. Côté, M. Lacombe, B. Loiseau, B. Moussallam, R. Vinh Mau, PRL48 (1982) 1319, « On the nucleon-antinucleon optical potential » pre-LEAR (CERN) data mainly (T=0 + T=1),  2 /data=2.80 for 915 data. Paris 99 : B. El-Bennich, M. Lacombe, B. Loiseau, R. Vinh Mau, PRC59 (1999) 2313, « Refining the inner core of the Paris potential » previous data + more recent LEAR :  2 /data=2.95 for 3814 data. Paris 03 : M. Lacombe, B. Loiseau, R. Vinh Mau, S. Wycech, in preparation, data used in Paris 99 + scattering lengths (antiprotonic hydrogen and deuterium, M. Auberger et al. (1999)) + «Antineutron-proton total cross-section from 50 to 400 MeV/c » F. Iazzi et al. PLB475 (2000) 378. Paris 03 :  2 /data = 3.19 for 3934 data. Paris antinucleon-nucleon potentials Paris 94 : M. Pignone, M. Lacombe, B. Loiseau, R. Vinh Mau, PRC50 (1994) 2710, « Paris potential and recent proton-antiproton low energy data » + LEAR data in particular (T=1 - T=0),  2 /data=2.46 for 3295 data.

6 Allowed final states of pairs J PC conservation limits number of slow final states - i.e. for small - J PC (J/  ) = e + e - collision   being angle of final photon with direction of the beam, BES Collaboration favours 1 + cos 2  over sin 2  angular distribution  pseudoscalar ( 1 S 0 ) or scalar ( 3 P 0 )

7  In channel f :  Large ReA ff > 0 possiblity bound (quasi-bound) state.  Large ReA ff < 0 virtual state likely.  Needs to extrapolate below threshold.  S-wave K-matrix low-energy multichannel system : See H. Pilkuhn, « Interaction of hadrons », North Holland P.C., Final state interaction

8  For P wave  Here formation amplitude unknown, but up to terms  final state interaction factor in an appropriate partial wave  In many open annihilation channels : ImA ff large.  : formation amplitude, L angular momentum. Formation amplitude

9  Paris potential for  Close to threshold (at T lab = 300 MeV, x = 289.2MeV) Final state interaction factor

10 Solid curve : fit by background (dashed curve) plus S-wave Breit- Wigner ( 1 S 0 ) : and width R < 30 MeV/c (  2 /d.o.f. = 56.3/56). Note : If P-wave ( 3 P 0 ) Breit- Wigner  2 /d.o.f. = 59/56 and M R =  0.9 MeV/c 2, width = 4.6  1.8 (sta) MeV/c 2. Fig. 1: (a) From BES Collaboration : the near threshold distribution for the event sample. Experimental results for

11  The unknown formation amplitude C parametrized as  Numbers of Events = For Paris 03 at x = 7 MeV and x = 66.2 MeV  c 0 and c 1 11 S S 0 13 P P 0 13 P P 1 c0c c1c  Experimental points and errors extrapolated from figures of BES Collaboration PRL91 (2003) Model fit for

12 Comparison of the result to the BES event sample, data from Fig. 3 of J. Z. Bai et al. PRL91 (2003) ). Fig. 2

13 Weighted events compared to data. Fig. 3

14 Bound states in 11 S 0 Re E (MeV) Width (MeV) Paris 03 : Paris 99 : Paris 94 : none Paris 82 : none final state factor compared to data. Fig. 4

15 Comparison of the result to the BES event sample. Fig. 5

16 Weighted events compared to data. Fig. 6

17 final state factor compared to data Resonances in 13 P 0 Mass (MeV) Width (MeV) Paris 03 : Paris 99 : Paris 94 : Paris 82 : Fig. 7

18 Fig. 8 (a) From BES Collaboration : the distribution events for the selected decay. Solid curve fit by Experimental results for

19  As for 33 S 1, t(x) does not vanish at threshold  choice of  For 31 P 1  For 33 S 1 and 31 P 1 : N events = For Paris 03 at x = 7 MeV and x = 41.7 MeV  c i, i=0,1.2  The pair has to be in I=1 (J/  is I=0) 33 S 1 31 P 1 c0c c1c c2c Model for

20 Comparison of the result to the BES event sample Fig. 9

21 final state factor compared to data. Bound states in 31 P 1 ReE (MeV) Width (MeV) Paris 03 : Paris 99 : Paris 94 : none Paris 82 : none Fig. 10

22  For Paris 03 : 11 S 0 (ReE = -4.8 MeV, Width = 52.5 MeV) and 33 P 1 (ReE = -4.5 MeV, Width = 18.1 MeV).  Existence of these states needs confirmation.  For Paris 03 the resonance 13 P 0 (ReE = 1873 MeV, Width = 10.7 MeV). This well-established resonance orginates from the strong attraction from one-pion exchange.  Such a model predicts quasi-bounds states close to the threshold in particular and and a resonance in.  New results of BES Collaboration : natural explanation from a traditional model of interaction based on G transformation, dispersion theoric treatment of two-pion exchange and semi- phenomenological absorptive and short range potentials.  Each of these states gives a reasonable representation of the BES decay data. Some concluding remarks

23 33 S 1 or 31 P 1 waves occuring in the decays. Here isospin conservation forces the pair to be I = 1. Our final state emission model gives ratio of branching of the  and  0 channels of order 1 as in the experience (1/4 from isospin conservation). OUTLOOK  Needs the experimental data points to be more quantitative (  2 /d.o.f.)  - in progress - a more specific semi-quantitative (dominance of magnetic transition) favors and  Final state off-shell effects.  Microscopic quark model of the annihilation followed by pair creations and then  or emission could generate some formation amplitude C.  No narrow quasi-bound states or resonance close to the threshold

24 Other antiproton-proton graphs

25 Comparison of the result to the BES event sample. Fig. 11

26 Fig. 12 Weighted events ( 3 P 1 ) compared to data

27 final state factor compared to data Bound states in 33 P 1 ReE (MeV) Width (MeV) Paris 03 : Paris 99 : Paris 94 : Paris 82 : Fig. 13

28 Comparison of the result to the BES event sample from Fig. 2 of J. z. Bai et al. PRL91 (2003) Fig. 14

29 final state factor compared to data Bound states in 33 S 1 ReE (MeV) Width (MeV) Paris 03 : Paris 99 : Paris 94 : Paris 82 : Fig. 15

30  tot p bar p

31  ann p bar p

32  ann 0-50 p bar p

33 Alston

34  ann n bar p

35 d  /d  elast

36 P elast

37  Cex

38 d  /d  Cex 147

39 P Cex

40 d  /d  Cex 206

41 d  /d  Cex 344