1. Study a0(980)-f0(980) mixing from charmonium decays
JiaJun WU
In collaboration with Pro. ZHAO and Pro. ZOU

2. Outline Introduction The theory of a0(980)-f0(980) mixing.
The predication of J/yaa0(980)f
ElectroMagnetic decay J/yag*aa0(980)f
Strong decay J/yaK*K+c.c.aa0(980)f
J/yaf0(980)faa0(980)f
The predication of cc1aa0(980)p0af0(980)p0
Summary

3. Introduction
The structures of a0(980) and f0(980) resonances are still unknown. They are supposed as eigenstates of isospin 1 and 0, respectively. In the late 1970s, the mixing between the a0(980) and f0(980) resonances was first suggested theoretically by N. N. Achasov.
N.N.Achasov PLB 88(1979),367
There are various models to explain these two resonances: qqbar models, 4-quark models, KKbar molecule models and qqbarg models et al. . This mixing is expected to help clarify the nature of two resonances.
This mixing has hence been studied extensively regarding its effects in various reactions .
For example: ddaap0h，pp-ahp0n。
N.N.Achasov G.N.Shestakov PRL 92,
WASA-at-COSY Collaboration, nucl-ex/

4. Introduction
There is only one experiment which gives the result of this mixing. In the ppaps(p0h)pf, they assume the a0(980) comes from the a0(980)-f0(980) mixing. But the width of a0(980) peak is much broader than the mixing width. So the a0(980) peak here is unlikely to be mainly due to mixing mechanism.
F.E.Close and A.Kirk PLB 489,24 (2000)
WA102 Collaboration PLB 488, 225 (2000)
For these reasons, there is no experiment really succeeded to measure this mixing.
With 109 J/y and 2.8*108 cc1 events expected in the BEPCII with the much improved BESIII detector, which can measure multiphoton final states well, the measurement of the J/yaa0(980)f and cc1 af0(980)p0 reactions are definitely possible. We can study the mixing from these two reactions.

5. The theory of a0(980)-f0(980) mixing
The amplitude of a0(980)-f0(980) mixing：
N.N.Achasov, G.N.Shestakov, PRL 92, (2004)
A narrow peak of 8MeV

6. Two types of mixing
Reactions for study f0(980)aa0(980) and a0(980)af0(980) mixing：

7. Comparison between xaf and xfa(1)
Different results are from the same parameters.
The parameters from KLOE (GeV)。
ma=0.983，gaph=3.02，gakk=2.24,
mf=0.973，gfpp=2.09，gfkk=5.92,

8. Comparison between xaf and xfa(2)
The two sets of parameters give almost identical xfa but very different xaf.

9. Comparison between xaf and xfa(3)
For the xaf and xfa, we find two facts:
1. When we use the same parameters, we can get the different values of these two intensities.
2. The two sets of parameters give almost identical xfa but very different xaf.
We had better to measure both of them because xaf and xfa are the same important.

10. The predication of mixing intensity in various models and indirect experiments
There are uncertainties in various models and indirect experiments.
It’s very interest-ing to measure these mixing intensities in the direct way.

11. The discussion for J/yaa0(980)f
Three mechanisms for J/yaa0(980)f：
EM decay ： J/yag*aa0(980)f
Strong decay ：J/yaK*K+c.c.aa0(980)f
J/yaf0(980)faa0(980)f
Jia-Jun Wu， Qiang Zhao and B. S. Zou PRD 75, (2007)

12. J/yag*aa0(980)f
Br(J/yaf0(980)faa0(980)f)=2.59*10-7

13. J/yaK*K+c.c.aa0(980)f

14. J/yaf0(980)faa0(980)f
There is a clear peak of f0(980) in the reaction J/yaf0(980)f at BES2.
BES Collaboration, PLB 607,
Then we can get the invariant mass spectrum of ph by multiplying the mixing intensity. The a0(980) peak from mixing is very narrow~8MeV。
From calculation: Br(J/yaf0(980)faa0(980)f)=2.0*10-6. The parameters are all from CB collaboration.
Assuming the detection efficiency is about 30%, we can get about 600 events at BESIII by 109 J/y.

16. The predication of cc1aa0(980)p0af0(980)p0
From CLEO: Br(cc1aa+0(980)p-)=2*10-3
From calculation : Br(cc1aa0(980)p0af0(980)p0)=4.6*10-6
The parameters are all from CB collaboration.
Assuming the detection efficiency is about 30%, we can get about 300 events at BESIII by 2.8*108 cc1。
Jia-Jun Wu, and B. S. Zou Phys.Rev.D78:074017,2008.
8 MeV
CLEO Collaboration, Phys. Rev. D75, (2007)

17. Summary(1)
The a0(980)-f0(980) mixing was suggested theoretically about 30 years ago. We can study the structures of two resonances from the mixing which should give a 8MeV peak.
There are two types of reactions to study this mixing: a0(980)af0(980) and f0(980)aa0(980), and corresponding to two mixing intensities xaf and xfa. From the calculation, we find：
1.The results from indirect experiments suffer large uncertainties, hence they can’t distinguish the different models.
2. xaf and xfa should be measured because both of them are important.

18. Summary(2)
The predications of the reactions J/yaa0(980)f and cc1aa0(980)p0af0(980)p0 ：
Brach Ratio Events at BES3 Width
J/yaf0(980)faa0(980)f : * MeV
J/yag*aa0(980)f : * MeV
J/yaK*K+c.c.aa0(980)f： 1* MeV
cc1aa0(980)p0af0(980)p0: 4.6* MeV
From above predications, we find the a0(980)-f0(980) mixing intensities can be measured accurately at BESIII.

19. Thank you