Proton-Antiproton Annihilation in Baryonium

1. Proton-Antiproton Annihilation in Baryonium Outline Mu-Lin Yan (USTC) hep-ph/0502127(to appear in PRC(2005)) (collaborate with Gui-Jun Ding (USTC)) • BES experiment • Possible Interpretations • The coherent state method for -annihilations • The construction of coherent state and its prediction • Summary

2. Enhancement Observed By BES fitted peak location J/ygpp acceptance weighted BW +3 +5 -10 -25 M=1859 MeV/c2 G < 30 MeV/c2 (90% CL) c2/dof=56/56 0 0.1 0.2 0.3 M(pp)-2mp (GeV) 3-body phase space acceptance

3. Possible Interpretations • bound state ---most simple and natural, simular to deuteron (studied from Skyrmion model by M.-L.Yan, B.-Q. Ma et.al,from linear sigma model by Y.-B.Ding, X.-Q. Li et.al and from constituent quark model by C.H.Chang, H.-R.Rong ) ; (call it as X(1860)) • Final state interaction(studied by B.S. Zou and H. C. Chiang ); • Quark fragmentation mechanism(by J.L.Rosner); …..

4. In order to ascertain whether or not theX(1860)exists, more evidence is needed. • Feature of X(1860)-decays are mainly due to p-p\bar annihilation in the baryonium. • It has well been known that: p-p\bar annihilations favor the processes with 4—7 pion final states over those with 2—3 pion’s. This is a significant feature for p-p\bar annihilations in their scattering at low energies. • Are there similar feature for X(1860)-decay?

5. A Toy Model( collision in Baryonium Baryonium decay ) . ( Yan,Li,Wu, Ma, hep-ph/0405087) • Model: p-p\bar with a double well potential , This model can be solve analytically.

6. Using WKB approximation, the tunnelling coefficient is The total width of X(1860) is We find = −17.2 MeV p-p\bar collision frequency:

7. Basis of The Coherent State • From Skyrmion model studies, annihilation proceeds very rapidly. • The rapid annihilation leads to pion pulse forms basis of the coherent state. [Amado et al., PRL 72, 970 (1994).] • Should use the conhereht states to describe the pions radiated from p-p\bar annihilations.

8. Coherent State Method for P-P\bar annihilation • Coherent state is the eigenstate of annihilation operator (a is annihilation operator, is the eigenvalue)in quantum mechanics .Then is given by • The free quantum scalar field is : The coherent state associated with a given classical state,is the quantum state that is an eigenstate of the positive frequency part of the field ,and

9. The normalized coherent state • Then the normalized quantum state defined by : this is a coherent statein whicheach model carries weight It is clear that is the eigenstateof thepositive part of the field , , is given by .

10. The coherent state with fixed four-momentum and isospin [R.D.Amado et.al Phys.Rev. C50, 640(1994); C52 ,2158(1995)]

11. Mesons radiated from annihilation described by conherent states • Starting from the above coherent state the mean number pion of and the branch ratios of nucleon-antinucleon annihilation et.al can be predicted, all these quantity are in good agreement with experiment.

12. Construct Coherent State with fixed G- and P-parity • We should construct coherent state not only with fixed isospin and four momentum but also definite P-parity and G-parity.Since Then where is the isospin-triplet creation operator ,and isospin-singlet creation operator.

13. The field operator that create or at space point x and pointing in the isospin direction ,is Under G transformation , become And under P transformation In the above and for simplicity we have take

14. X(1860) with as meson radiation souce • The desired coherent state with fixed four-momentum, fixed isospin and also with G-parity(+) and P parity(-) is :

15. The state is are orthogonal where N(K) is the normalization factor where

16. Using the expansion method, the normalization integral is where • Note that the effect of phase space for the decay has been taken into account via the in function I(K,m, n).

17. For X(1860) + ,the probability of the decay due to annihilations is where : even; : odd.

18. The probability of X(1860) to is: Where Since the branch ratio for is proportional to P(m,n),also considering charge conservation,we have the ratios between these branch ratios are as follows

19. Parameter Choosing and Prediction • Following the work of Amado et. al, the meson field source turns on at t = 0 and then decays exponentially in time, and that it has a spherical symmetric Yukawa shape, then f(k)-function (which is a Fourier transformation of the meson field source) is where , C is a strength and can be fixed by required that the average energy be the energy released in annihilation, which is equal to 2 . In the unit of pion mass ( = 1),we take 2. This corresponds to an annihilation region with a time and distance scale of half a pion Compton wave length— a reasonable size and leading also to a reasonable agreement with experimentaldata. Since both and belong to the pseudoscalar meson octet we argue that g(k) should be same with f(k) except that should be replaced by

20. Main Results • With the above parameter chosen, the ratios between branch ratio is: We see that is heavily suppressed comparing with The experimental check to it is expected.

21. Summary and Discussion • If X is the p-p\bar bound state, then: Br(X )>> Br(X ) • A naïve interpretation: (Gluon-content in Baryon)>> (Gluon-content in meson) So, (G in X=(pp\bar))>>(G in ). The natural process should be: (G: “redundant gluons”) X = = I.e., X • Therefore,

22. BES New Results Reported in this Meeting: • BES reported in this meeting there is a narrow resonance of ( ) at M=1835MeV though to observe ( )-resonance. This is an important support to the prediction of our baryonium-decay theory.

23. Thank you!