BESIII Detector
In charmornium family, ψ(2S) is in a special position. ψ(2S) can decay into η c
,
J/ψ, χ cJ
(J=0,1,2), and possibly into
1
P
1
states. Therefore, by collecting sufficiently large ψ(2S) data sample, one can not only study the property of ψ(2S), η c,
J/ψ, χ cJ
(J=0,1,2), but also search for
1
P
1
states.
The ψ(2S) data sample collected at BEPC/BESI is 4 millions, and at
BEPC/BESII 14 millions, with which the BES collaboration has made various studies on ψ(2S), J/ψ and χ cJ
(J=0,1,2), and copious results have been reported
[1-14]
. At
BEPCII, one year running will produce 3x10
9 ψ(2S) events, which is a factor of 150 more than that at the BESI and the BESII combined. Statistical error will be improved by at least a factor of 12. In addition, the designed performance of the BESIII detector is much improved with respect to that of BESII, the systematic error is expected to be reduced by a factor of 4 on average for all measurements.
3.6.1
The BES collaboration has measured branching fractions or upper limits for various hadronic decay channels listed in Table 3.6-1. The statistical errors are in the range of 10% to 30%, and the systematic errors are in similar values. At
BEPCII/BESIII, the statistical and systematic errors will be reduced to (1-3)% and
(2.5-8)%, respectively, corresponding to a total error of (2.7-8)%. For the upper limits, the sensitivity of BESIII will improve by a factor of at least 100.
Since J/ψ and ψ(2S) decays into light hadrons via ggg, γ*, or γgg, their partial widths of decays are proportional to |ψ(0)| 2 , where ψ(0) is the wave function at the origin in the non-relativistic quark model for cc . Thus, it is reasonable to expect [15] on the basis of the perturbative QCD that, for any hadronic final state h, the ratio Q h should follow:
Q h

B

2 S )


 h ) h )

B

2 S )

 
)
)

( 14 8

2 2 (1) where the leptonic branching fractions are taken from PDG2000
[15]
. This relation is sometimes called PQCD 15% rule. The Q h values measured at BES for various ψ(2S) hadronic decays based on PDG’s value for J/ψ branching fractions are listed in Table
3.6-1.
( pp ,
Most of decay channels, including AP( b
1

), VS(
 f
0
), BB
,
0 0
,
 
,
 
,
  *

) and multi-hadron final states, have
59

BESIII Detector relative branching fractions in agreement with PQCD expectations. The intriguing puzzle, reported in 1983 by the Mark II experiment
[12]
, is that the Q h for

and
K K
*

 confirmed by the BES results with much higher sensitivity branching fractions of

( 2 S )
 
and

( 2 S )

[7]
K K
. The upper limits on the

*

 more than a factor of 60 and 20, respectively, lower than the 15% rule predictions.
The four

( 2 S )

VT decay modes(
  a
2
,
 f
2
'
, K
*0
K
2
*0
) are suppressed also by a factor of at least 3
[2]
. For the AP decay channel, the BES collaboration observed flavor-SU(3)-violating K
1
(1270)-K
1
(1400) asymmetries with opposite characters for the

(2S) and J/
 [5]
, which cannot be accommodated by adjustments of the singlet-triplet mixing angle
[18]
. All these suppressions and anomaly can be further studied with higher accuracy and higher statistics at BEPCII/BESIII.
Table 3.6-1 BESI measured ψ(2S) decay branching fractions and PQCD 15% rule test(# denotes preliminary results; upper limits at C.L.=90%)
Channel

Br(ψ(2S)) (10 -4 )
0.53

0.31

0.08
Br(J/ψ) (10 -3 )
0.86

0.08
Q h
(%)
6.2

3.8
γX
 
1.54

0.31

0.20 4.31

0.30 3.6

0.9 b
1

5.2

0.8

1.0 3.0

0.5 17.3

5.1
AP K
1

( 1270 ) K

10.0

1.8

2.1 < 3.0 >33.3
K
1

( 1400 ) K

<3.1 3.8

1.4 < 8.2
VT  f
2
<1.7 4.3

0.6 < 4.0
 a
2
<2.3 10.9

2.2 < 2.1
 f
2

( 1525 )
K
*0
K
2
*0  c c
<4.5
<1.2
1.23

0.06

0.20
6.7

2.6
< 3.7
< 1.8
VP
# K
*0
K
*0
2
#

 c c
#
K K
*

( 892 )
 c c
0.798

0.528
<0.29
<0.23
6.7

2.6
12.8

1.0
5.0

0.4
1.20

0.93
< 0.23
< 0.46
60

BESIII Detector
VS
VV
#
*0
( 892 )
 c c
#
 f
0
1.30

0.34

0.16
0.63

0.18
K
*0
K
*0  c c
#

K K
#
 pp
#
#

K K
#
#
 pp

#
   0 pp
BB
#
#
 pp pp
 pp
  *

  *0
3.49

0.64
2.47

0.96
<1.8
2.16

0.39
1.81

0.34
1.2

0.6
0.94

0.31
1.28

0.35
1.1

0.4
<0.81
0.392

0.103
1.25

0.56
0.64

0.26
1.68

0.32
0.58

0.22
0.082

0.052
6.04

0.90
4.2

0.4
0.32

0.09
0.29

0.04

0.06 13.6

4.9
0.74

0.24
1.30

0.25
16.9
5.

9.4

2.2
0.80

0.12
0.83

0.13
0.045

0.015
21.0

5.1
7.0

2.9
18.1

12.8
2.3

0.9
2.09

0.18
2.12

0.10
1.30

0.12
1.27

0.17
0.9

0.2
1.10

0.29
1.03

0.13
3.1

1.0
19.6

7.8
15.2

6.6
< 8.6
10.1

1.9
13.9

2.9
9.4

4.6
10.4

4.1
11.6

4.5
11

4
<0.73
61

BESIII Detector
By using the Vector Dominance model, a radiative decay might (or might not) be connected to the corresponding hadronic decay. It is therefore interesting to examine whether suppressions exist for radiative decays too. The BESI has measured the branching fractions of
 
' channels (also listed in Table 3.6-1) and calculates the corresponding Q  =6.2% and Q 
'
=3.6%, clearly a suppression by a factor of about 2 and 4, respectively. We will further study these suppressions and extend to more channels, such as , f
1
, f
2
, f
2

, ... etc. at BEPCII/BESIII with higher accuracy and statistics. BEPCII also provides an opportunity to search for glueball candidates such as η(1440), f
J
(1710), ξ(2230), etc. via radiative decays.
3.6.2
BESI has determined the most accurate branching fraction of J/ψ leptonic decay
B ( l
 l

)

( 5 .
87

0 .
04

0 .
09 )% [3] , via processes of

( 2 S )
  
J /

, J /
  l l , J /
  anything .
At BEPCII/BESIII, the statistical error will be negligible and systematic error will be reduced to 0.03%, thus the relative error of ) will be lower than 0.5%.
3.6.3
cJ
BESI has measured many branching fractions of
 cJ decays
[6]
, with much improved accuracies and many of them the first measurements (see Table 3.6-2).
From PDG1998
[19]
to PDG2000
[16]
, the scenery for
However, the statistical and systematic errors for
 cJ decays are greatly changed.
 cJ
decay branching fractions are still too large, at the level of (6-20)% and (15-30)% respectively. At BEPCII/BESIII, the statistical errors will be negligible and the systematic errors will be reduced to about (4-8)%.
The widths of
 cJ
decaying into light hadrons are theoretically interesting, since the contribution of the color octet component in the cc wave function might also be involved, in addition to the
3
P
J
color singlet component, according to the
NRQCD theory
[15]
. The widths of
 cJ and χ c2 are measured precisely by E760, and the width of χ c0
by BESI
[6] . At BEPCII/BESIII, the error of χ c0
can be reduced by a factor of two.
A careful study of the angular distribution of the radiative decay
 cJ
   with high statistics at BESIII will provide more information on the transition matrix elements, which are closely related to the cc wave functions and interquark forces.
62

BESIII Detector
Table 3.6-2 Measured χ cJ
width and branching fractions by the BESI.
(upper limits at C.L.=90%)
Channel BES results PDG2000
 c 0
 c 2

    
(4.68
(1.49

0.26

0.65)

10 -3

0.14

0.22)

10 -3
(5.0
(1.52

0.7)

10 -3

0.25)

10 -3
 c 0

K K

(5.68

0.35

0.85)

10 -3 (5.9

0.9)

10 -3
 c 2
 c 0
 c 1
 c 2

K K

 pp
 pp
 pp
(0.79
(1.59
(4.2
(5.8

0.14

0.13)

10 -3

0.43

0.53)

10 -4


2.2
3.1


2.8 )
3.2 )


10
10
-5
-5
(8.1
(2.2
(8.2
(9.8

1.9)

10 -4



1.3)

10 -4
1.3)
1.0)


10
10
-5
-5
 c 0
 (15.4

0.5

3.7 )

10 -3 (2.0

0.9)

10 -2
 c 1

(4.9

0.4

1.2 )

10 -3 (5.6

2.6)

10 -3
 c 2
 (9.6

0.5

2.4 )

10 -3 (1.2

0.5)

10 -2
 c 0
  
K K

(14.7

0.7

3.8 )

10 -3 (1.8

0.6)

10 -2
 c 1
  
K K

(4.5

0.4

1.1 )

10 -3 (4.9

1.2 )

10
 c 2
  
K K

(7.9

0.6

2.1 )

10 -3 (1.0

0.4)

10 -2
 c 0
 c 2
 c 0
 c 2
 c 0
 c 0
 c 1
 c 2
    pp
   pp

   pp

3 (
 
)
 c 0
 c 1
 c 2

3 (
 
)

3 (
 
)



K K
0 s


K K
0 s


(1.57
(0.49
(1.23
(11.7
(5.8
(9.0
(1.96
(0.61


0.13

0.17)

10 -3

0.20

0.35)

10 -3

0.21
0.55

0.7
(0.92

0.34

(2.00
K K K K

(2.14
 
0.54)

0.61)

10 -3
1.2 )
0.38)


10 -3 (6.3

1.4)

10 -2
10 -3

10 -3
(1.8

0.9)

10 -3

1.0

2.3 )

10 -3 (1.24

0.22)

10 -2

1.0

2.0 )


0.28

0.52)

10 -3

0.17

0.16)

10 -3

0.26

0.40)

10 -3
 c 1
 c 2
 c 0
 c 1
 c 2




K K K K

(0.42

K K K K

(1.48
K K

K K

K K




(2.46

0.15

0.12)

10 -3

0.26

0.32)

10 -3


0.44

0.65)

10 -3

10
10
-3
-3
10 -3
(5.4
(1.4
(9.2

2.1)

10 -4

0.6)

10 -3

2.2)

10 -3
-3

 c 0
14.3

2.0

3.0 MeV 14.9+2.6-2.3MeV
63

BESIII Detector
The radiative decay rates of
 c 0
,
 c 2

2

are also interesting, to which both
QCD radiative correction and relativistic correction may be important. The estimated branching ratio is roughly
B

2 S )
  c 0
)

B (
 c 0

2

)

.
 

4  

5
(2)
Due to the limited statistics and poor photon energy resolution, this measurement is not feasible at BEPC/BESI. However, with one year of running at BEPCII, about
40000 signal events of this channel can be collected(assuming an efficiency of 40%) , which will produce a statistic uncertainty no more than 1%.
 c 0
The
 cJ
may decay into light hadrons via gluon intermediate state, e.g.,

2 g
 hadrons. It is plausible that a pair of glueballs could be favorably produced in its decay process. With higher statistics and better particle ID of
BEPCII/BESIII, it is possible to study hadronic decays like
 c 0

2 (
 
),
      
,
 
,... (3) and look for some 0
++
and 0
-+
glueballs, e.g., f
0
( 1500 )
    
, f
0
( 1400 )
 
, f
0
( 975 )
 
, KK ,

( 1440 )

KK

.
(4)
3.6.4
1
1
The R704
[23]
, E760
[24]
and E705
[25]
experiments claimed the existence of
1
P
1 state in 1986, 1992 and 1994, respectively. However, the signal statistics is so low(5,
59 and 42 events respectively in these three experiments) that the existence of the
1
P
1 state still needs to be confirmed.
Some theoretical calculations taking into account the effect of S-D mixing
[21] gives
B

2 S )
 1
P
1
 0
)

4
(6)
In addition, 1 P
1
  c
is expected to be the dominant decay mode. Therefore, we can search for
1
P
1 via the decay mode

( 2 s )
  0 1 P
1
  c
 
4 K . (7)
The branching ratio of
 is 2.9

10
-6
. From 3

10
9

( 2 c
S
to 4K is 2.1

10
-2 ， so the total branching ratio of (7)
) event, we can obtain 8700 event, which is enough for confirming the existence of
1
P
1
.
64

BESIII Detector
0

( 2 S )
 n
 
4 Pr ong

( 2 S )
Table 3.6-3 Signal and background channels in 1 P
1
search
 
0 1
P
1
  c
 
4 K
B ( 10

6
)
2.90
No. Of MC events
8700
1

( 2 S )
  c 1
 
J /
    
4 K 2.29 6870
2

( 2 S )
  c 2
 
J /
    
4 K 1.02
3

( 2 S )
 
J /
    
4 K 1.02
3060
3060
4

( 2 S )
 
0

0
J /
 
5
 
5

4 K 17.26 51780
5

( 2 S )
 
0

0
J /


( 2 S )
 
0

0
J /

 
0

0

K

K
 
0

0
4 K

4

4 K

4

4 K
88
127
645000
(sum of two)
From Table 3.6-3 we can see that most of the background channels have J /
 resonance. For J /

, the branching ratios of 4K+X is less than those of
(

)
   through
    
, (

)
   
K

K

, (

3

4 K than through 3
) K
 
  

 
 
 
 
. This makes the search much easier

, 3
   
K

K

, 3

K
      
. In the process, 1 P
1 is almost at rest. Therefore the signal event has the following characters that we can use to select the signal and reject the background.
1)
2)
M
4 K
M
4 K ,


2980 MeV ( the mass of
 c
)

3526 MeV (the mass of
1
P
1
)
3) E 
1

504 MeV (

1 is almost monotonous energy )
4) cos

4 K ,

1
 
1
5) M

2

3

M

0
Based on the parameters of BEPCII/BESIII, a full simulation of 3

10
9

( 2 S ) events is performed.
After all the selection, the backgrounds is only 1%, as shown in Fig. 3.6-1 —
3.6-2. We can see that the peaks of
1
P
1
and
 c can be observed clearly.
65

BESIII Detector
Fig 3.6-1. invariant mass of

1
4K （ 1T ） for
1
P
1
signal Fig.3.6-2. invariant mass of 4K （ 1T ） for
 c signal
[1] J.Z.Bai et al., BES Collab., Phys. Rev. Lett. 81 (1998) 3091.
[2] J.Z.Bai et al., BES Collab., Phys. Rev. Lett. 81 (1998) 5080.
[3] J.Z.Bai et al., BES Collab., Phys. Rev. D58 (1998) 092006.
[4] J.Z.Bai et al., BES Collab., Phys. Rev. D58 (1998) 097101.
[5] J.Z.Bai et al., BES Collab., Phys. Rev. Lett. 83 (1999) 1918.
[6] J.Z.Bai et al., BES Collab., Phys. Rev. D60 (1999) 072001.
[7] J.Z.Bai et al., BES Collab., Phys. Rev. D62 (2000) 032002.
[8] J.Z.Bai et al., BES Collab., Phys. Rev. D63 (2001) 032002.
[9] J.Z.Bai et al., BES Collab., Phys. Rev. D65 (2002) 052004.
[10] X.H.Li, representing BES Collab., Nucl. Phys. B (Proc. Suppl.) 75B (1999)
181.
[11] F.Liu, representing BES Collab., Nucl. Phys. A675 (2000) 71c.
[12] X. Y. Shen, representing BES Collab., Recent results from BES, IV Intern.
Conf. on Hyperons, Charm and Beuty Hadrons. June 26-30, 2000, Valencia,
Spain. Will be published in Nucl. Phys..
66

BESIII Detector
[13] Y.S. Zhu representing BES Collab.,Recent results of charmonium physics from
BES, Proc. 30 th
Inter. Conf. on High Energy Physics,Jul.27-Aug.2,2000,Osaka,
Japan
[14] Y.S.Zhu, representing BES Collab., Recent results of

( 2 S ) decay branching ratios and dacay widths from BES,IX Inter. Conf. on Hadron Spectroscopy,
Aug.26-Sep.1,2001,Protvino,Russia.
[15] S.J. Brodsky and M.K. Karliner, Phys. Rev. Lett. 78 (1997) 468,Yu-Qi Chen and Eric Braaten, Phys. Rev. Lett. 80 (1998) 5060; and references therein.
[16] D.E.Groom et al., Particle Data Group, Eur. Phys. J. C15 (2000) 1.
[17] M.E.B. Franklin et al., Mark II Collab., Phys. Rev. Lett. 51 (1983) 963.
[18] Preliminary results from this analysis are discussed in the context of SU(3) symmetry breaking, in M. Suzuki, Phys. Rev. D55 (1997) 2840.
[19] C.Caso et al., Particle Data Group, Euro. Phys. J. C3(1998) 1.
[20] G.T.Bodwin et al., Phys. Rev. D46 (1992) 1914.
[21] C.Z.Yuan, BES97(1997)191.
[22] Edwards et al.Phys.Rev.Lett. 1982,48:70.
[23] C.Baglin et al., Phys. Lett. B171 (1986) 135
[24] T.A.Armstrong et al., Phys. Rev. Lett. 69 (1992) 2337
[25] L. Antoniazzi et al., Phys.Rev. D50 (1994) 4258
[26] Y.P.Kuang et al., Phys. Rev. D37 (1988) 1210
67