The BESIII Detector Physics Goals and...
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Chapter 4 The BESIII Detector Physics Goals and Design 4.1 Introduction 4.1.1 Major achievements of BES It has been 12 years since the commission of the Beijing Spectrometer (BES) at Beijing Electron Positron Collider (BEPC). Both machine and detector have undergone the upgrade. The upgraded BES is named BESII and the machine stays the same name as BEPC. So far the peak luminosity of the machine is about 510 30 /cm 2 s at the J/ resonance. The major parameters of the detector performance of both BESI and BESII are listed in table 1. With the data collected, BES collaboration has been studying light hadron spectroscopy, searching for 1
Transcript of The BESIII Detector Physics Goals and...
The BESIII Detector Physics Goals and Design
Chapter 4 The BESIII Detector Physics Goals and Design
4.1 Introduction
4.1.1 Major achievements of BES
It has been 12 years since the commission of the Beijing Spectrometer (BES) at Beijing Electron Positron Collider (BEPC). Both machine and detector have undergone the upgrade. The upgraded BES is named BESII and the machine stays the same name as BEPC. So far the peak luminosity of the machine is about 5(1030/cm2s at the J/( resonance. The major parameters of the detector performance of both BESI and BESII are listed in table 1.
With the data collected, BES collaboration has been studying light hadron spectroscopy, searching for glueball, exotic states, charmed mesons, baryonic excited states, rare decays, and test of QCD in the BEPC energy region. Table 3 lists the entries contributed to the Particle Data Group from the BES. Following are some of the important results:
Table 1. Major parameters of the BES detector performance
Detector
Major para.
BESI
BESII
VC
(x,y ((m)
200
100
MDC
(xy ((m)
(p/p (%)
(dE/dx (%)
200-250
1.78 ((1+p2)
7.9
~220
1.78 ((1+p2)
8.4
BTOF
(T (ps)
375
180
ETOF
(T (ps)
720
BSC
(E/(E (%)
(z (cm)
23.8
4.5
20.3
2.3
Table 2. Data Collected with BESI and BESII
Ecm (GeV)
Physics
BES Data
3.1
J/(
7.8(106
0
4
8
12
16
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
y
(2S) decay
braching ratio
G
c
0
(total)
B(
c
c0,1,2
->ppbar)
B(
c
c0,2
->
p
+
p
-
/k
+
k
-
)
B(J/
y
->
L
L
bar
B(J/
y
->e
+
e
-
/
m
+
m
-
)
B(D
s
+
->e
+
X/
f
X), B(D->
m
n
)
f
D
f
D
s
B(J/
y
->
g
f
J
)B(f
J
->K
+
K
-
)
G
f
J
m
f
J
B(
x
)
m
x
R scan
m
t
s
syst
/
s
stst
3.69
((2S)
3.7(106
4.03
(
1.0(105
4.03
DS, D
22.3 pb-1
~3.55 (m( scan)
m(
5 pb-1
l
l
c
c
¢
L
m
m
g
g
p
2
4
2-5 (R scan)
R value
6+85 points
3.1
J/(
2.5(107
Table 3. Entries contributed from BES to the Particle Data Group
Total entries=84.
Physics
J/(
((2S)
D+DS
(
Entry
34
44
5
2
6
5
5
10
3
.
8
)
/
(
10
9
.
4
)
/
(
10
7
.
2
)
/
(
-
-
+
-
-
+
-
-
+
´
<
®
Y
´
<
®
Y
´
<
®
Y
e
J
Br
J
Br
e
J
Br
m
m
t
t
Figre 1. The J/((left) and ((2S)(right) event sample in the world. BES accumulated
the world largest J/( and ((2S) events samples. Unit in million.
· The precision measurement of the mass of the (,
20
.
0
18
.
0
16
.
0
19
.
0
96
.
1776
+
+
-
-
=
t
m
MeV/c2. This value differs 7.1 MeV/c2 from the previous PGD value, and plays an important role in understanding the lepton universality.
· Confirmation of the glueball candidate ((2230) in K+K- and KS0KS0 decay modes, and for the first time found the evidence of ((2230) in decay modes (+(-, (0(0,
p
p
.
· More than ten first measurements of the ((2S) and (cj decays. E.g. the first measurement of ((2S)((+(-, baryon+anti-baryon. Confirmed the vector pseudo-scalar suppressions in ((2S) in
.
.
*
,
c
c
K
K
+
-
+
rp
; Found new vector tensor suppression modes were in
'
2
0
*
2
0
*
2
2
.,
.
,
,
f
c
c
K
K
a
f
j
r
v
+
;and large isospin violating effect in ((2S) decay in
.
.
)
892
(
.,
.
)
892
(
,
,
*
0
*
0
c
c
K
K
c
c
K
K
+
+
-
-
+
vp
rp
The study of the decays of the ((2S) and its decayed products significantly helps understand NQCD.
· Direct measurement of decay constant fDs from pure leptonic decay,
)
40
430
(
150
130
±
=
+
-
Ds
f
MeV.
· The first direct model-independent measurement of Br(DS(((),
)%
9
.
3
(
)
(
8
.
1
1
.
5
1
.
1
9
.
1
+
+
-
-
=
®
jp
S
D
B
· R values in 2-5 GeV energy region. A factor of 2-3 improvement in the uncertainty of the R-value has a great impact on the predicted Higss mass and the interpretation of the g-2 measurement carrying out at BNL.
4.1.2 From BESII to BESIII
Although the detector has achieved its design goal at the time when it was first built and then upgraded and great achievement has been made by BES at BEPC, the BESII detector was designed for accepting single bunch and the machine luminosity below 1031/cm2(s. It's actually almost a copy of MarkIII, of which the technology utilized is about twenty years old. The following are its shortcomings needed to be overcome.
1. The sampling type barrel electromagentic calorimeter is working with SQS mode
and has been running for 12 years. It has never been upgraded. The poor energy resolution significantly limited the detection for the photons. On the other hand, the output signal is very much sensitive to the content of the n-pantane and the BES hall temperature. The pulse height fluctuates about 30% while operating the detector from autumn to the spring of next year. A better detection for the photons is crucial in many important physics topics, particularly in searching for glueballs since there is little doubt that the radiative decay of the J/( is the best place to hunt them.
2. The tracking system does not use low Z gas and wires. The momentum and dE/dx resolution are marginal accepted for conventional physics topics. Both momentum and dE/dx resolution should be improved for better particle identification.
3. The endcaps of the detector cannot be opened without removing all the electronics in front of the endcaps and breaking the vacuum of the beam pipe around the detector. This drawback seriously limits us to repair electronics. e.g. preamplifiers, and the broken wires of the VC, MDC and BSC. On the other hand, the detection information from the endcap detectors, which is consisted of ETOF and ESC, has never been really used for physics analysis due to its insufficient resolution of time-of-flight of ETOF (700 ps) and incomplete track finding and fitting.
4. The muon counter has too small a coverage.
5. The electronics system has never been upgraded. It is suffering aging problem seriously. Many spares are no longer available in the nowadays market, therefore it's extremely difficult to maintain the electronics for normal data taking.
6. There is no slow control system.
It is known that generally speaking, (exp = ((stat2 + (syst2)1/2, where (exp , (stat and (syst are the total experimental error, statistic error and systematic error respectively.
Since the goal of the BEPC II is to increase the peak luminosity from about 5(1030/cm2(s to 5(1031/cm2(s at the J/( resonance, using multi-bunch train. A factor of ten improvements in statistics needs about a factor of three improvements in systematic error, which requires a better detector.
Figure 2 shows the ratio between the systematic error and the statistic error for the results from most of the published paper from BES. One sees that the errors are mostly dominated by systematic errors. This indicates that BESII is actually not good enough to match the present BEPC luminosity.
.
)
(
)
(
/
)
(
)
(
X
q
B
q
A
J
p
e
p
e
+
+
®
Y
®
-
+
+
-
-
+
Figure 2. Ratio between the systematic error and the statistic error for the results from most of the published paper from BES.
4.1.3 Design philosophy for BESIII
Learn the lessons from the BESII, our design philosophy for BESIII is to improve the particle identification; increase the power for the photon detection; be able to open the endcaps fast (e.g. within in two to three days); increase the coverage by building new endcap detector; improve the stability of the long term performance of the detector; replace all the aging electronics and equipments. The detector should be able to adapt the new environment of BEPCII, particularly in the interaction region. Following are the major requests to the BESIII:
· Improve the photon detection so that the energy resolution can be better than 10%/(E (GeV) and the spatial resolution is comparable to BESII.
· Improve the resolution of the time-of-flight measurement to about 120 ps.
· Improve the momentum and dE/dx resolutions to the detection of charged particles by using helium based gas and aluminum wires for the drift chamber.
· New trigger system using pipeline; new DAQ system which extensively adopt data buffer, parallel processing and network techniques; new electronics to adapt about 20 times higher event rate and much more noisy environment.
· New vertex chamber and luminosity monitor to adapt the new face of IR of BEPCII.
4.2 Physics at BEPCII
4.2.1 Physics feature in BEPC energy range
Physics feature in the BEPC energy region (2-5 GeV center-of-mass energy) are (1) rich of resonances, charmonum and charmed mesons; (2) distinct threshold characteristics; (3) transition energy region between smooth and resonances, perturbative and non-perturbative QCD; (4) it's an energy location of glueball, hybrid and exotic states. Significant contribution in the study of physics in this energy region was done by many experiments at VEPP-2M, VEPP2, SPEAR, ADONE, DCI and DM2 in the early seventy's. However, these laboratories soon moved to higher energy for hunting new particles, giving BES at BEPC an unique position in the world in the study of light hadron spectroscopy, charmonia and charmed mesons, search for gluenic matter and test of low energy QCD.
,
|
|
1
-
+
-
+
´
×
´
×
=
q
q
p
q
q
p
O
r
r
r
r
r
r
Figure1. Physics feature in the energy of 2-5 GeV range.
4.2.2 Charmonium decay physics
4.2.2.1 J/( Physics at BESIII/BEPCII
Our knowledge of mesons and in parallel, our understanding of the strong interactions have undergone several major revisions since Yukawa [1] introduced ( meson as the exchange boson for the strong interaction between nucleons. Our present understanding of the strong interactions is that they are described by a non-Abelian gauge field theory Quantum Chromodynamics (QCD) [2], which describes the interactions of quarks and gluons and thus predicts the existence of other types of hadrons with explicit gluonic degrees of freedom -- glueballs and hybrids. Therefore, the observation of glueballs and hybrids is, to certain extent, a direct test of QCD, and the study on the light hadron spectroscopy, as well as the glueball and hybrid spectroscopy will be a good laboratory for the study of the strong interactions in the strongly coupled non-perturbative regime.
After more than 20 years of theoretical effort, it has not yet been possible to calculate the glueball or hybrid spectrum from first principles, since PQCD cannot be applied at hadronic mass scale. Therefore, many QCD-based phenomenological models and calculations, such as bag models [3], flux-tube models [4], QCD sum rules [5] and lattice QCD [6] are developed to make predictions to the properties of glueballs and hybrids. Of them, lattice QCD is considered as more relevant since it originated from QCD, though it is very computer time consuming and only numerical results can be obtained without any corresponding physical insight.
1. Glueball search
In spite of using different approximations, all the models predict the existence of the lightest glueballs in the 1-2.5 GeV mass range, which is BES/BEPC's running energy region. Naively, one can expect the glueballs have the following signatures:
· no place in
q
q
nonet
· enhanced production in gluon rich processes such as central production, J/( radiative decay and
p
p
annihilation
· decay branching fractions incompatible with SU(3) predictions for
q
q
states
· reduced (( couplings
However, the glueball may mix with an ordinary
q
q
meson which has the similar mass and same quantum numbers, and thus it makes the identification of a glueball more complicated. Even so, there are some candidates of glueballs: f0(1500), fJ(1710), ((2230), etc.
a. Experimental status of some glueball candidates
· f0(1500)
The f0(1500) was observed in many experiments, such as pion induced reactions (- p ,
p
p
annihilation [7,8], central collisions [9,10] and J/( radiative decays [11,12] , while in glueball suppressed processes (( collision to KsKs and (+(-, f0(1500) is absent. All those favor f0(1500) to be a non-
q
q
state.
· fJ(1710)
The fJ(1710) is a main competitor of f0(1500) for status as the lightest 0++ glueball candidate due to its large production rate in gluon rich processes, such as J/( radiative decays, pp central production etc., and because of the lattice QCD calculation of the lightest 0++ glueball mass . The spin-parity of fJ(1710) in the observed processes is then crucial in determining whether fJ(1710) is a
s
s
or glueball.
· ((2230)
The ( (2230) was first observed by MARKIII collaboration in J/( ((
K
K
[13]. Later, GAMS [14] reported a narrow structure at 2220 MeV/c2 decaying into ((' in (-p ( (('n interactions at 38 GeV and 100 GeV. With 7.8 ( 106 J/( events, BES[15] measured J/( radiative decays and observed ((2230) in
K
K
, (( and
p
p
invariant masses. In addition, stringent limits have been placed on the two-photon coupling of the ( (2230)
by the CLEO collaboration in the reactions (( ( KsKs [16] and (( ( (+(- [17]. The copious production of ((2230) in J/( radiative decays, the narrow width and a small two-photon width of ((2230) suggest it be the lightest tensor glueball candidate. However, ((2230) was not seen in the inclusive ( spectrum by Crystal Ball collaboration and
p
p
annihilation in flight experiments at CERN .
b.Glueball search at BESIII/BEPCII
The luminosity of BEPCII will be increased by a factor of 10. Therefore, a large J/( event sample can be obtained in a relatively short time. After the upgrade of BESII to BESIII, a new barrel electromagnet calorimeter with an energy resolution of about 8% will be installed, and hopefully a new TOF with a better time resolution will replace the old one. A better calorimeter will give access to all-neutral and multi-photon final states, and a good particle identification will suppress the background effectively.
Except for some (-p reaction and pp central production results, most of the data on f0(1500) is from Crystal Barrel collaboration, who resolved two scalar states in this mass region, and determined its decay branching ratios to a number of final states, including (0(0, ((, ((', KLKL and 4(0, using
p
p
annihilation to rest. If f0(1500) is a scalar glueball, it should be copiously produced in J/( radiative decays. However, f0(1500) was only observed in J/( ( ((+(-(+(- from MARKIII and BESI 7.8(106 J/( data. Therefore, searching for more decay modes of f0(1500), such as ((, ((, ((' etc. and studying its spin-parity are important in determining f0(1500)'s nature. With 5(107 BESII J/( events, a partial wave analysis can be performed in J/( ( ((+(- channel to investigate the structure around 1500 MeV. But, this analysis will suffer a big (( contamination, compared with analyzing J/( ( ((0(0. However, due to the relatively poor energy resolution of BESII shower counter, it's very difficult to study the neutral channels and multi-photon processes by using BESII J/( data. With BESIII/BEPCII, we can study more decay modes of f0(1500) and then determine its spin-parity, which will be very important to study the nature of f0(1500).
The spin-parity of fJ(1710) is crucial in determining if fJ(1710) is a glueball or a
s
s
meson. If J=0, then the fJ(1710) and f0(1500) might well represent the glueball and the
s
s
state, or more likely each is a mixture of both. Nevertheless, if J=2, it will be difficult to assign a glueball status to fJ(1710), since that would be at odds with all current lattice gauge calculations. Recently, BES performed a partial wave analysis on J/( ( (K+K- with BESI J/( data and found a 0++ to be dominant in fJ(1710) mass region of K+ K-. fJ(1710) is also seen in other decay channels, such as J/( ( ((0(0, (((, (((' etc.. However, we encounter the same problems as we do in studying f0(1500), even with BESII 5(107 J/( events. After the upgrades of both BES and BEPC to BESIII and BEPCII, a large J/( data sample could be collected by a high performance detector, consequently, the spin-parity study of fJ(1710) from the above channels becomes possible.
For ((2230), if we combine CERN
p
p
scan result [18]
Br(((2230) (
p
p
) ( Br(((2230) ( KsKs) ( 7.5 ( 10-5 (95% C.L.)
with BES results [15]
Br(J/( ((()Br( (( KsKs)=(
2
7
0
9
1
1
.
.
.
-
+
(0.8) ( 10-5
and
Br(J/( ((()Br( ((
p
p
) = (
1
5
0
5
0
6
.
.
.
-
+
(0.5) ( 10-5
we have the lower bound
Br(J/( ((() ( (2.3 ( 0.6) ( 10-3 .
This is a large branching ratio for a radiative decay. Nevertheless, no ((2230) was observed in the inclusive ( spectrum by Crystal Ball collaboration. This lower bound also implies that all the branches, reported by BES, represent only about 10 % of the total decay width of the ((2230). One possibility is that the branching ratio to
p
p
is over estimated, and another possibility is we haven't found more decay modes or the main decay modes of ((2230). According to some theoretical predictions, ((2230) can be strongly coupled to ((', ('(', provided it is a glueball. Then, it turns out that ((2230) ( ((', ('(' would probably be the dominant decays. However, the final states of these channels have multi-prong and multi-photon. So, we require high statistics, good particle identification and good photon energy resolution to analyze these decays and search for more decay modes of ((2230), for instance, J/( ((((, ((0(0, (((, ((( etc.. On the other hand, the study of the inclusive ( spectrum directly becomes possible with a good photon energy resolution.
2 Hunting for hibrid states at BESIII/BEPCII
Hybrid mesons are color-singlet mixture of constituent quarks and gluons, such as
q
q
EMBED Equation.3
g
bound states. The evidence of the existence of the hybrid mesons is also a direct proof of the existence of the gluonic degree of freedom and the validity of the QCD theory. The conventional wisdom is that it would be more fruitful to search for low mass hybrid mesons with exotic quantum numbers than to search for glueballs. Hybrids have the additional attraction that, unlike glueballs, they span complete flavour nonets and hence provide many possibilities for experimental detection. In addition, the lightest hybrid multiplet includes at least one JPC exotics.
In searching for hybrids, there are two ways to distinguish them from conventional states. One approach is to look for an access of observed states over the number predicted by the quark model. The drawback to this method is that it depends on a good understanding of hadron spectroscopy in a mass region that is still rather murky, the experimental situation is sufficiently unsettled that the phenomenological models have yet to be tested to the extent that a given state can be reliably ruled out as a conventional meson. The situation is further muddied by expected mixing between conventional
q
q
states and hybrids with the same JPCquantum numbers. The other approach is to search for quantum numbers which cannot be accommodated in the quark model. The discovery of exotic quantum numbers would be irrefutable evidence of something new.
According to Quantum Field Theory, the JPC of the ordinary
q
q
mesons can not be: 0+-, 0--, 1-+, 2+-, 3-+, …… .These quantum numbers are called exotic quantum numbers. Hybrid mesons can have exotic quantum numbers. The hybrid state with the exotic quantum numbers is called exotic meson or exotic state. Exotic mesons can not be ordinary
q
q
states, so they must be hybrids, glueballs or multiquark states. Therefore, it is important to search for the evidence of the existence of exotic states. Recently, E852 experiment at BNL has found some evidences of the existence of exotic states at (-p collisions. The JPC’s of these exotic states are 1-+.
According to theoretical estimation, we know that :
((J/( ( MH) > ((J/( ( MM’) > ((J/( ( MG),
where M stands for ordinary
q
q
mesons, G stands for glueballs and H stands for hybrids. It means that the process of J/( hadronic decays to hybrid states will have relatively large branching ratios. So the J/( hadronic decay is an ideal place for us to study hybrid states and to search for exotic states.
Two exotic states at 1.4 and 1.6 GeV were observed by BNL[19,20]. According to BES preliminary results, there are some hints of the existence of these two states in (( invariant mass spectrum in J/((((( channel. It is expected that we could perform better study in this channel to search for exotic states at BESIII/BEPCII, for we will have much larger statistics and much better energy resolution for neutral tracks at BESIII/BEPCII. It should be stated that a good energy resolution for neutral tracks is important for the study of the exotic states, and it will help us to reduce background events and to get much better signals of (0 and (.
Some phenomenological models predict that the dominant decay channels of exotic mesons are (b1(1235) and (f1(1285). The dominant decay channel of b1 is (( and the dominant decay channels of f1 are ((( and 4(. So, it seems that these exotic states should appear in the invariant mass spectrum of 5( or (3(. If these exotic states are produced through J/(((X, then we had to study the following decay channels:
J/( ( (X, X ((((;
J/( ( (X, X (5(
J/( ( (X, X ((3(
Besides, we can study iso-scalar exotic mesons through the following channels:
J/( ( (X, X (( ((1300), ((1300) (((
J/( ( (X, X (( a1(1260), a1(1260) (((
J/( ( (X, X (K K1(1400), K1(1400) (K*(
Since there are lots of neutral and charged tracks in each channels, a large coverage of solid angle is highly necessary to preserve high data selection efficiency. Good energy resolution for neutral and charged tracks is also required to accurately measure the mass and width of these exotic states.
3 Other interesting topics at BESIII/BEPCII
The 0-+ and 1++ states in 1440 MeV mass region have been controversial for many years. There is a long time argument about whether 0++ f0(980) and a0(980) are
K
K
molecular states or not. In addition, several extra 2++ states have been observed, and they are inconsistent with quark model predictions. The baryonic decays of J/( and the study of the excited baryonic states are also important topics at BESIII/BEPCII. With the high statistics available it may even be possible to perform a partial wave analysis of (cJ decay products generated in ( ' (((cJ radiative decays. For example, (c1 ( ( H is sensitive to the hybrid exotic sector H (JPC=1-+), while (c0 ( f0(980) X would be a source of 0++.
References
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Weinberg, S., Phys. Rev. Lett. 31 (1973) 494
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Morningstar, C., et al., Phys. Rev. D 56 (1997) 4043
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14. Alde, D., et al., GAMS collaboration, Phys. Lett., B177(1986) 120
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Bai, J. Z., et al., BES collaboration, Phys. Rev. Lett., 81(1998) 1179
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4.2.2.2 ψ(2S) decay
(1) Introduction
In charmornium family, ψ(2S) is in a special position. ψ(2S) can decay into J/ψ, ψ, χcJ (J=0,1,2), and possibly into η c, η’ c and 1P1 states, therefore, by collecting sufficient ψ(2S) data sample, one can not only study the property of resonances of ψ(2S), J/ψ, χcJ (J=0,1,2), ηc, but also search for η’c and 1P1 states.
The ψ(2S) data sample collected by BEPC/BESI is 3.96 million, by which BES collaboration has made various studies on ψ(2S), J/ψ and χcJ (J=0,1,2), and copious results have been reported [1-9]. For the BEPCII, the luminosity will be optimized at beam energies of 1.55 GeV (J/ψ) and 1.84 GeV (ψ(2S)), and the designed luminosity at 1.55 GeV is 5x1031cm-2 s-1. It is reasonable to assume that at 1.84 GeV beam energy, the luminosity can reach 7.5x1031cm-2 s-1, namely increase to a factor of 1.5. Based on this value, one year running of BEPCII will produce 1.5x108 ψ(2S) events, which is a factor of 38 higher than the data sample collected by BESI detector, and will improve the statistical error by a factor of 6. Besides, the designed performance of BESIII detector is much better than that of BESI with time resolution of TOF decreasing from 330 ps down to 110 ps, momentum resolution from 1.7%
)
(
1
2
2
GeV
p
+
to 0.5%
)
(
1
2
2
GeV
p
+
, and energy resolution of electromagnetic calorimeter from 0.25/
E
GeV
(
)
to 0.08/
)
(
GeV
E
,which will increase the detection efficiency (therefore also increase the statistics, too), enhance the capability of particle ID and improve the momentum measurement for charged track, the energy measurement for electron and photon, in turn, improve the systematic error by a factor of 2 -3 averagely for all measurements.
(2) ψ(2S) decays
(a) Hadronic decays
BES collaboration has measured branching fractions or upper limits for various hadronic decay channels listed in Table 1. The statistical errors are in the range of 10% to 30 % , and the systematic errors are in similar values. In the BEPCII/BESIII case, the statistical and systematic errors will be down to (2-5)% and (3.5-10)%, respectively, which give the total error of (4-12)%, namely, a factor of 3 improvement compared to the BESI results. For the upper limits, BESIII will set the results of BESI down to a factor of 38 lower level.
One expects that the J/ψ and ψ(2S) decays into light hadrons via ggg, or γ*, or γgg. In either case, the partial width for the decay is proportional to |ψ(0)|2, where ψ(0) is the wave function at the origin in the non-relativistic quark model for
c
c
. Thus, it is reasonable to expect [10] on the basis of the perturbative QCD that, for any hadronic final state h, the ratio Qh can be estimated by :
Q
B
S
h
B
J
h
B
S
e
e
B
J
e
e
h
º
®
®
@
®
®
=
±
+
-
+
-
(
(
)
)
(
/
)
(
(
)
)
(
/
)
(
.
.
)%
y
y
y
y
2
2
14
8
2
2
(1) where the leptonic branching fractions are taken from PDG2000[11]. This relation is sometimes refered to as PQCD 15% rule.
The Qh values for BES measured ψ(2S) hadronic decays based on PDG’s value for J/ψ branching fractions are also listed in Table 1. A major part of decay channel
Table 1 BESI measured ψ(2S) decay branching fractions and PQCD 15% rule test
(# denotes preliminary results; upper limits at C.L.=90%)
Channel
B(ψ(2S)) (10-4)
B(J/ψ) (10-3)
Qh (%)
γX
gh
0.53
±
0.31
±
0.08
0.86
±
0.08
6.2
±
3.8
g
h
¢
1.54
±
0.31
±
0.20
4.31
±
0.30
3.6
±
0.9
b
1
p
5.2
±
0.8
±
1.0
3.0
±
0.5
17.3
±
5.1
AP
K
K
1
1270
±
(
)
m
10.0
±
1.8
±
2.1
< 3.0
>33.3
K
K
1
1400
±
(
)
m
<3.1
3.8
±
1.4
< 8.2
w
f
2
<1.7
4.3
±
0.6
< 4.0
r
a
2
<2.3
10.9
±
2.2
< 2.1
VT
j
¢
f
2
1525
(
)
<4.5
1.23
±
0.06
±
0.20
< 3.7
K
K
c
c
*0
*0
.
.
2
+
<1.2
6.7
±
2.6
< 1.8
#
K
K
c
c
*0
*0
.
.
2
+
0.798
±
0.528
6.7
±
2.6
1.20
±
0.93
VP
#
rp
<0.29
12.8
±
1.0
< 0.23
#
K
K
c
c
+
-
+
*
(
)
.
.
892
<0.23
5.0
±
0.4
< 0.46
#
K
K
c
c
0
892
*0
(
)
.
.
+
1.30
±
0.34
±
0.16
4.2
±
0.4
3.1
±
1.0
VS
#
j
f
0
0.63
±
0.18
0.32
±
0.09
19.6
±
7.8
VV
K
K
c
c
*0
*0
.
.
+
0.392
±
0.103
0.29
±
0.04
±
0.06
13.6
±
4.9
#
w
K
K
+
-
1.25
±
0.56
0.74
±
0.24
16.9
±
9.4
#
w
p
p
0.64
±
0.26
1.30
±
0.25
5.0
±
2.2
#
jp
p
+
-
1.68
±
0.32
0.80
±
0.12
21.0
±
5.1
#
j
K
K
+
-
0.58
±
0.22
0.83
±
0.13
7.0
±
2.9
#
j
p
p
0.082
±
0.052
0.045
±
0.015
18.1
±
12.8
#
K
K
c
c
*
.
.
-
+
+
p
6.04
±
0.90
#
p
p
p
+
-
0
p
p
3.49
±
0.64
2.3
±
0.9
15.2
±
6.6
#
hp
p
+
-
p
p
2.47
±
0.96
#
h
p
p
<1.8
2.09
±
0.18
< 8.6
p
p
2.16
±
0.39
2.12
±
0.10
10.1
±
1.9
L
L
1.81
±
0.34
1.30
±
0.12
13.9
±
2.9
S
S
0
0
1.2
±
0.6
1.27
±
0.17
9.4
±
4.6
BB
X
X
-
+
0.94
±
0.31
0.9
±
0.2
10.4
±
4.1
D
D
+
+
-
-
1.28
±
0.35
1.10
±
0.29
11.6
±
4.5
S
S
*
*
-
+
1.1
±
0.4
1.03
±
0.13
11
±
4
X
X
*0
*0
<0.81
W
W
-
+
<0.73
branching fractions have no large deviation from PQCD expectations, which includes AP (
b
1
p
), VS (
j
f
0
),
B
B
(
p
p
,
,
,
,
,
*
*
L
L
S
S
X
X
D
D
S
S
0
0
-
+
+
+
-
-
-
+
) and multi-hadron final states. The intriguing puzzle, reported in 1983 by Mark II [12]: the Qh for
rp
and
K
K
c
c
+
-
+
*
.
.
lower than an order of magnitude of PQCD expectations, is comfirmed by BES results at much higher level of sensitivity [7]. The upper limits on the branching fractions of
y
rp
(
)
2
S
®
and
y
(
)
2
S
®
EMBED Equation.3
K
K
c
c
+
-
+
*
.
.
are found to be more than a factor of 60 and 20 lower than the 15% rule predictions, respectively. The four
y
(
)
2
S
VT
®
decay modes (
w
r
f
f
a
f
K
K
2
2
2
2
,
,
,
'
*0
*0
) are suppressed by a factor of at least 3 [2]. For the AP decay channel, BES collaboration has observed flavor-SU(3)-violating K1(1270)-K1(1400) asymmetries that have opposite character for the ¦×(2S) and J/¦×[5], which cannot be accommodated by adjustments of the singlet-triplet mixing angle [13]. All these suppressions and anomaly will be further studied with higher accuracy and higher statistics in BEPCII/BESIII.
(b) Radiative decays
By using the Vector Dominance model, a radiative decay might (or might not) be connected with corresponding hadronic decay,it is therefore interesting to examine if suppressions exist for the radiative decays too. BESI has measured the branching fractions for
gh
gh
,
'
channels (also listed in Table 1) and calculates the corresponding
Q
gh
=6.2% and
Q
gh
'
=3.6%, which are suppressed by a factor of roughly 2 and 4, respectively. We will further study these suppressions and extend the study to more channels, such as
gp
g
g
g
0
1
2
2
,
,
,
,
f
f
f
¢
... at BEPCII/BESIII with higher accuracy and statistics.
BEPCII also pvovide an opportunity to search for some glueball candidates such as η(1440), fJ (1710), ξ(2230), etc. via radiative decays. This might be helpful to distinguish glueballs from
q
q
radial excitation states for some theoretical models.
(3) J/ψ letponic decay width
BESI has determined the most accurate branching fraction for J/ψ leptonic decay via processes of
y
p
p
y
y
y
(
)
/
,
/
,
/
2
S
J
J
l
l
J
anything
®
®
®
+
-
+
-
:
B
l
l
(
)
+
-
=(
5
87
0
04
0
09
.
.
.
±
±
) % [3]. In the BEPCII/BESIII case, the tatistical error will be negligible and systematic error will be reduced to 0.05%, as a result, the relative error of
B
l
l
(
)
+
-
will be lower than 1%.
(4) χcJ physics
BESI has measured many channel’s branching fractions for χcJ decays [6], with much improved accuracies, in which many of them are the first measurements (see Table 2). Therefore, from PDG1998 [14] to PDG2000 [11], the whole scenery for χcJ decays are greatly changed. However, the statistical and systematic errors for χcJ decay branching fractions are still too large, ranging (6-20)% and (15-30)% respectively. In the case of BEPCII/BESIII, the statistical errors will be negligible and the errors will be governed by the systematic one ranging (5-10)% .
Table 2. BES measured χcJ width and branching fractions
(upper limits at C.L.=90%)
Channel
BES results
PDG98
c
p
p
c
0
®
+
-
(4.68
±
0.26
±
0.65)
´
10-3
(7.5
±
2.1)
´
10-3
c
p
p
c
2
®
+
-
(1.49
±
0.14
±
0.22)
´
10-3
(1.9
±
1.0)
´
10-3
c
c
K
K
0
®
+
-
(5.68
±
0.35
±
0.85)
´
10-3
(7.1
±
2.4)
´
10-3
c
c
K
K
2
®
+
-
(0.79
±
0.14
±
0.22)
´
10-3
(1.5
±
1.1)
´
10-3
c
c
p
p
0
®
(1.59
±
0.43
±
0.53)
´
10-3
<9.0
´
10-3
c
c
p
p
1
®
(4.2
±
2.2
±
2.8 )
´
10-3
(8.6
±
1.2)
´
10-5
c
c
p
p
2
®
(5.8
±
3.1
±
3.2 )
´
10-3
(10.0
±
1.0)
´
10-5
c
p
p
p
p
c
0
®
+
-
+
-
(15.4
±
0.5
±
3.7 )
´
10-4
(3.7
±
0.7)
´
10-2
c
p
p
p
p
c
1
®
+
-
+
-
(4.9
±
0.4
±
1.2 )
´
10-5
(1.6
±
0.5)
´
10-2
c
p
p
p
p
c
2
®
+
-
+
-
(9.6
±
0.5
±
2.4 )
´
10-5
(2.2
±
0.5)
´
10-2
c
p
p
c
K
K
1
®
+
-
+
-
(14.7
±
0.7
±
3.8 )
´
10-3
(3.0
±
0.7)
´
10-2
c
p
p
c
K
K
1
®
+
-
+
-
(4.5
±
0.4
±
1.1)
´
10-3
(9
±
4 )
´
10-3
c
p
p
c
K
K
2
®
+
-
+
-
(7.9
±
0.6
±
2.1 )
´
10-3
(1.9
±
0.5)
´
10-2
c
c
0
®
EMBED Equation.3
p
p
+
-
p
p
(1.57
±
0.21
±
0.54)
´
10-3
(5.0
±
2.0)
´
10-3
c
c
1
®
EMBED Equation.3
p
p
+
-
p
p
(0.49
±
0.13
±
0.17)
´
10-3
(1.4
±
0.9)
´
10-3
c
c
2
®
EMBED Equation.3
p
p
+
-
p
p
(1.23
±
0.20
±
0.35)
´
10-3
(3.3
±
1.3)
´
10-3
c
c
0
®
3
(
)
p
p
+
-
(11.7
±
1.0
±
2.3 )
´
10-3
(1.5
±
0.5)
´
10-2
c
c
1
®
3
(
)
p
p
+
-
(5.8
±
0.7
±
1.2 )
´
10-3
(2.2
±
0.8)
´
10-2
c
c
2
®
3
(
)
p
p
+
-
(9.0
±
1.0
±
2.0 )
´
10-3
(1.2
±
0.8)
´
10-2
c
c
0
®
EMBED Equation.3
K
K
s
s
0
0
(1.96
±
0.28
±
0.52)
´
10-3
c
c
2
®
EMBED Equation.3
K
K
s
s
0
0
(0.61
±
0.17
±
0.16)
´
10-3
c
c
0
®
EMBED Equation.3
jj
(0.92
±
0.34
±
0.38)
´
10-3
c
c
2
®
EMBED Equation.3
jj
(2.00
±
0.55
±
0.61)
´
10-3
c
c
0
®
EMBED Equation.3
K
K
K
K
+
-
+
-
(2.14
±
0.26
±
0.40)
´
10-3
c
c
1
®
EMBED Equation.3
K
K
K
K
+
-
+
-
(0.42
±
0.15
±
0.12)
´
10-3
c
c
2
®
EMBED Equation.3
K
K
K
K
+
-
+
-
(1.48
±
0.26
±
0.32)
´
10-3
c
c
0
®
EMBED Equation.3
K
K
c
c
s
0
+
-
+
p
.
.
< 0.71
´
10-3
c
c
1
®
EMBED Equation.3
K
K
c
c
s
0
+
-
+
p
.
.
(2.46
±
0.44
±
0.65)
´
10-3
c
c
2
®
EMBED Equation.3
K
K
c
c
s
0
+
-
+
p
.
.
< 1.06
´
10-3
G
c
c
0
14.3
±
2.0
±
3.0 MeV
13.5
±
3.3
±
4.2MeV
The width of χcJ decaying into light hadrons are interesting theoretically, since in addition to the 3PJ color singlet component the contribution of the color octet component in the
c
c
wave function might also be involved according to the NRQCD theory [15]. The widths of χc1 and χc2 are measured precisely by E760, and the width of χc0
(
M
=
±
±
3414
1
0
6
0
8
.
.
.
EMBED Equation.3
=
±
3414
1
1
0
.
.
MeV) by BESI [6]. With BEPCII/BESIII, the error of χc0 can be reduced to 0.3-0.4 MeV.
A careful study of the angular distribution of the radiative decay
c
g
y
cJ
J
®
/
with high statistics in BESIII will provide more information on the transition matrix elements, which are closely related to the
c
c
wave functions and interquark forces.
The radiative decay rates of
c
c
g
c
c
0
2
2
,
®
are also interesting, to which both QCD radiative correction and relativistic correction may be important. The estimated branching ratio is roughly
B
S
B
c
c
(
(
)
)
(
)
.
.
y
gc
c
g
2
2
0
09
4
10
3
6
10
0
0
4
5
®
´
®
@
´
´
=
´
-
-
. (2)
Due to the limited statistics and bad photon energy resolution in BEPC/BESI, this measurement is not feasible. However, with one year running of BEPCII/BESIII, about 2000 signal events for this channel can be expected (assuming efficiency of 40%) , which will produce (2-3)% statistical uncertainty only.The χcJ decay into light hadrons via gluon intermediate state,e.g.,
c
c
g
0
2
®
®
hadrons. It is plausible that a pair of glueballs could be favorably produced in its decay process. With BEPCII/BESIII high statistics and better particle ID, it is possible to study hadronic decays like
c
p
p
p
p
hh
p
p
h
h
hhhh
p
p
c
K
K
K
K
0
2
®
¢
+
-
+
-
+
-
(
),
,
,
,
,
.
.
.
(3)
and look for some 0++ and 0-+ glueballs, e.g.,
f
0
1500
(
)
,
,
,
®
¢
¢
pp
hh
h
h
f
0
1400
(
)
,
®
pp
f
K
K
0
975
(
)
,
,
®
pp
h
p
(
)
.
1440
®
K
K
(4)
This study might provide useful information on distinguishing between
q
q
states,
q
q
states, and glueballs, if any.
(5)
¢
h
c
search
Crystal Ball Collaboration reported in 1982 the observation of
¢
h
c
at 3592 MeV, but its existence has never been confirmed. With 3.8 milion ψ(2S) events, the
¢
h
c
search is tried in BESI with invariant mass of all charged particles,
¢
h
c
-like signal seems to appear in
p
p
p
p
+
-
+
-
+
-
K
K
,
(
)
3
channels, but the existence of
¢
h
c
can not be claimed [16].
Since Crystal Ball gives
B
S
c
(
(
)
)
y
g
h
2
1
10
3
®
¢
³
´
-
, and assuming for any exclusive hadronic channel h based on the same argument as for J/ψ and ψ(2S) decays (see(2)(a))
R
B
h
B
h
B
g
B
g
c
c
c
c
º
¢
®
®
»
¢
®
®
»
(
)
(
)
(
)
(
)
h
h
h
h
2
2
1
,
(5)
then we can design the event selection criteria by assuming the same decay channels and same branching fractions for
h
c
and
¢
h
c
decays. Since the radiative photon in
y
(
)
2
S
®
EMBED Equation.3
g
h
¢
c
decay is of lower energy, this study is difficult in BESI because of its bad photon energy resolution and lower detection efficiency for low energy photon, and
also low statistics. However, all these factors are improved in BEPCII/BESIII, which makes the search for
¢
h
c
possible. The final states which can be studied for this search are listed in Table 3.
Table 3. Final states and branching ratios for
¢
h
c
search
( branching ratios taken from PDG)
¢
h
c
decays (f)
B
¢
h
c
(f) (10-2)
B
y
(
)
2
S
(γf) (10-5)
p
p
p
p
+
-
+
-
1.2
1.2
p
p
+
-
+
-
K
K
2.0
2.0
K
K
K
K
+
-
+
-
2.1
2.1
(
K
K
p
)
5.5
K
K
K
+
-
+
+
-
-
®
0
p
p
p
p
0.629
0.629
K
K
K
-
+
-
+
-
+
®
0
p
p
p
p
0.629
0.629
K
K
K
K
+
-
+
-
®
p
gg
0
0.629
0.629
hpp
ggp
p
®
+
-
1.28
1.28
y
g
h
(
)
2
S
c
®
¢
®
B (10-5)
Nevt (1y)
g
4
P
6.56
9840
3
2
g
P
1.91
2865
As it can be seen from Table 3 that, for both
g
4
P
and
3
2
g
P
topology, sufficient signal events can be produced for
¢
h
c
search in BEPCII/BESIII. However, a severe background from
y
gc
g
(
)
2
4
2
S
P
c
®
®
will disturb the
¢
h
c
search in the
g
4
P
mode because of its large branching fraction (2.48
´
10-3) and small mass difference of
¢
h
c
(3592 MeV) and
c
c
2
(3556 MeV). On the other hand, for the
3
2
g
P
mode, the background comes mainly from
y
gh
(
)
2
S
c
®
EMBED Equation.3
®
+
-
+
-
gp
ghp
p
0
K
K
,
with the branching fraction of 5.35
´
10-5, which is only a factor of 2.8 higher than that of the
¢
h
c
signal. In addition , the energy of the radiative photon in these two processes is very different (93 MeV and 639 MeV for
y
g
h
(
)
2
S
c
®
¢
and
y
gh
(
)
2
S
c
®
respectively), therefore the background of
h
c
can be easily removed.
We have made a fast simulation for the
¢
h
c
search by
3
2
g
P
mode with the BEPCII/BESIII performances [17]. Based on the character of the
y
g
h
(
)
2
S
c
®
¢
®
+
-
+
-
gp
ghp
p
0
K
K
,
events topology, we abstract following selection criteria to distinguish signal from background:
1.
2
=
c
N
,
Q
i
i
å
=
0
, PID=
K
,
p
, |
cos
q
ci
|<0.75.
2. 3
£
£
N
g
5, select 3 most energetic
g
’s. |
cos
q
g
i
|<0.75.
Construct 6 (
g
-
g
) combinations:
c
s
s
g
g
g
p
p
1
2
1
93
2
2
3
2
93
0
0
=
-
+
-
(
)
(
)
E
M
M
M
,
c
s
s
g
g
g
h
h
2
2
1
93
2
2
3
2
93
=
-
+
-
(
)
(
)
E
M
M
M
,
s
s
s
g
h
p
E
MeV
M
M
=
93
0
,
,
determined by M.C. are 24.9, 45.7, 16.6 MeV, respectively. The pattern with smallest
c
2
is chosen (
p
0
or
h
is determined).
3.
c
2
<10
4.
M
P
2
< 3 GeV
5. If
h
is assigned,
M
g
g
2
3
Ì
(0.35, 0.75) GeV; If
p
0
is assigned,
M
g
g
2
3
Ì
(0.35, 0.75) GeV,and
P
l
<1.3 GeV (
P
l
is the lower momentum in two charged tracks) . The results of this simulation is shown in Table 4. We see that if collecting one year
y
(2S) data, about 456 signal events will be selected with 55 background events from
y
gh
(
)
2
S
c
®
. The ratio of signal to noise is 8.3, this indicates the possible success for the
¢
h
c
search with BEPCII/BESIII, if it exists.
Table 4. Selection of
y
g
h
(
)
2
S
c
®
¢
events
Decays
y
g
(
)
2
S
®
EMBED Equation.3
¢
h
c
EMBED Equation.3
®
y
g
(
)
2
S
®
EMBED Equation.3
h
c
EMBED Equation.3
®
ghp
p
+
-
gp
0
K
K
+
-
ghp
p
+
-
gp
0
K
K
+
-
B
1.28
´
10-5
0.629
´
10-5
3.59
´
10-5
1.76
´
10-5
N0
18690
9180
5241
25690
N1
11048
3166
3005
9027
N2
3666
1509
1237
4619
N3
3626
986
17
371
N4
3573
901
17
370
N5
3572
870
17
369
e
0.191
0.095
0.003
0.014
N(1y)
367
89
17
38
(6) 1P1 search
The R704 [18], E760 [19] and E705 [20] collaborations claim the existence of 1P1 state in year of 1986,1992 and 1994, respectively. However, the signal statistics is very low (signal events for these three experiments are 5, 59 and 42 respectively). The existence of 1P1 state still needs to be confirmed.
Some theoretical calculation considering the effect of S-D mixing [21] gives
B
S
P
(
(
)
)
y
p
2
2
10
1
1
0
4
®
=
´
-
, (5)
in addition 1P1
®
gh
c
is expected to be the dominant decay mode. Therefore, we can search for 1P1 via
y
p
(
)
2
0
s
®
1P1
®
gggh
c
EMBED Equation.3
®
ggg
4
P
(6)
decay mode. The decay channels of
h
c
into 4 prong’s and corresponding branching ratios are listed in Table 3 already, and the total branching ratios of
h
c
into 4 prong’s is 6.56
´
10-2. Therefore, the combined branching ratio for process (6) is estimated to be 1.312
´
10-5. Assuming detection efficiency of 0.1, collecting one year
y
(
)
2
S
events (1.5
´
108), 197 signal events for process (6) can be expected, which is sufficient to confirm the existence of 1P1 state.
The 1P1 and
p
0
in process (6) are generated almost at rest, therefore, the signal events of process (6) have following characteristic :
1.
M
MeV
P
4
2980
»
(mass of
h
c
)
2.
M
MeV
g
g
2
3
135
»
(mass of
p
0
)
3.
M
MeV
P
4
3526
,
g
»
(mass of 1P1)
4.
E
MeV
g
1
504
»
5.
cos
q
g
g
2
3
1
»
-
6. cos
q
g
4
1
P
,
EMBED Equation.3
»
-
1
,
based on which we can easily distinguish the signal from possible backgrounds, which could be the processes of
y
(
)
2
S
®
2
(
)
p
p
p
+
-
0
, (plus one fake photon)
y
(
)
2
S
®
EMBED Equation.3
p
p
y
0
0
J
/
,
J
P
/
y
®
4
, (one photon not detected)
y
(
)
2
S
®
EMBED Equation.3
gc
c
0
EMBED Equation.3
®
gg
y
J
/
,
J
P
/
y
®
4
, (plus one fake photon)
y
(
)
2
S
®
EMBED Equation.3
gc
c
1
EMBED Equation.3
®
gg
y
J
/
,
J
P
/
y
®
4
, (plus one fake photon)
y
(
)
2
S
®
EMBED Equation.3
gc
c
2
EMBED Equation.3
®
gg
y
J
/
,
J
P
/
y
®
4
,(plus one fake photon).
References
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. X.H.Li, representing BES Collab., Nucl. Phys. B (Proc. Suppl.) 75B (1999) 181.
8. F.Liu, representing BES Collab., Nucl. Phys. A675 (2000) 71c.
9. 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..
10. 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.
11. D.E.Groom et al., Particle Data Group, Eur. Phys. J. C15 (2000) 1.
12. M.E.B. Franklin et al., Mark II Collab., Phys. Rev. Lett. 51 (1983) 963.
13. Preliminary results from this analysis are discussed in the context of SU(3)
symmetry breaking, in M. Suzuki, Phys. Rev. D55 (1997) 2840.
14. C.Caso et al., Particle Data Group, Eur. Phys. J. C3(1998) 1.
15. G.T.Bodwin et al., Phys. Rev. D46 (1992) 1914.
16. C.Z.Yuan, BES97(1997)191.
17. Y.S.Zhu et al., Search for
¢
h
c
at BEPCII/BESIII, 中国高能物理发展战略研讨会报告文集，加速器物理分册，82页。
18. C.Baglin et al., Phys. Lett. B171 (1986) 135
19. T.A.Armstrong et al., Phys. Rev. Lett. 69 (1992) 2337
20. L. Antoniazzi et al., Phys.Rev. D50 (1994) 4258
21. Y.P.Kuangg et al., Phys. Rev. D37 (1988) 1210
Charmed Meson Physics[1]
Charmed mesons
0
D
,
+
D
and
+
S
D
are the bound states of
q
c
(
q
=
u
,
d
,
s
) quarks. Since the charm quark is sufficiently massive, some aspects of perturbative QCD are applicable both in their productions and decays. Because the weak couplings of the charm quark are theoretically determined in standard model with three quark generations, charm decays offer a clean laboratory to study strong interaction effects at the boundary between the perturbative and nonperturbative regions. There are three classes of charmed meson decays: Pure Leptonic, Semileptonic and Hadronic Decays.
1. Study of Pure Leptonic Charmed Meson Decays
For the pseudoscalar charmed
+
D
and
+
S
D
mesons, the decay rates for
n
m
+
+
®
)
(
S
D
determine the decay constants
D
f
and
s
D
f
. The decay rates can be rigorously calculated in the Standard Model. The theoretical prediction for these branching fractions are given by
,
1
|
|
8
)
(
2
2
2
2
2
)
(
2
2
)
(
)
(
)
(
)
(
)
(
÷
÷
ø
ö
ç
ç
è
æ
-
=
®
+
+
+
+
+
s
s
s
s
D
l
l
s
cd
D
D
F
D
l
s
m
m
m
V
m
f
G
l
D
Br
p
t
u
where
|
|
)
(
s
cd
V
is the CKM matrix element and
)
(
s
D
f
are the so-called decay constant. The decay constants contain all the nonperturbative QCD information in the leptonic decays. The
2
l
m
term represents the helicity suppression of the leptonic decays of the pseudoscalar mesons.
The
D
f
and
s
D
f
are two fundamental constants in particle physics. They describe the overlapping of the meson wave function at origin and play an important role in predicting the branching fractions of meson semileptonic decays, noleptonic decays, and in understanding hadronic wave functions and second order weak processes including
D
D
mixing and CP violation. Therefore, the precise measurements of
D
f
and
s
D
f
are very important. However, since the leptonic decay branching fraction becomes smaller as
)
(
s
D
m
becomes larger, it is much more difficult to meaure
D
f
and
s
D
f
via
n
m
+
+
®
D
and
n
m
+
+
®
S
D
than
p
f
and
K
f
. At present the errors for
4
17
5
10
)
8
(
)
(
-
+
-
+
+
´
=
®
n
m
D
Br
and
3
10
)
9
.
1
6
.
4
(
)
(
-
+
+
´
±
=
®
n
m
s
D
Br
are large [2]. The high precision of data in the BEPCII is expected to give accurate measurements of the
D
f
and
s
D
f
.
The theoretical evaluation of the decay constants relies on nonperturbative methods of QCD such as QCD sum rules, chiral perturbation theory, Bethe-Salpeter equation and lattice gauge calculations in the full theory. Usually the QCD sum rules calculations [3]—[7], the lattice gauge theory simulations [8]—[10] and the Bethe-Salpeter equation approach [11] predict that
D
f
is around the value 200 MeV (take
130
=
p
f
MeV). The ratio
D
D
f
f
S
has also been calculated by QCD sum rules [12] and the lattice gauge theory [9]. This value is about 1.3 in these two approaches.
Different model calculations lead to different values and each of them has its own uncertainties. Therefore, the precise measurements of the decay constants can test those nonperturbative methods and help us to get a deeper understanding about the features of non-perturbative QCD. It can also provide a test on the heavy quark effective theory. Since
B
m
is much heavier than
D
m
and
002
.
0
|
|
»
bu
V
, it is very difficult to measure
B
f
.
B
f
is also a very important constant which plays a fundamental role in experiments, such as
0
0
B
B
mixing experiment and measurement of CP violation. The test of nonperturbative QCD methods via
D
f
can provide a solid ground for attempts to extrapolate to
B
f
and better description for
D
D
mixing.
The ratio of
D
D
f
f
S
would also be interesting since the measurement of this ratio can test the heavy quark effective theory[12].
Precise measurements of pure leptonic
+
D
and
+
S
D
decays require singly tagged event sample and would therefore be accessible at the BEPCII. The tagged event samples are necessary both to suppress backgrounds and to provide a constrained fit for the mass of the missing neutrinos. Monte Carlo simulation[13][14] indicates that the signal can be clearly distinguished from backgroud processes. With one year’s data, each of the decay constants
D
f
and
S
D
f
can be measured with the error about 7%.
2．Semileptonic Decays and CKM Matrix Elements
In the diverse phenomenology of weak interections, semileptonic and leptonic decay of hadrons have a special standing. In both types of decays, the final-state particles including a single charged lepton, the clearest experimental signature for a weak process should be mediated by the W boson. Because these decays are relatively simple from a theoretical perspective, they provide a means both to measure fundamental standard-model parameters and to perform detailed studies of the decay dynamics.
The semileptonic decays of Charmed mesons are more complicated than the pure leptonic decays but simpler than the nonleptonic decays. For a process
n
Xl
D
®
, where
X
is a final state, the lepton part
n
l
can be factorized out. What is left is the matrix element of the weak current between
D
and
X
,
>
<
D
j
X
u
|
|
where
m
j
is the weak current. The decay width of
n
Xl
D
®
is also related to the CKM matrix element
cq
V
where
q
is the daughter quark after the transition of c by the emission of W boson and the
q
quark is combined with another quark in D mesons to form the meson
X
. In general the decay width
G
can be written as
G
=
G
2
|
|
cq
V
where
G
is proportional to
2
|
|
|
|
>
<
D
j
X
u
. Hence all the nonperturbative information is included in
G
. It depends on the initial and final state hadronic wave functions and the hadronization mechanism. On the ground of Lorentz invariance, the matrix element
>
<
D
j
X
u
|
|
can be decomposed as (for
X
is a pseudoscalar meson)
),
(
)
(
|
|
2
0
2
2
2
2
1
2
2
2
q
F
q
q
m
m
q
F
q
m
m
p
p
D
j
P
X
D
X
D
X
D
m
m
m
-
+
÷
÷
ø
ö
ç
ç
è
æ
-
-
+
>=
<
and (for
X
is a vector meson)
),
(
2
)
(
2
)
(
)
(
)
(
)
(
)
(
2
|
|
2
0
2
*
2
3
2
*
2
2
*
2
1
*
2
*
q
A
q
m
q
q
i
q
A
q
m
q
q
q
A
p
p
m
m
q
q
A
m
m
i
q
V
p
p
m
m
D
j
P
V
V
V
D
V
D
V
D
V
D
V
D
m
m
m
m
m
s
r
n
mnrs
m
e
e
e
e
e
e
×
+
÷
÷
ø
ö
ç
ç
è
æ
×
-
+
+
×
-
+
+
+
>=
<
where
D
p
and
X
p
are the four momenta of D and X respectively and q is the momentum carried by
n
l
. The form factors
)
(
2
1
q
F
,
)
(
2
0
q
F
,
)
(
2
q
V
,
)
(
2
1
q
A
and
)
(
2
2
q
A
are governed by nonperturbative hadron dynamics and, therefor, are very difficult to calculate from the first principles of QCD. At the maximum recoil point
0
2
=
q
, the condition
)
0
(
)
0
(
0
1
F
F
=
and
)
0
(
)
0
(
0
3
A
A
=
must be satisfied.
3
A
can be expressed in terms of
1
A
and
2
A
)
(
2
)
(
2
)
(
2
2
2
1
2
3
q
A
m
m
m
q
A
m
m
m
q
A
V
V
D
V
V
D
-
-
+
=
.
At present, there are some phenomenological models to deal with these form factors. Each of these models has its own assumptions and hence limitations. In the quark model approach, the form factors at the maximum recoil point
0
2
=
q
[15] or at the zero recoil point
2
2
max
2
)
(
X
D
m
m
q
q
-
=
=
[16] are calculated and the functional
2
q
dependence is obtained through the nearest pole dominance assumption. The form factors at zero or maximum recoil points depend on the hadronic wave function models. Comparison of these models in the semileptonic decays of the Charmed meson are given in [ 15].
Contrary to the quark model approach, QCD sum rules are appropriate to study the
2
q
dependence of the form factors [17]—[23]. The results from QCD sum rules indicate that
1
F
and
V
of the vector current have the nearest pole dominance behaviour while for
1
A
and
2
A
of the axial current such dependence is absent. However, the lattice QCD calculations [24]—[26] seem to support the pole dominance behaviour of all the form factors. Some form factors are also calculated by the effective QCD Lagrangian[27]
The present precision of experimental data is not enough to give a definite test of the form factor behaviour and the existing hadronic wave function models. The BEPCII data are expected to extract more information about the wave functions of the Charmed mesons and the light mesons and consequently, that of the B meson.
The accurate data from BEPCII will provide the information on the distribution of the final decay products and also the shape of the hadronic form factors. Consequently, the CKM matrix elements
cq
V
can be measured more accurately than the present sensitivity (at present the CKM charm matrix elements are poorly measured (
%
20
10
-
±
)). Further more, since nonperturbative models are applied both in the Charmed and B mesons, the test of them in Charmed mesons can help us to extrapolate to the B meson and therefore, the CKM matrix element
ub
V
which is very poorly measured at present can be known much better.
At the BEPCII the semileptonic decay branching fractions of Charmed mesons can be measured with an accuracy at about 2% and 6% for the decays
e
e
K
D
n
+
-
®
0
and
e
e
D
n
p
+
-
®
0
, respectively [14], whereas the present error are about 5% for
e
e
K
D
n
+
-
®
0
and 50% for
e
e
D
n
p
+
-
®
0
. This high precision would make the above statement be possible.
Similar to the pure leptonic decay case, theoretical uncertainties are largely suppressed by taking the ratios such as
)
(
)
(
n
n
p
Kl
D
l
D
®
G
®
G
where the only uncertainty comes from SU(3) breaking. In this way, the more reliable ratio
cs
cd
V
V
can be obtained to accuracy around 8%.
By measuring the inclusive semileptonic decays of the Charmed meson
l
dE
d
G
where
l
E
is lepton energy the heavy c quark distribution function
)
(
x
f
can be extracted from the relation
parton
l
l
dE
d
x
dxf
dE
d
ò
÷
÷
ø
ö
ç
ç
è
æ
G
=
G
)
(
.
At present, only some ansatz for
)
(
x
f
exists [28]. The precise measurement of
)
(
x
f
could give important information about the inner structure of the Charmed mesons.
The analysis of the semileptonic decays of the Charmed mesons based on the high precision data to be obtained at the BEPCII will surely help us to learn about nonleptonic decay processes where not only the matrix
>
<
D
j
X
|
|
m
appears but also the decay mechanism plays an important role. Just as in the case of pure leptonic decays, all the related theoretical techniques such as heavy quark expansion, QCD sum rules, Bethe-Salpeter equation, chiral perturbation theory and lattice gauge simulations will be tested.
3. Non-Leptonic Decays and Weak Decay Mechanisms
Although 25 years have passed since the discovery of Charm, many nonleptonic decay modes of the charm mesons are still not explored. The present experimental precision on Charm decay properties is also not satisfactory [29]. The measured branching fractions of
0
D
,
±
D
decays have large errors (more than 20%). Even the absolute branching fractions for many decay modes of
±
S
D
are not known reliably. Some of them affect the precise measurement of B meson decays. For example, in order to extract the branching fraction
)
(
X
D
B
Br
S
®
from a measurement of the bottom decay
X
X
D
B
S
jp
®
®
for a final state X, we need to know the absolute branching fraction
)
(
±
±
®
fp
S
D
Br
. Unfortunately, we do not have good data on
)
(
±
±
®
fp
S
D
Br
. The BEPCII will provide the only way to improve the precision of the absolute branching fraction for
D
mesons to about 2% level, and to estabilish absolute branching fraction for
±
S
D
,
L
,
C
X
, etc. to about 15% level.
The rich varity of available charm decay modes (meson and baryon decays, Cabbibo allowd, Cabbibo suppressed, and double Cabbibo suppressed decays) offers a possibility to study decay mechanism of the charm hadrons and to test the different theoretical methods. For instance, for
D
meson decay, we have six different quark diagrams as shown in Figure 1. As expected theoretically the decay through diagram (b) should be color suppressed because of the color mismatch. Actually, the present charm data show no color suppression. There are theoretical speculations on the strength of the different diagrams (a)-(f). We definitely need precise data to test these speculations. Another examples is
f
0
0
K
D
®
. At the quark level this decay can only go through diagram (c) in Figure 1, i.e., the so-called exchange diagram. But theoretical estimation shows that its branching fraction should be very small. Recent data shows [2]
%
1
10
)
0
.
1
6
.
8
(
)
(
3
0
0
»
´
±
=
®
-
f
K
D
Br
, which is surprisingly large. There are theoretical arguements [30] saying that this is because of final state interactions (rescattering). Up to now there is no convincing explanation. Again because of the rich varity, charm decays are ideal places for studying final state interactions. For example, if sufficiently large number of branching ratios are well measured, we can extract the size of contributing isospin amplitudes and their phase shifts.
Because charm hadrons are heavier than light hadrons but lighter than bottom hadrons, charm study will teach us good lessons for applying and testing the different theoretical methods, such as , QCD Sum Rule, Lattice Simulations of QCD, Heavy Quark Effective Theory, and
Q
M
1
expansions, etc..
4.
0
0
D
D
-
Mixing
The process of particle–antiparticle mixing is a sensitive probe of the weak interaction in the neutral K-, D-, and B- mesons. In the standard model, the mixing is expected to be small for
0
D
. Because mixing is very sensitive to phenomena such as a new quark generation, it is a good place to look for new physics. Similar to the neutral Kaon system, the mass eigen states are different from the CP eigen states. Taking the phase convention as
>
>=
0
0
|
|
D
D
PC
, we can construct symmetric and antisymmetric CP eigen states
1
D
and
2
D
respectively:
(
)
>
+
>
>=
0
0
1
|
|
2
1
|
D
D
D
,
(
)
>
-
>
>=
0
0
2
|
|
2
1
|
D
D
D
.
The physical mass eigen states (also weak decay eigen states) can be described by
(
)
>
+
>
>=
2
1
|
|
2
1
|
D
D
D
S
e
,
(
)
>
+
>
>=
1
2
|
|
2
1
|
D
D
D
L
e
In contrast to
S
K
,
L
K
, here
S
D
,
L
D
have comparable lifetimes due to large number of decay channels of the D mesons.
Experimentally we measure the mixing rate defined as
2
)
(
)
(
2
2
0
0
0
y
x
Decays
D
N
Decays
D
D
N
r
D
+
»
®
®
®
=
,
where
G
D
=
/
m
x
,
)
2
/(
G
DG
=
y
,
m
D
and
DG
are the mass and width differences of
S
D
and
L
D
respectively.
In the Standard Model,
D
r
is expected to be very small. A recent estimate [31] claims that the short and long range contributions are in the same order of magnitude and
9
10
10
10
~
-
-
-
D
r
. Any measurement
4
10
-
>
D
r
means new physics. BEPCII can provide
6
10
reconstructed D mesons per year data-taking. A sensitivity of
3
10
-
in
D
r
measurements is possible for one year data taking.
At the BEPCII, the
0
0
D
D
pair can be produced in the electron positron annihilation at the center-of-mass energy of 3.77 GeV in the physics interaction
0
0
D
D
e
e
®
-
+
, where the
0
0
D
D
is in
1
-
=
C
state and can be described by
[
]
)
(
)
(
)
(
)
(
2
1
|
0
0
0
0
0
0
k
D
k
D
k
D
k
D
D
D
-
-
-
>=
.
-
+
®
p
K
D
0
is Cabbibo favoured decay. But
-
+
®
p
K
D
0
can occur through Double Cabbibo suppressed Decay. So,
0
D
,
0
D
have identical final states and can be regarded as identical particles. Therefore their coherent wave function is symmetric and must has charge parity C = +1. But we are considering C = -1 coherent state. So DCSD can not be contribute to
-
+
®
p
K
D
0
. Only mixing
-
+
®
®
p
K
D
D
0
0
contributes. So, we can tag
-
+
p
K
to measure
0
0
D
D
-
mixing free from DCSD contamination. The observation of the processes
)
(
)
(
0
0
+
-
+
-
-
+
®
®
®
p
p
K
D
K
D
e
e
or
)
(
)
(
0
0
0
+
-
+
-
-
+
®
®
®
p
p
p
K
D
K
D
e
e
would be unambiguious evidence for the existence of
0
0
D
D
-
mixing. The final states of the above decay modes are very clean because all final particle are observed and D mass peak must be seen. Another method for measuring
0
0
D
D
-
mixing is to use the semileptonic decay. This methods is free of DCSD contamination.
In summary,
0
0
D
D
-
mixing can be studied unambiguously in two or more than two independent modes. The reaching sensitivity can approach to the order of
3
10
-
.
5. Rare Decays
Studies of the rare decays can be used to test the weak decay mechanisms. There are a number of models, such as extended Technicolor[32], leptonquarks [33], and some supperstring-inspired models[34], in which large flavor-changing neutral current effects would be present in ch
