1. Pseudo-scalar Pseudo-scalar final states and 12% rule
Wang Ping, Yuan ChangZheng, Mo Xiaohu
IHEP, Beijing
Symposium on 12% rule and  puzzle
March 18-20, 2011, Beijing, China
Mo Xiaohu

2. Outline Phase between strong and EM Phase study and 12% rule
Mixing model and 12% rule
BESIII results
Conclusion ?
Mo Xiaohu

3. Phase between strong and EM
Mo Xiaohu

4. Possible hadronic excess in ψ(2S) decay and  puzzle
The Relative Phase φ
J/ψ Decays:
1. AP : 90 ° M. Suzuki, PRD63, (2001)
2. VP : (106 ±10) ° J. Jousset et al., PRD41, 1389 (1990)
D. Coffman et al., PRD38, 2695 (1988)
N. N. Achasov, talk at Hadron2001
3. PP : (89.6 ±9.9) ° M. Suzuki, PRD60, (1999)
4. VV : (138 ±37) ° L. Köpke and N. Wermes,
Phys. Rep. 74, 67 (1989)
5. NN : (89 ±15) ° R. Baldini et al., PLB444, 111 (1998)
Large
| phase |
~ 90º
ψ’ Decays:
???…
M. Suzuki, PRD63, (2001):
Possible hadronic excess in ψ(2S) decay and  puzzle
Mo Xiaohu

5. ± φ The phase study in e+e – experiment Phase
interference
interference
Take the continuum contribution and its interference effect into consideration , we could determine not only the magnitude but also the sign of the phase.
Mo Xiaohu

6. A.Seiden,H.F.-W. Sadrozinski and
Phase in VP and VT mode
A.Seiden,H.F.-W. Sadrozinski and
E.Haber : Phys.Rev.D38, 824 (1988)
P.Wang, C.Z.Yuan, X.H.Mo:HEP&NP27(2003)465
Contribution of one-photon annihilation at ψ(2S) in e+ e experiment
P.Wang, X.H.Mo, C.Z.Yuan :PLB557(2003)192
The form factor of  0 and +   at ψ(2S)
P.Wang, C.Z.Yuan, X.H.Mo:PRD70(2004)114014
J/ψ Decays:   , K*0 K0,   , K*+K
φ = –72.0 ° ± 3.6° or ° ± 3.6°
ψ’ Decays :  , K*0 K0,   , K*+ K
φ = –90 ° or 180 °
VP -Parameterization
VT -Parameterization
 f : g(1sg) +e
 a : g(1sg) +e
K* K*2 : g(1sg)  2 e (1se/2)
 f2' : g(1sg)  2 e (1se)
Mo Xiaohu

7. φ PP -Parameterization Phase in PP mode PP -Parametrization π﹢π﹣ : E
π﹢π﹣ : (E+EC)
K﹢K﹣: (√3/2)M +(E+EC)
KS KL : (√3/2)M
Phase in PP mode
E.Haber and J.Perrier:
Phys.Rev.D32, 2961 (1985)
M. Suzuki, PRD60, (1999)
Yuan, Wang, Mo: PLB567 (2003)73
PP -Parametrization
π﹢π﹣ : E
K﹢K﹣: (√3/2) M +E
KS KL : (√3/2) M
+Continuum
Contribution
B’ (π﹢π﹣) and
A’+B’ (K﹢K﹣) known, KS KL is needed to extract the phase between A’ and B’. φ
Mo Xiaohu

8. Phase in PP mode First measurement of the phase in ’ decays!
CLEO: B (’ KS KL )
=5.810 – 5
First measurement of the phase in ’ decays!
Phase in PP mode
K+K– & +
 inputs ;
Input 1: DASP;
Input 2: BESI ;
Input 3: K+K–
from BESI &
+ by form
factor.
BES:B (’ KS KL )
=5.2410 – 5
BES:PRL 92, (2004);
CLEO:PRD74, (2006).
–82°, – 80°
Mo Xiaohu
+121°, +120°

9. J/, ’  KSKL Ks mass sidebands signal PRL 92, 052001 (2004) signal
14M ψ(2S)
Bkg MC
signal
Ks mass sidebands
58M J/ψ
PRL 92, (2004)
B ’  Ks KL = (5.24± 0.47 ± 0.48 )  10 – 5
signal
MC Bkg
K*0KS+c.c.
PRD 69, (2004)
B J/  Ks KL =(1.82 ± 0.04 ± 0.13 )  10 – 4
Mo Xiaohu

10. 12% rule, mixing model
Mo Xiaohu

11. J/ , ’ ρπ A solution of ’ suppress
J.L. Rosner: PRD64, (2001)
Wang, Yuan and Mo: PLB574,41(2003)
To measure B(  ρπ), the best
way is to do the energy scan!
The band is for non-zero
B(ψ(2S)ρπ)!
σ(K*0K0+c.c.)
For φ=﹣90°!
MK3 UL (<6.3pb)
Favors φ=﹣90°!
Missing ρπ signal and/or
enhanced K*0K0 signal
indicate BRs at 10-4 level.
Mo Xiaohu

12. Mixing model Mixing : (=12º) “12%” rule:
P.Wang, X.H.Mo and C.Z.Yuan: PRD70, (2004)
(3.8±1.1)  10 =0º
J.L. Rosner: PRD64, (2001)
Mixing : (=12º)
<f |> = <f | 23S1> cos – <f | 13D1>sin,
<f |  > = <f | 23S1> sin + <f | 13D1>cos.
“12%” rule:
|<f|J/>|2/|<f|23S1>|2 = ee(J/)/ee(23S1)
 <f | 23S1> (Rosner’s assumption)
1. <f |> = < f | 23S1 > cos – <f | 13D1 > sin
< f |> & < f | 23S1 >  < f | 13D1 >
2. < f |  > = < f | 23S1 > sin + < f | 13D1 > cos
 < f |  >  Br(  f)
(0.12±0.07)  10 = ±180º
The variation of B(  K0S K0L )  10 5
against the pahse  .
(0.12±0.07)  10 –5  B  ’’  Ks KL  (3.8±1.1)  10 –5
 is the relative phase between <f | 23S1> and <f | 13D1>
PRD 70, (2004)
B  ’’  Ks KL < 2.1  10 – 4 (90% C.L.)
Mo Xiaohu

13. 模 型 预 言
实验检验
Mo Xiaohu

14. BESII /p=0.017(1+p2)1/2 (π)= 65 MeV (K)=62 MeV Two peaks
merge together,
undistinguishable
p(π)– p(K)=62 MeV
Mo Xiaohu

15. BESIII ’ ’’ J/ Simulation results K  K  K  p() =1.837GeV
() =11.7MeV
p(K) =1.775GeV
(K) =11.0MeV
Events ’
p() =1.542GeV
() =8.5MeV
p(K) =1.467GeV
(K) =7.9MeV
p() =1.881GeV
() =12.0MeV
p(K) =1.820GeV
(K) =11.3MeV K 
momentum (GeV)
J/
’’
Events
Events K  K 
momentum (GeV)
momentum (GeV)
Mo Xiaohu
All fit error around the level of 10 – 4 GeV

16. BESIII Experimental results
Mo Xiaohu

17.  workshop BESIII Very preliminary Unpublished results;
Before cited, ask permission from BESIII collaboration, otherwise,collaboration will be unpleasant. 
Mo Xiaohu

18. preliminary results: J/  & , ,LS
K K 
  
LS

 
preliminary results: J/  & , ,LS
  
K K 
LS

 
Mo Xiaohu

19. ? ? 12% rule test in P-P f.s. enhanced !!
Exception for  final state, there is something unclear, and need more detailed analysis.    contamination is heavy and difficult to be eliminated, more hard for it. ?
Mo Xiaohu

20. Fit for the phase between the strong and the electromagnetic amplitudes
Mo Xiaohu

21. ' Pseudoscalar-Pseudoscalar
Form factors of  and  can be calculated in framework of Hadronic Helicity Conservation (HHC), the measurement results can provide test for HHC.
S.J. Brodsky and G.P. Lepage :
PRD24, 2848 (1981).

 
kf(10–1 GeV2)
9.61.0 0.4
7.30.5 0.2
E=3.65GeV
|Ff(s)|(10–2)
5.50.4 0.2
E=3.65GeV
10.11.0 0.4
8.50.5 0.2
E=3.671GeV
7.50.8 0.5
6.30.4 0.1
pQCD : F / FK = 0.670.01
BESIII: F / FK = 1.310.19
CLEO: F / FK = 1.190.11
Mo Xiaohu

22. Mo Xiaohu, Yuan ChangZheng and Wang Ping
Study of the ρπ puzzle in charmonium decays
Mo Xiaohu, Yuan ChangZheng and Wang Ping
Getting it all right is a big challenge. And big challenges are worthy of big effects.
E.S.Swanson, “The New Heavy Mesons, A Status Report”
Mo Xiaohu

23. Conclusion ? Very good! 山重水复疑无路 柳暗花明 ? ? ? ?
柳暗花明 ? ? ? ?
Symposium on the“12% rule” and “rho-pi puzzle” in vector charmonium decays
Very good!
Mo Xiaohu

24. THANKS 谢谢

25. Backup
Mo Xiaohu

26.
Mo Xiaohu

27. 14 M ’ events 14 M 58M J/ events 6.4pb–1 ’ con. data @ 3.65 GeV
27pb–1 ’’ data
@ GeV
14 M 4M 3M
Mo Xiaohu

28. non-DD decay Mixing : “12%” rule: 13 % charmless decay
J.L. Rosner: PRD64, (2001)
13 % charmless decay
Wang, Yuan and Mo, PRD70, (2004)
2.5 % radiative transition
J.L. Rosner: hep-ph/
0.18% + – J/
CLEOc, hep-ph/
Maximum 16%
non-DD decay
Mixing :
<f |> = <f | 23S1> cos – <f | 13D1>sin,
<f |  > = <f | 23S1> sin + <f | 13D1>cos.
(=12º)
“12%” rule:
|<f|J/>|2/|<f|23S1>|2 = ee(J/)/ee(23S1)
 <f | 23S1> (Rosner’s assumption)
1. <f |> = < f | 23S1 > cos – <f | 13D1 > sin
< f |> & < f | 23S1 >  < f | 13D1 >
2. < f |  > = < f | 23S1 > sin + < f | 13D1 > cos
 < f |  >  Br(  f)
With the results of J/ and  we can obtain the decay information at  , the only undetermined variable
here is the phase between | 23S1> and | 13D1>
Mo Xiaohu

29. non-DD decay R is Sensitive to phase variation
A prediction of ’’ charmless decays
Wang, Yuan and Mo, PRD70, (2004)
R is
Sensitive
to phase
variation
Phase=0
Average enhancement factor
Non-zero phase btwn matrix elements
Prediction on ψ(3770) charmless decay branching fraction: 13% (or 3.0MeV)
Mo Xiaohu

30. The Relative Phase φ J/ψ Decays: ψ’ Decays:
1. AP : 90 ° M. Suzuki, PRD63, (2001)
2. VP : (106 ±10) ° J. Jousset et al., PRD41, 1389 (1990)
D. Coffman et al., PRD38, 2695 (1988)
N. N. Achasov, talk at Hadron2001
3. PP : (90 ±10) ° M. Suzuki, PRD60, (1999)
4. VV : (138 ±37) ° L. Köpke and N. Wermes,
Phys. Rep. 74, 67 (1989)
5. NN : (89 ±15) ° R. Baldini et al., PLB444, 111 (1998)
Large
phase
~ |90º|
ψ’ Decays:
1. VP : φ =﹣90 °
or ° P. Wang et al. , PRD69, (2004)
2. PP : φ = (﹣82 ±29)°
or (+121 ±27) ° J. Z. Bai et al. , PRL9, (2004)
Large
phase
~ – 90º
Mo Xiaohu

31.
Mo Xiaohu

32.
Mo Xiaohu

33. non-DD decay Theoretical motivation:
Test S- and D- wave mixing scenario
Study the phase between S- and D- wave
matrix elements (the dynamics of charmonium decay)
Experimental need:
Neglecting non-DD decay in previous scan experiments
Neglecting continuum contribution in exclusive channel measurement
Inconsistency between previous measurements (reason remain unknown)
Three Experimental approaches :
Exclusive
Quasi-inclusive
Inclusive (leading particle)
Mo Xiaohu

34. Exclusive Two points: Con. contr. and its interference with res.
Experimental details refer to
Wang, Yuan and Mo: PLB574,41(2003)
Wang, Mo and Yuan: PRD70, (2004)
BR(´´KSKL) <2.1x BESII, C.Z.Yuan, PRD70, (2004)
(e+e– 0) = ( ± 1.7) pb (e+e–  ) = ( ± 0.08) pb (e+e–  ') <28 pb BESII, L.L.Ma et al. , PRD70, (2004)
BR(´´ ρπ ) in progress BESII, Z. Wang.
CLEOc can improve the measurement!
–4.1
–3.5
Two points:
Con. contr. and its interference with res.
ISR correction and efficiency
Mo Xiaohu

35. Quasi-inclusive ´´ f DD Scan Exp. B (DDf ) 1. F(DDf ) B(´´ DD)
B(´´f)= B(´´ DD) • F(DDf )
+B (DDf )
R.M.Baltrusaitis et al., PRL56,2149(1986)
2. B(´´f)
F(DDf )
Scan Exp.
3. B (DDf )
B (DDf )
Mo Xiaohu

36. ´´ Inclusive pmaximum < 1GeV pcut > 1.1GeV
D0 D0
K– +
K+ –
non-DD decay
pmaximum < 1GeV
pcut > 1.1GeV
Leading particle method
Mo Xiaohu