1. Hadronic decays of (2S)
Yuan Changzheng (苑 长 征)
IHEP, Beijing
June 26, 2008

2. The world of quarks

3. Onia cc J/y 0.09 3.1 Quarkonium is the bound state of quark and
FORCES
System
Ground triplet state 13S1
(v/c)2
Number of states below dissociation energy
binding
decay
Name
G (MeV)
Mass (GeV)
n3S1
all
POSITRONIUM EM
e+e-
Ortho-
0.001
~0.0 2 8
QUARKONIUM S T R O N G
uu,dd r
150.00
0.8
~1.0 ss f
4.40
1.0
~0.8
“1”
“2” E M cc
J/y
0.09
3.1
~0.25 bb Υ
0.05
9.5
~0.08 3 30
weak tt
(3000.0)
(360.)
<0.01
Quarkonium is the bound state of quark and
anti-quark by the gluon.
Charmonium is charm anti-charm bound state!

4. Discovery of the J/ψ “November Revolution of Particle Physics!”
Charm quark was proposed in 1964, first application in 1970!
PRL33, 1404 (1974)
PRL33, 1406 (1974)
PRL33, 1408 (1974)
ADONE
confirmed!
BNL
SLAC
郁闷的Adone!
Designed:
Maximum Ecm~3 GeV!

5. Discovery of the ψ(2S) Predictions of the charmonium spectroscopy
Argument and Potential model
PRL33, 1453 (1974)
PRL34, 365 (1975)
PRL34, 369 (1975)
SLAC
From then on, there is a new field in HEP: Charmonium Physics.

6. Potential models Cornell potential： V(r) = -S/r + kr （库仑势+线性势）
解薛定谔方程能级, 波函数

7. Potential models vs experiments

8. This is the famous “12% rule”.
The “12% rule”
M. Appelquist and H. D. Politzer, PRL34, 43 (1975)
This is the famous “12% rule”.

9. H.D.Politzer 和 “12%规则” 著名的“12%规则”!
PRL30, 1346 (1973)通过检验2004年诺贝尔奖
+M. Appelquist, PRL34, 43 (1975)?
著名的“12%规则”!
(2S)与J/唯一的差别是主量子数不同，“12%规则”是一个干净、简单的理论推论，预期普遍成立。
“规则”的破坏意味着强相互作用中非常基本的、不为人知的规律的存在！

10. “12% rule” and “ puzzle”
Violation found by Mark-II , confirmed
by BESI at higher sensitivity.
Extensively studied by BESII/CLEOc
VP mode:  , K*+K-+c.c., K*0K0+c.c., 0,…
PP mode: KSKL, K+K-, +-
BB mode: pp, , …
VT mode: K*K*2, f2’, a2, f2
3-body: pp0, pp, +-0, …
Multi-body: KSKShh, +-0 K+K- , 3(+-), …
MARK-II
K*K ρπ
The assumptions:
1. pQCD is valid at c-quark mass
2. “pQCD rule” derived for inclusive decays holds for
exclusive channels.

11. J/, (2S)衰变模式 衰变模式 J/ 分支比 (%) (2S) 跃迁 强子跃迁 辐射跃迁 0.0 1.3 51.5 26.3
跃迁 强子跃迁
辐射跃迁
0.0
1.3
51.5
26.3
轻子对衰变
11.8
1.7
强子衰变 电磁衰变
强衰变
13.5
69.1
17.7
辐射衰变
4.3
1.1
稀有衰变
<<1.0 总和
100.0

12. What we observed in experiment

13. 连续态振幅对物理的显著影响
分支比 相角
与共振态之间的干涉应考虑
连续态贡献应被扣除
连续态贡献不能忽略!

14. A universal -90°phase? |φ| J/ψ Decays: ψ(2S) 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)
(103±7)° BES, PRD69, (2004)
4. VV: (138 ±37)° L. Köpke and N. Wermes, Phys. Rep. 174, 67 (1989)
5. NN: (89 ±15)° R. Baldini et al., PLB444, 111 (1998)
ψ(2S) Decays:
1. VP: φ=180° (± 90 ° ruled out!) M. Suzuki, PRD63, (2001)
φ=180° or φ=-90° P. Wang et al., PRD69, (2004)
2. PP: (-82±29)° or (121±27)° BES, PRL92, (2004)
& Yuan, Wang, Mo, PLB567, 73 (2003)
|φ|=(95±15)°, CLEO, PRD74, (2006)

15. 如何测量分支比
纯强衰变末态
纯电磁衰变末态
强+电磁衰变末态

16. φ ψ(2S)PP (赝标量介子对) ψ(2S) π+π- 电磁衰变 ψ(2S) KS KL 强衰变
ψ(2S) K+K 强+电磁衰变
B’ (+-) and
A’+B’ (K+K-) known,
KS KL is needed to extract
the phase
between A’ and B’. φ
When extract A’/B’ from experimental information,
Continuum contribution should be considered!

17. 纯强衰变末态
No continuum contribution
Count number of events
Use formula

18. 纯强衰变末态 利用重建KS BESII, 58 Million J/ψ BESII, 14 Million ψ(2S)
PRD 69, (2004)
B (J/  Ks K L) =
(1.82 ± 0.04 ± 0.13) ×10-4
B ((2S)  Ks K L) =
(5.24 ± 0.47 ± 0.48) ×10-5
MC Bkg K*0KS+c.c.
etc.
Ks mass sidebands
B ((2S)  Ks K L)
= (28.8±3.7)%
B (J/  Ks K L)
PRL 92, (2004)
利用重建KS

19. 纯电磁衰变末态
共振态与连续态间关系确定
在一个能量点采集数据，计算分支比

20. 强+电磁衰变末态 K
共振态与连续态间关系不确定，依赖电磁与强衰变间的振幅比例和相角
至少在三个能量点采集数据，计算分支比

21. ψ(2S)PP
假设形状因子相同
三个测量，三个未知数
引进理论假设，利用共振峰数据，计算分支比和相角

22. ’  PP First measurement of the phase in ’ decays! K+K– & +
B (’ KS KL )
=5.810 – 5
K+K– & +
 inputs ;
Input 1: DASP;
Input 2: BESI ;
Input 3: K+K–
from BESI &
+ by form
factor.
B (’ KS KL )
=5.2410 – 5
Yuan, Wang, Mo: PLB567 (2003)73
–(80??)°
(120??)°

23. “ puzzle”
MARK-II
Violation found by Mark-II , confirmed by BESI at higher sensitivity.
Further studied by BESII and CLEOc
Can/should be improved at BESIII
K*K ρπ

24. ’ + - 0 BESII CLEOc BES and CLEOc in good agreement! 229 0s
BESII: PLB619, 247 (2005)
CLEOc: PRL94, (2005)
229 0s
196 0s
BESII
CLEOc
BES and CLEOc in good agreement!

25. ’ + - 0
Dalitz plots after applying 0 mass cut!
Very different from J/ 3!
CLEOc
BESII
J/
Similar Dalitz plots, different data handling techniques:
PWA vs counting!
’ is observed, it is not completely missing, BR is at 10-5 level!

26. J/ + - 0 Make  mass cut, and count events
PWA analysis assuming  interferes with excited  states
L. P. Chen and
W. Dunwoodie, Hadron’91, MRK3 data
PDG04: 1.270.09%
Very
different!

27. J/ , ’  ρπ
Greatly suppressed!

28. J/, ’ VP BESII : PLB614, 37 (2005); PRD73, 052007 (2006)
CLEOc: PRL94, (2005)
mode
BESII:
B(’)(×10-5)
CLEOc:
PDG06/BESII/…
B(J/)(×10-4)
B(’)/B(J/)
(%) 
5.1±0.7±1.1
±0.2
234±26
0.13±03
(2150)
19.4±
N/A
+-0
18.1±1.8±1.9
±2.8
200±9
0.92±11
K*0K0+c.c.
13.3±2.7±1.7
±0.9
42±4
2.6±0.6
K*+K-+c.c.
2.9±1.7±0.4
±0.3
50±4
0.34±0.20 
±0.28
±0.2
5.38±0.66
3.7±1.2 
±0.17
±0.2
1.93±0.23
10.9±3.4
’
±0.33
1.05±0.18
18±16 
<0.40
<0.064 
3.3±1.1±0.5
±0.4
8.98±0.92
3.0±1.2
’
3.1±1.4±0.7
5.46±0.64
5.7±3.0 
<3.1
<1.1
23.5±2.7
<0.53
’
±0.7
2.26±0.43
14±11

29. pQCD rule and “ρπ puzzle” VT
ωf2(1270)
Φf2’(1525)
BESII, PRD69,
072001(2004)
14 Million ψ(2S)
6.0σ
4.3σ
3.6σ
VT mode
B(2S) X (10 – 4)
(BES-II)
B J/X (10 – 3)
(PDG2002)
Qh(%)
 f2
2.05± 0.41 ± 0.38
4.3±0.6
4.8±1.5
 a2
2.55± 0.73± 0.47
10.9±2.2
2.3±1.1
K* K*2
1.86± 0.32 ± 0.43
6.7±2.6
2.8±1.3
 f2'
0.44 ± 0.12 ± 0.11
1.23±0.21 †
3.6±1.5
ρa2(1320)
K*K2*(1430)
† This value from DM2 only
5.3σ
Suppressed!!
BESII first observations!
VT is suppressed less than VP!

30. Very small in ’’ decays
’’ + - 0
Very small in ’’ decays φ
phase
interference
interference
Continuum contribution is crucial in ’’ analysis:
Total ’’ charmless decays (<2nb) is much less than total continuum process (~16nb),
Inteference between amplitudes
BESII

31. ’’ + - 0 3.773GeV 3.670GeV 3.773GeV 3.650GeV
BESII: PRD72, (2005)
CLEO: PRD73, (2006)
BESII
CLEOc
3.773GeV
3.670GeV
3.773GeV
3.650GeV
BES and CLEOc are in good agreement!
X-section at ’’ peak is smaller than at continuum!

32. BESII: PRD72, (2005)
CLEO: PRD73, (2006)
’’ + - 0
BESII
CLEOc
3.773
3.65
3.773
3.67
Subtle difference in handling efficiency and ISR correction.
BES and CLEOc are in good agreement!
X-section at ’’ peak is smaller than at continuum!
non-zero ’’ amplitude.

33. ’’   Total cross section Three unknowns with two equations ---
Wang, Yuan and Mo:PLB574,41(2003)
Total cross section
Three unknowns with two equations ---
One can plot the BR versus phase .
B depends on efficiency and ISR correction,
efficiency and ISR correction depends on B(s) !
Iteration is necessary!

34. ’’   BES data restrict BR and phase in a wide range (@90% C.L.):
BESII: PRD72, (2005)
CLEOc: PRD73, (2006)
’’  
BES data restrict BR and phase in a wide range C.L.):
CLEOc data further restrict BR and phase in a ring*. At =-90:
*Toy MC is used to get BR from CLEOc data (not CLEO official results)!

35. pQCD rule and “ρπ puzzle” Models
Recent review:
Mo X. H., Yuan C. Z., Wang P.,
HEP&NP31,686(2007)
Models before BES:
J/-vector glueball mixing;
BLT model Hou-Soni (1983)
Brodsky et al. (1987)
2. Sequential quark pair creation Karl-Roberts (1984)
Exponentially falling form factor Chaichian & Tornqvist
(1989)
Generalized hindered M1 transition Pinsky (1990)

36. pQCD rule and “ρπ puzzle” Models
Models after BES:
Final-state interactions Li-Bugg-Zou (1997)
Intrinsic charm |qqcc>
Fock components of the light
vector mesons Brodsky-Karlin (1997)
3. Fock state with ccbar pair
in a color-octet Chen-Braaten (1998)
cc annihilation into 5g
via 2 steps Gerard-Weyers (1999)
5. Decays thru light-quark Fock
component by a soft mechanism Feldmann-Kroll (2000)
6.  (2S)-vector glueball mixing Suzuki (2001)
7. (2S)-(1D) mixing Rosner (2001)

37. pQCD rule and “ρπ puzzle” Models
Model predictions Test results Theo. Exp.
HS/BLT Glueball at Not seen  
M3.0 GeV 0 not
all VP suppressed suppressed.
CT All two-body (2S) (2S) b1
decays suppressed not suppressed 
B()7 <310-5
Pinsky Q()2  ! 
f2 suppressed No
f2 not suppressed Suppressed
KR B() small Big 
 cross section
btwn (2S) & J/ No data !

38. pQCD rule and “ρπ puzzle” Models
Model predictions Test results Theo. Exp.
LBZ Big rates for Not seen !
(2S)  a1, K1*K*
BK All VP suppressed 0 not
suppressed  
CB Many VP BRs Agree !
b1 not suppressed Agree
a2 a bit suppressed Agree
Angular distributions No data !

39. pQCD rule and “ρπ puzzle” Models
Model predictions Test results Theo. Exp.
GW Copious h1(1170)
in (2S) No ? !
FK VP BRs Agree 
cVV BRs Agree
cVV suppressed No data
Suzuki Vector glueball at
M3.7 GeV No data !
Rosner Measurable
VP No data !

40. “12%” rule ’ VP suppressed
’ PP enhanced
’ VT suppressed
’ BB obey/enh
Multi-body –obey/sup
Seems no obvious rule to categorize the suppressed, the enhanced, and the normal decay modes of J/ and ’.
The models developed for interpreting specific mode may hard to find solution for other (all) modes.
Model to explain J/, ’ and ’’ decays naturally and simultaneously?
S-D mixing in ’ and ’’ [J. L. Rosner, PRD64, (2001)]
DD-bar reannihilation in ’’ (J. L. Rosner, hep-ph/ )
Four-quark component in ’’ [M. Voloshin, PRD71, (2005)]
Survival cc-bar in ’ (P. Artoisenet et al., PLB628, 211 (2005))
Other model(s)?

41. pQCD rule and “ρπ puzzle” Conclusions
Many experimental results
Many theoretical models
Explanation still not satisfactory
*()&%*)(#%дмфёЊ
حشع٣ؤضء
ž¤&ùÐ…
Questions need to be fixed:
Is the abnormal in J/ψ or in ψ(2S) decays or in both?
Are there assumptions behind the experiments and/or theories?
What is the key issue to solve the problem?
The puzzle remains a puzzle …
Both experimentalists and theorists are working hard …

42. Outlook The End Lots of fun in charmonium physics,
Lots of fun in charmonium decays,
Lots of puzzles in hadronic final states,
All wait for you, a smart guy
To solve them by joining us,
And to win the ??? prize!
联系电话： (O)
The End
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