Observation of Anomalous Line Shape of ψ (3770)
Production and Measurements of Branching Fractions for
J/ψ , ψ (3686) and ψ (3770) → K 0/K ∗0X
Gang Rong (for the BES collaboration)
Institute of High Energy Physics, Beijing 100049, People’s Republic of China
Abstract. We observe an obviously anomalous line shape of the cross sections for e+ e− → hadrons and e+ e− → DD̄ in
the energy region between 3.700 and 3.872 GeV. They are inconsistent with the explanation for only one simple ψ (3770)
resonance in the range from 3.70 to 3.87 GeV, which indicates that either there is likely a new structure in addition to the
ψ (3770) resonance around 3.773 GeV, or there are some physics effects reflecting the DD̄ production dynamics. With the
data taken around 3.097, 3.686 and 3.770 GeV, we measure the inclusive K 0 /K ∗0 decay branching fractions of the J/ψ ,
ψ (3686) and ψ (3770) resonances for the first time.
Keywords: non-DD̄ decays of ψ (3770), new structure, production and decays of ψ (3770), inclusive K 0 /K ∗0 decays of J/ψ and ψ (3770)
PACS: 13.20.Gd, 13.66.Bc, 14.40.Gx, 14.40.Lb
INTRODUCTION
The structure around 3.770 GeV, discovered in e+ e− annihilation by MARK-I experiment in 1977, is interpreted as a
13 D1 wave mixing with 23 S1 wave of cc̄ bound state, which is called the ψ (3770) resonance. This is a popular interpretation of the structure. However, some theoretical models [1] expect that four-quark state or molecular D D̄ threshold
resonance exists in the energy region around the DD̄ production threshold. Assuming that ψ (3770) is a pure cc̄ bound
state, the perturbative QCD (pQCD) calculation of the branching fraction for ψ (3770) → LH (light hadron) [2] plus
the measured exclusive non-DD̄ decay branching fractions of ψ (3770) [3] show that the total non-D D̄ decay branching
fraction of ψ (3770) should be about 2% [2]. However, if the four-quark state or molecular D D̄ threshold resonance
really exists in the energy region, one may observe some unusual properties of ψ (3770) production and decays. In
assumption that there is only one simple ψ (3770) resonance around 3.773 GeV, the BES collaboration previously
measured a large non-DD̄ decay branching fraction of ψ (3770), B[ψ (3770) → non−D D̄] = (14.7 ± 3.2)% [4]. This
unusual large non-DD̄ decay branching fraction indicates at least three possibilities: 1) there may be some new structure in addition to the ψ (3770) around 3.773 GeV; 2) there may be some additional dynamics affecting the ψ (3770)
production and decays [5]; 3) ψ (3770) may not be a pure cc̄ bound state [6].
In experiment, measurements of the line shapes of the cross sections for e + e− → hadrons, e+ e− → D0 D̄0 , e+ e− →
+
D D− , e+ e− → DD̄, and e+ e− → PX [where P is a particle such as K 0 ,K ∗0 , φ , ω , η , J/ψ ,..., and X is any particle(s)]
can provide some important information about the nature of the ψ (3770) resonance. In addition to these, measurements
of the inclusive P branching fractions of ψ (3770) decays can also provide some important information about the nature
of the ψ (3770) resonance. These measurements can help probe some dynamics of the ψ (3770) production and decays.
With the data taken at 3.773 GeV, the data taken in the energy region between 3.65 and 3.88 GeV, and the data
taken around 3.097 GeV, the BES collaboration studied the line shapes of the cross sections for e + e− → hadrons,
e+ e− → K 0 /K ∗0 , e+ e− → D0 D̄0 , e+ e− → D+ D− and e+ e− → DD̄ in these energy regions and measured the inclusive
K 0 /K ∗0 branching fractions of J/ψ , ψ (3686) and ψ (3770) decays for the first time.
ANOMALOUS LINE SHAPE OF σ (e+ e− → hadrons)
Measurements of the observed inclusive hadronic cross sections are discussed in detail in the Refs. [7, 8, 9, 10]. The
observed inclusive hadronic cross sections are illustrated in Fig. 1 by dot with error bars, where the error bars are the
combined statistical and point-to-point systematic uncertainties. A close examination of the energy region (from 3.74
to 3.80 GeV) around 3.777 GeV shows that the slopes of the observed cross sections on the two sides of the peak
are quite different; with the slope of the high energy side of the peak substantially larger than that of the low energy
side. It conflicts with the expectations for only one resonance in this energy region, since the effects of the initial state
radiation (ISR) and the DD̄ production threshold as well as the energy dependence of the D D̄ scattering amplitudes
due to the Blatt-Weisskopt barrier [11] would all make the slope at the high energy side of the peak less steep relative
to the slope on the low-energy side. It indicates that one simple resonance hypothesis is quite questionable to fit the
current data.
(a)
25
20
obs
σhad
[nb]
3.75
3.8
3.85
(b)
10
10
2
5
0
3.7
3.7
3.75
3.75
3.8
3.8
3.85
3.85
Ecm [GeV]
FIGURE 1. The observed inclusive hadronic cross sections versus the nominal c.m. energies; the fit was done with two coherent
amplitudes for Rs(3770) (see text).
To investigate whether there are some new structures in addition to the ψ (3770) resonance in the energy region
between 3.700 and 3.872 GeV, we fit the observed cross sections with one or two amplitudes in the energy region. The
exp
expected cross section σhad (Ecm ) can be given as
exp
exp
exp
exp
(s) = σRs(3770)(s) + σJ/ψ (s) + σψ (3686)(s) + σhC (s),
σhad
exp
exp
exp
(1)
2 , where σ
with s = Ecm
(s), σJ/ψ (s), σψ (3686) (s), and σhC (s) are, respectively, the expected cross sections for
Rs(3770)
Rs(3770) → hadrons, J/ψ → hadrons, ψ (3686) → hadrons, and continuum light hadron production at the c.m.
energy Ecm , and Rs(3770) denotes the full structure (being with one or two structures hypothesis) around 3.773
GeV. The expected cross sections are obtained from the Born order cross sections for these processes and the ISR
corrections [12, 13]. For the Rs(3770) resonance(s), we use one or two pure P-wave Breit-Wigner amplitude(s) with
energy-dependent total widths [7, 8, 9] to fit the observed hadronic cross sections. For two amplitude hypothesis,
concerning the possible interference between the two amplitudes, we use two extreme schemes to see if we can get
better description for the anomalous line shape. In the first scheme, we ignore the possible interference; and in the
second, we assume the complete interference between the two amplitudes.
Fits to the observed cross sections presented in Fig. 1 are performed in different cases. In the first and second cases,
the fits give the results of the Solution 1 and Solution 2, respectively. As a comparison, a fit to the cross sections with
the conventional one Briet-Wigner form of ψ (3770) resonance as the definition of the R s (3770) for the one resonance
hypothesis is also made. The red lines in the Fig. 1 and in the sub-figures (a) inserted in the Fig. 1 represent the fitted
values of the cross sections for the Solution 2. The green lines in the sub-figures (a) show the fit to the observed cross
sections for the one amplitude hypothesis. The circles with error bars in red shown in the sub-figures (b) inserted in the
Fig. 1 show the measured net cross sections, corresponding to the two amplitudes themselves in Rs(3770) definition
for the Solution 2, while the blue line shows the fit to the net cross sections of the two resonances for the Solution 2.
The 2nd, the 3rd and the 4th columns of table 1 summarize, respectively, the results of the fits for the Solution 1 and
the Solution 2 of the two amplitude hypothesis, and for the one amplitude hypothesis, where the first errors are from
the fit and the second systematic.
We also fit the observed cross sections with other hypotheses. Ref. [14] reports the details about this.
TABLE 1. The fitted results, where M, Γtot and Γee are the mass, total and leptonic widths of
resonance, φ is the phase difference between the two amplitudes and AM stand for amplitude(s) [14].
Quantity
two AM (Solution 1)
two AM (Solution 2)
one AM
χ 2 /ndo f
125/103 = 1.21
3685.5 ± 0.0 ± 0.5
312 ± 34 ± 1
2.24 ± 0.04 ± 0.11
3765.0 ± 2.4 ± 0.5
28.5 ± 4.6 ± 0.1
155 ± 34 ± 8
3777.0 ± 0.6 ± 0.5
12.3 ± 2.4 ± 0.1
93 ± 26 ± 9
–
0.4 ± 5.6 ± 0.6
112/102 = 1.10
3685.5 ± 0.0 ± 0.5
311 ± 38 ± 1
2.23 ± 0.04 ± 0.11
3762.6 ± 11.8 ± 0.5
49.9 ± 32.1 ± 0.1
186 ± 201 ± 8
3781.0 ± 1.3 ± 0.5
19.3 ± 3.1 ± 0.1
243 ± 160 ± 9
(158 ± 334 ± 5)
5.2 ± 2.5 ± 0.6
182/106 = 1.72
3685.5 ± 0.0 ± 0.5
304 ± 36 ± 1
2.24 ± 0.04 ± 0.11
3773.3 ± 0.5 ± 0.5
28.2 ± 2.1 ± 0.1
260 ± 21 ± 8
–
–
–
–
0.0 ± 0.5 ± 0.6
Mψ (3686) [MeV]
Γtot
ψ (3686) [keV]
Γee
ψ (3686) [keV]
M1 [MeV]
Γtot
1 [MeV]
Γee
1 [eV]
M2 [MeV]
Γtot
2 [MeV]
Γee
2 [eV]
φ [o ]
f
Anomalous line shapes of σ (e+ e− → D0 D̄0 , D+ D− , DD̄)
Measurements of the line shapes of the cross sections for D+ D− , D0 D̄0 and DD̄ production in e+ e− annihilation and
the ratios of the production rates of D+ D− and D0 D̄0 at a series of energy points across the ψ (3770) resonance in the
same experiment have special significance in studies of the properties of ψ (3770) and D meson production and decays
as well as their interaction mechanism. This kind of measurements can also serve as a probe for some unknown effects
which may partially be responsible for the measured large non-D D̄ branching fraction of ψ (3770) decays [4, 15]. The
BES Collaboration observed an anomalous line shape for e+ e− → hadrons [14] discussed in Section II, which may be
attributed to some unknown effects or some new structure additional to one simple ψ (3770) resonance in the energy
region between 3.70 and 3.87 GeV. If so, the line shapes of the D + D− , D0 D̄0 and DD̄ production and the ratios of the
production rates as a function of the center-of-mass energy would deviate from the theoretical expectation in assuming
that there is only one simple ψ (3770) resonance in the region.
6
4
(a1)
0
6
σ obs [nb]
4
(a2)
2
0
6
(a3)
4
2
0
3.74
3.76
3.78
Ec.m. (GeV)
3.8
obs
σDobs
+ D− /σD0 D̄0
2
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
(b)
3.74
3.76
3.78
3.8
Ec.m. (GeV)
FIGURE 2. (a): the observed cross sections versus the nominal c.m. energies, where (a1) is for e+ e− → D+ D− , (a2) is for
e+ e− → D0 D̄0 , and (a3) is for e+ e− → DD̄; (b): the ratio of production rate of D+ D− and D0 D̄0 versus the nominal c.m. energy.
Figures 2(a1), (a2) and (a3) show the observed cross sections for D + D− , D0 D̄0 and DD̄ production at different
center-of-mass energies [16], respectively. The error bars represent the combined statistical and point-to-point systematic uncertainties including the statistical uncertainties in the luminosity, the uncertainties in efficiencies for detection
of Bhabha events, singly tagged D events and the uncertainties in fitting parameters of the invariant mass spectra. As
we discussed the anomalous line shape of the cross sections for e + e− → hadrons, the slopes of the observed DD̄ cross
sections on the two sides of the peak around 3.777 GeV are quite different, with the line shape being similar to the
one of cross sections for e+ e− → hadrons observed in the c.m. energy range [14], which are discussed in Section II.
obs
Figure 2(b) shows the ratios of σDobs
+ D− /σD0 D̄0 measured at the different center-of-mass energies. The error bars are the
combined statistical and point-to-point systematic uncertainties [16].
B[J/ψ → K 0 /K ∗0 X], B[ψ (3686) → K 0 /K ∗0 X] AND B[ψ (3770) → K 0 /K ∗0 X]
Examining the line shapes of the inclusive K 0 , K ∗0 , φ , J/ψ , etc. production in e+ e− annihilation in the energy region
covering both the ψ (3770) and ψ (3686) resonances can help understand the nature of the ψ (3770) resonance, and
may help understand the origin of the ρ -π puzzle in ψ (3686) decays, since any significant deviation of these line
shapes from the expected ones in assuming that there is only one simple structure around 3.770 or 3.686 GeV may
indicate existing some new structure(s) in this region or existing some new dynamics which affects these resonances
production and decays.
σ obs [nb]
(a)
10
10
2
(b)
10
3
(c)
(d)
10
2
10
2
2
10
10
10
10
1
1
3.65
3.7
3.75
3.8
3.85
Ecm (GeV)
3.65
3.7
3.75
3.8
3.85
1
-1
3.07
3.08
Ecm (GeV)
3.09
3.1
3.11
Ecm (GeV)
10
3.12 3.07
3.08
3.09
3.1
3.11
3.12
Ecm (GeV)
FIGURE 3. The observed inclusive K 0 /K ∗0 cross sections versus the nominal c.m. energies, where (a) and (c) are the cross
sections for e+ e− → K 0 X, while (b) and (d) are the cross sections for e+ e− → K ∗0 X.
With the energy scan data samples, we measured the observed cross sections for inclusive K 0 /K ∗0 production
at different center-of-mass energies in the range from 3.65 to 3.88 GeV and in the range around 3.097 GeV. The
dots with error bars in figure 3(a), (b), (c) and (d) show these cross sections. Fitting these cross sections to the
expectations for ψ (3770), ψ (3686) and J/ψ production yields the inclusive K 0 /K ∗0 decay branching fractions of
ψ (3770), ψ (3686) and J/ψ . The second column of table 2 summarizes the preliminary results of the measured
inclusive decay branching fractions of ψ (3770), ψ (3686) and J/ψ , where the first errors are statistical, and the second
systematic. The third column of the table shows the total branching fraction summed over the exclusive branching
fractions for the decay modes containing at least one K 0 /K ∗0 in the final states. By comparing the measured branching
fractions for J/ψ → K 0 X and ψ (3686) → K 0 X to the ones summed over the known branching fractions for the decay
modes containing at least one K 0 in the final states given in PDG08 [17], we find that there are more rooms for
searching for the exclusive decay modes containing at least one K 0 in the final states of J/ψ and ψ (3686) decays.
By selecting the inclusive K 0 decay events which do not come from the D0 and D+ decays, we measure the inclusive
non-DD̄ K 0 branching fraction of ψ (3770) decays to be
B[ψ (3770) → K 0 |non−DD̄ X] = (11.5 ± 6.9 ± 1.5)%,
which is preliminary results.
SUMMARY
In summary, by analyzing the line-shape of the cross sections for e + e− → hadrons, we find that it does not describe
the cross section shape well with the hypothesis that only one simple ψ (3770) resonance exists in the energy region
from 3.700 to 3.872 GeV. If there are no other dynamics effects which distort the pure D-wave Breit-Weigner shape
of the cross sections, the analysis shows that the fit is inconsistent with the explanation for only one simple ψ (3770)
resonance there at 7σ statistical significance, indicating that there is likely a new structure additional to the single
ψ (3770) resonance. However, if there are some dynamics effects distorting the pure D-wave Breit-Weigner shape of
the cross sections, such as the rescattering of DD̄ leading to the significant energy dependence of the wave function
TABLE 2. The preliminary results of the inclusive K 0 /K ∗0
decay branching fractions of ψ (3770), ψ (3686) and J/ψ
Decay mode
B [%]
→ K0X
ψ (3770)
ψ (3770) → K ∗0 X
ψ (3686) → K 0 X
ψ (3686) → K ∗0 X
J/ψ → K 0 X
J/ψ → K ∗0 X
71.3 ± 2.5 ± 8.4
23.1 ± 3.1 ± 2.5
28.3 ± 0.7 ± 2.9
10.6 ± 0.7 ± 0.5
20.4 ± 0.5 ± 1.3
7.7 ± 0.5 ± 0.4
Summed B [%]
N/A
N/A
<7
< 10
in the DD̄ decays of the ψ (3770) resonance, one has to consider those effects in the measurements of the resonance
parameters of ψ (3770), since these effects would definitely shift the measured values of the resonance parameters.
In addition to these, we measured the line shapes of the observed cross sections for D + D− , D0 D̄0 and DD̄ production
in e+ e− annihilation in the energy region from 3.73 to 3.80 GeV. These line shapes are similar to the anomalous line
shape of cross sections for e+ e− → hadrons observed in the center-of-mass energy range from 3.70 to 3.87 GeV [14].
With the energy scan data samples, we measured the inclusive K 0 /K ∗0 decay branching fractions of ψ (3770),
ψ (3686) and J/ψ for the first time.
We thank the staff of BEPC for their hard efforts. This work is supported in part by the National Natural Science
Foundation of China under contracts Nos. 10935007, 19991480,10225524,10225525, the Chinese Academy of Sciences under contract No. KJ 95T-03, the 100 Talents Program of CAS under Contract Nos. U-11, U-24, U-25, and
the Knowledge Innovation Project of CAS under Contract Nos. U-602, U-34(IHEP); by the National Natural Science
Foundation of China under Contract No.10175060(USTC),and No.10225522(Tsinghua University).
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