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Production of the charmed baryon�cð2940Þþ at PANDA
Jun He,1,3 Zhen Ouyang,1,3 and Xiang Liu1,2,*1Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS,
Lanzhou 730000, China2School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
3Nuclear Theory Group, Institute of Modern Physics of CAS, Lanzhou 730000, China
Xue-Qian Li
School of Physics, Nankai University, Tianjin 300071, China(Received 27 September 2011; published 8 December 2011)
In this work we evaluate the production rate of the charmed baryon�cð2940Þþ at PANDA. For possible
assignments of �cð2940Þþ: JP ¼ 1=2�, 3=2� and 5=2�, the total cross section of p �p ! ��c�cð2940Þþ is
estimated, which may exceed 1 nb. With the designed luminosity (2� 10�32 cm�2=s) of PANDA, our
estimate indicates that ten thousand events per day if �cð2940Þþ is of JP ¼ 1=2þ or 108 per day if it is of
JP ¼ 5=2þ can be expected. Those values actually set the lower and upper limits of the �cð2940Þþproduction. In addition, we present the Dalitz plot and carry out a rough background analysis of the
�cð2940Þþ production in the p �p ! D0p ��c and p �p ! �0;þþc �þ;� ��c processes, which would provide
valuable information for accurate determination of the �cð2940Þþ identity.
DOI: 10.1103/PhysRevD.84.114010 PACS numbers: 14.20.Lq, 13.60.Rj, 13.75.Cs
I. INTRODUCTION
The charmed baryon �cð2940Þþ with mass m ¼2939:8� 1:3ðstatÞ � 1:0ðsystÞ MeV and width � ¼17:5� 5:2ðstatÞ � 5:9ðsystÞ MeV was first observed inthe D0p invariant mass spectrum by the BABARCollaboration [1]. Later, �cð2940Þþ was confirmed bythe Belle Collaboration in the �cð2455Þ0;þþ�þ;� channels[2], where the obtained mass and width are m ¼ 2938:0�1:3þ2:0
�4:0 MeV and � ¼ 13þ8þ27�5�7 MeV respectively.
Obviously the values achieved by the two collaborationsare consistent with each other within the error tolerance[1].
Actually, comparing with the meson case, the structureof baryons is more intriguing from both theoretical andexperimental aspects. Recently, along with the experimen-tal progress at the BABAR, Belle and BES, a great numberof new states of mesons have been observed and some ofthem are identified as exotic, i.e., these states cannot becategorized into the regular q �q0 structure. It is natural toconjecture that the possibility also exists for the baryons.However, this situation is much more complicated than themeson case. By the regular structure, the baryon is com-posed of three quarks, so the exotic configuration of bary-ons would be much more difficult to be identified. On theother side, this study can enrich our knowledge on thefundamental structure of hadrons; namely, it will answerthe long-standing question that the SUð3Þ theory indeedallows existence of the non q �q and qqq configurations,and, if yes, where do we search for them? That is the job oftheorists of high energy physics.
Experimentally, some peculiar phenomena have beenobserved. Before we can attribute them to new physics ornew hadronic configuration, a thorough study of whetherthey can be interpreted by the regular quark structure andthe standard model (SM) must be carried out.The observation of �cð2940Þþ has stimulated theorists’
extensive interest in understanding its structure. Since theobserved charmed baryon �cð2940Þþ is close to the pro-duction threshold of D�p, a conjecture that �cð2940Þþmay be a D�N molecular state, was naturally proposed[3]. The masses ofD�N molecular states were calculated inthe potential model, and the results support the statementthat �cð2940Þþ is an S-wave D�0p molecular state withspin parity JP ¼ 1
2� or JP ¼ 1
2þ [3]. Recently, the authors
of Ref. [4] systematically studied the interaction betweenD� and the nucleon, and concluded that the D�N systemsmay behave as JP ¼ 1=2�, 3=2� baryon states. With theJP ¼ 1
2� and JP ¼ 1
2þ assignments, the strong decays of
�cð2940Þþ have been investigated by the authors ofRef. [5], but their result determines that the assignmentof �cð2940Þþ as a D�N molecular state with JP ¼ 1
2�
should be excluded. Later, the radiative and strong three-body decays of �cð2940Þþ were explored in Refs. [6,7],where �cð2940Þþ was assigned as a D�N molecular stateof JP ¼ 1
2þ.
Besides supposing �cð2940Þþ to be a molecular state,the alternative theoretical explanation that �cð2940Þþ isjust a conventional charmed baryon has also been widelydiscussed. The calculation in terms of the potential modelshows that the masses of the conventional charmed baryonsof JP ¼ 5
2� and JP ¼ 3
2þ are 2900 MeV and 2910 MeV,
respectively [8,9], which are close to the mass of�cð2940Þþ. In Ref. [10], the authors suggested that*Corresponding author: [email protected]
PHYSICAL REVIEW D 84, 114010 (2011)
1550-7998=2011=84(11)=114010(9) 114010-1 � 2011 American Physical Society
�cð2940Þþ is the first radial excitation of �cð2520Þ ofJP ¼ 3
2þ and possesses the quantum number of JP ¼ 3
2þ.
In their calculations of the mass spectrum the relativisticquark-diquark model was used. In addition, �cð2940Þþ asthe first radial excitation of the �c was also suggested viasolving the Faddeev equations for three-body systemsin the momentum space [11]. In the heavy hadronchiral perturbation theory, the ratio �ð�cð2940Þþ !��
c�Þ=�ð�cð2940Þþ ! �c�Þ was obtained if the spin-parity of �cð2940Þþ is JP ¼ 5
2� or JP ¼ 3
2þ [12]. These
ratios will be applied to distinguish different JP assign-ments of �cð2940Þþ [12]. In Ref. [13], the authors calcu-lated the strong decays of newly observed charmedhadrons in the 3P0 model. Here, �cð2940Þþ could only
be a D-wave charmed baryon ��0c1ð12þÞ or ��0
c1ð32þÞ while�cð2940Þþ as the first radial excitation of �cð2286Þþ iscompletely excluded since �cð2940Þþ ! D0p was ob-served by the BABAR Collaboration [1]. The result ob-tained in terms of the chiral quark model indicates that�cð2940Þþ could be a D-wave charmed baryon �2
cD��32þ
[14].As summarized in Table I, a great deal of theoretical
ansatz for the structure�cð2940Þþ was proposed, by whichits spectrum was calculated, and the results are quite modeldependent. At present the properties of �cð2940Þþ are stillunclear, the fact means that more work is needed to deter-mine its real structure, especially investigating from differ-ent angles.
The current information of �cð2940Þþ is extracted fromthe eþe� collision [1]. Thus, it is interesting to investigatethe �cð2940Þþ production in other processes. The PANDAexperiment [16] at the Facility for Antiproton and IonResearch (FAIR) will be carried out in the near future,which will definitely provide valuable data for understand-ing of nonperturbative QCD. Study of the charmed baryon
is one of the main physics goals of PANDA since its beammomentum p ¼ 5–15 GeV just covers the productionthreshold of charmed hadron. Encouraged by the prospect,in this work, we study the �cð2940Þþ production atPANDA. Some parallel theoretical investigations of theproduction of the charminium-like states Xð3872Þ,Zþð4430Þ at PANDA [17,18] were also carried out.This paper is organized as follows. After the
Introduction, we will present the effective Lagrangianand the corresponding coupling constants used in thiswork. The formulation and the numerical result of the�cð2940Þþ productions at PANDA will be given inSec. III. In Sec. IV, considering the sequential decay�cð2940Þþ ! D0p, we make the Dalitz plot analysis on
p �p ! ��c�cð2940Þþ ! ��cD0p, where p �p ! ��c�c !
��cD0p forms the background. Finally the paper ends
with our discussion and conclusion.
II. EFFECTIVE LAGRANGIANS ANDCOUPLING CONSTANT
Associated with a ��c production, �cð2940Þþ could beproduced in the proton and antiproton collision by ex-changing a D0 meson, as shown in the Fig. 1. It is noted
that direct p �p annihilation into ��c�cð2940Þþ is negligible
TABLE I. The possible JP assignments to the�cð2940Þþ in the literature [3–15]. Here, we use
‘‘!’’ or ‘‘�’’ to denote that the corresponding studies suggest or exclude that JP assignment for�cð2940Þþ. Additionally, the upper and lower values in the bracket denote the decay widths(MeV) for its D0p and �þþ
c �� channels obtained in the literature corresponding to the quantumnumber assignments.
1=2þ 1=2� 3=2þ 3=2� 5=2þ 5=2�
He et al. [3] ! !Dong et al. [5] (0:20� 0:090:95� 0:37) �Dong et al. [6,7] !He et al. [4] ! !Capstick et al. [8,9] ! ! !Cheng et al. [12] ! !Zhong et al. [14]
�1:081:06
�Chen et al. [13]
�112:2
� �110:6
�Ebert et al. [10] !Valcarce et al. [11] !Chen et al. [15] !
FIG. 1 (color online). The diagram for the process p �p !��c�cð2940Þþ by exchanging the D0 meson.
JUN HE et al. PHYSICAL REVIEW D 84, 114010 (2011)
114010-2
in comparison with the mechanism shown in Fig. 1, be-cause the annihilation channel is Okubo-Zweig-Iizuka(OZI) suppressed. Thus, in this work we do not considerits contribution at all.
For being at most model-independent, we applythe effective Lagrangian approach to study the
p �p! ��c�ð2940Þþ process. In our calculation, we con-sider the production rates of �cð2940Þþ whose JP assign-ments are prior assumed. The following Lagrangiansdescribe the interaction of �cð2940Þþ with D0p for differ-ent JP assignments to �cð2940Þþ [5,19–22]:
L ð1=2Þþ ¼ gð1=2Þþ�cð2940Þþi�5pD0; (1)
L ð1=2Þ� ¼ gð1=2Þ��cð2940ÞþpD0; (2)
L ð3=2Þþ ¼ gð3=2Þþ��c ð2940Þþp@�D0; (3)
L ð3=2Þ� ¼ gð3=2Þ���c ð1940Þþi�5p@�D
0; (4)
L ð5=2Þþ ¼ gð5=2Þþ���c ð2940Þþi�5p@�@�D
0; (5)
L ð5=2Þ� ¼ gð5=2Þ����c ð2940Þþp@�@�D0; (6)
where we use the subscripts 12�, 3
2� and 5
2� to distinguish
possible JP quantum numbers of �cð2940Þþ. The
Lagrangian for the interaction of ��c and �D0 �p can be easilyobtained by replacing �cð2940Þþ ðp;D0Þ in Eq. (1) with��c ð �p; �D0Þ. In the above Lagrangians, the coupling con-stants gJP � g�cð2940ÞþpD0 can be obtained by fitting the
measured partial width of the �cð2940Þþ ! D0p decay,i.e.,
�ð�cð2940Þþ ! pD0Þg2JP
¼ mN
4ð2J þ 1Þ�2jkjffiffiffis
p BSAJ (7)
with BS ¼ EN
mNþ S and S ¼ Pð�1ÞJþ1=2, where J is the
spin of �cð2940Þ, EN (mN) denotes the energy (mass) ofproton. AJ ¼ N
2J jkj2J�1 with N ¼ 1, 2, 2 corresponds to
J ¼ 1=2, 3=2, 5=2, respectively. k is the three-momentumof the daughter mesons in the center of mass frame of p �p.From BRð�cð2940Þþ ! D0pÞ, we extract the couplingconstant gJP . However, the BABAR and Belle experimentsonly measured the total width of �cð2940Þþ, and have notgiven the partial decay width of �cð2940Þþ ! D0p so far.Thus, to obtain gJP , one needs to invoke theoretical calcu-lations. In terms of different theoretical models to estimate,different groups have obtained different values of the decaywidth of �cð2940Þþ ! D0p which are listed in Table. I.
Since the cross section of p �p ! ��c�cð2940Þþ is propor-
tional to g2JP, the line shape of the cross section of p �p !
�cð2940Þþ ��c depends on the c.m. energyffiffiffis
p, but does not
depend on the gJP value. In this work, we choose a concrete
gJP value to calculate the cross section of p �p !��c�cð2940Þþ. Concretely, we set the partial decay widthto be �ð�cð2940Þþ ! D0pÞ ¼ 1:5 MeV and then deter-mine the coupling constant gJP as gð1=2Þ� ¼ 0:26; gð1=2Þþ ¼1:25; gð3=2Þ� ¼ 5:26 GeV�1; gð3=2Þþ ¼ 1:10 GeV�1;
gð5=2Þ� ¼ 4:23 GeV�2 and gð5=2Þþ ¼ 20:19 GeV�2. By an
approximate SUð4Þ flavor symmetry, the coupling constantg�cpD
0 is equal to g�NK ¼ 13:2 [23–26], which is larger
than g�NK ¼ 6:7� 2:1 estimated via the QCD sum rules[27,28].The propagators for a fermion of J ¼ 1=2, 3=2, 5=2 are
written as [22,29],
Gnþð1=2ÞðqÞ ¼ Pðnþð1=2ÞÞGRðq2Þ
¼ Pðnþð1=2ÞÞ 2MR
q2 �M2R þ iMR�R
(8)
with
P1=2ðqÞ ¼ 6qþMR
2MR
; (9)
P3=2�� ðqÞ¼ 6qþMR
2MR
��g��þ1
3����þ 1
3MR
ð��q����q�Þ
þ 2
3M2R
q�q�
�; (10)
P5=2�1�2�1�2
ðqÞ ¼ 6qþMR
2MR
�1
2ð~g�1�1
~g�2�2þ ~g�1�2
~g�2�1Þ
� 1
5~g�1�2
~g�1�2� 1
10ð~��1
~��1~g�2�2
þ ~��1~��2
~g�2�1þ ~��2
~��1~g�1�2
þ ~��2~��2
~g�1�1Þ�; (11)
where ~�� ¼ �� � q� 6q=q2 and ~g�� ¼ g�� � q�q�=q2. q
and MR are the momentum and the mass of the fermionparticle, respectively.
III. THE PRODUCTION OF �cð2940Þþ IN THEPROTON AND ANTIPROTON COLLISION
In this section we calculate the�cð2940Þ production ratein the proton-antiproton collision as shown in Fig. 1. For
the p �p ! ��c�cð2940Þþ process, the production ampli-tudes is
PRODUCTION OF THE CHARMED BARYON . . . PHYSICAL REVIEW D 84, 114010 (2011)
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M ¼ g�cpD0g�cð2940ÞþpD0 �uRðk2ÞCRðkÞupðp2Þ
� �v ��cðk1ÞCv �pðp1ÞGDðk2ÞF 2ðk2Þ; (12)
where CR or C describe the Lorentz structures of the
vertex for D0 interacting with �cð2940Þþp or ��c �p.They are derived in terms of the Lagrangians in Eqs.(1)–(6). k1, k2, p1, p2 and k are the momenta of
�cð2940Þþ, ��c, p, �p and the exchanged meson D0,respectively. Additionally, the monopole form factorF ðk2Þ ¼ ð�2 �m2
DÞ=ð�2 � k2Þ is introduced. As wellunderstood, the concerned hadrons at the effective verti-ces by no means are point-particles, but have compli-cated structures, thus the form factor phenomenologicallydescribes the inner structure effect of interaction verticesshown in Fig. 1 and moreover, it partly compensates forthe off-shell effect of the exchanged D0 meson as sug-gested in Ref. [30]. Indeed the monopole form factor is a
phenomenological ansatz and not derivable from thefield theory, thus errors are unavoidably brought up justlike any phenomenological computation. Since the in-volved parameters are fixed by fitting data, the model-dependence is greatly alleviated, therefore, it is observedthat for lower energy reactions, the scenario workswell.Before studying the cross section for the �cð2940Þþ
production at the p �p collision, let us first calculate thetotal cross section for the proton-antiproton scattering tothe�c and anti-�c pair in our theoretical frame, which hasbeen experimentally measured and carefully studied in the
literature [30,31]. In Fig. 2, the total cross section of p �p !�c
��c with different cutoffs is presented, where we restrictthe � value within a reasonable range from 2 GeV to3.25 GeV.
In Ref. [30], the reaction p �p ! �c��c was supposed to
occur via a meson-exchange mechanism, where the cutoff
� was set as 3 GeV. An obvious similarity between p �p !�c
��c and p �p ! ��c�cð2940Þþ suggests that we adopt
� ¼ 3 GeV to estimate the cross section of p �p !��c�cð2940Þþ.The cross sections for �cð2940Þþ production with dif-
ferent spin-parity assignments to �cð2940Þþ are presentedin Fig. 3.
FIG. 2 (color online). The total cross section for the processp �p ! �c
��c with different � values.
s (GeV)
(nb
)
5.25 5.30 5.35 5.40
10-1
100
101
102
103
104
105
JP = 1 / 2 +
JP = 3 / 2 +
JP = 5 / 2 +
5.25 5.30 5.35 5.40
10-1
100
101
102
103
104
105
JP = 1 / 2 -
JP = 3 / 2 -
JP = 5 / 2 -
FIG. 3 (color online). The cross section for the process p �p !��c�cð2940Þþ with different JP assignments of �cð2940Þþ.
FIG. 4 (color online). The diagrams for the p �p ! ��cD0p; the
left and right diagrams occur via the intermediate �cð2940Þþand �þ
c , respectively.
s (GeV)
(nb
)
5.10 5.15 5.20 5.25 5.30 5.35 5.4010-3
10-2
10-1
100
101
102
103
104
105
JP = 1 / 2 +
JP = 3 / 2 +
JP = 5 / 2 +
5.10 5.15 5.20 5.25 5.30 5.35 5.4010-3
10-2
10-1
100
101
102
103
104
105
JP = 1 / 2 -
JP = 3 / 2 -
JP = 5 / 2 -
FIG. 5 (color online). The dependence of the cross section forthe p �p ! ��c�cð2940Þþ ! ��cD
0p process onffiffiffis
p. Here, we
consider different JP assignments to �cð2940Þþ.
JUN HE et al. PHYSICAL REVIEW D 84, 114010 (2011)
114010-4
Our results of �cð2940Þþ production indicate that the
cross section of p �p ! ��c�cð2940Þþ strongly depends onthe JP assignments of �cð2940Þþ. If �cð2940Þþ is a JP ¼1=2� state, the cross section of the p �p ! ��c�cð2940Þþ
process is much smaller than that if �cð2940Þþ is a JP ¼5=2þ state by a big fraction of �104.
IV. THE DALITZ PLOTANDTHE BACKGROUND ANALYSIS
As shown in the above section, considerable events of�cð2940Þþ can be produced in the proton and antiprotoncollision. In this section, we present the Dalitz plot of
p �p ! ��cD0p, where �cð2940Þ or �c is an intermediate
state just shown in Fig. 4. A comparison of Fig. 2 with
Fig. 3 indicates that the cross section of p �p ! �c��c is
comparable with that of p �p ! ��c�cð2940Þþ. Thus, p �p !�c
��c ! ��cD0p where �c is off-shell, becomes a main
background contribution when we analyze the �cð2940Þþproduction in the p �p ! ��c�cð2940Þþ ! ��cD
0p process.
The amplitude of p �p ! ��c�cð2940Þþ ! ��cD0p
where �cð2940Þ can be an on-shell baryon, reads as
M¼g�cpD0g2
�cð2940ÞþpD0 �upðk2Þ�Rðk3Þ�Gnþð1=2Þ
R ðqÞ�RðkÞupðp2Þ� �v ��c
ðk1Þ�v �pðp1ÞGDðk2ÞF 2ðk2Þ; (13)
s (GeV)
(nb
)
5.10 5.15 5.20 5.25 5.30 5.35 5.4010-3
10-2
10-1
100
101
102
103
104
105
JP = 1 / 2 +
JP = 3 / 2 +
JP = 5 / 2 +
5.10 5.15 5.20 5.25 5.30 5.35 5.4010-3
10-2
10-1
100
101
102
103
104
105
JP = 1 / 2 -
JP = 3 / 2 -
JP = 5 / 2 -
FIG. 6 (color online). The cross section of p �p ! ��cD0p.
Here, we include the background contribution to p �p ! ��cD0p.
FIG. 7 (color online). The Dalitz plot and invariant mass spectra for p �p ! ��cD0p at
ffiffiffis
p ¼ 5:32 GeV and with J ¼ 1=2 assignmentto �cð2940Þþ. Here, the left or right column corresponds to the numerical result of the production of �cð2940Þþ with positive ornegative parity.
PRODUCTION OF THE CHARMED BARYON . . . PHYSICAL REVIEW D 84, 114010 (2011)
114010-5
where q, k2 and k3 are the four-momenta of the intermediatestate �cð2940Þþ and final states p and D0, respectively. We
can easily obtain the amplitude of p �p ! �c��c ! ��cD
0pby Eq. (13), where we only need to replace the relevantparameter of �cð2940ÞþðJP ¼ 1=2þÞ with that of �c.
In Fig. 5, we present the cross section of p �p !��c�cð2940Þþ ! ��cD
0p, which is dependent onffiffiffis
p. As
shown in Fig. 5, there exists a steep increase at aboutffiffiffis
p ¼5:2 GeV, where�ð2940Þþ approaches its mass-shell, so itspropagator contributes a cusp.
Taking the background contribution into account, the
dependence of the cross section of p �p ! ��cD0p on
ffiffiffis
pis shown in Fig. 6. Our calculation also indicates that the
order of magnitude of the cross section of p �p ! �c��c !
��cD0p is about 10 nb, which is far larger than that of
p �p ! �cð2940Þþ ��c ! ��cD0p as �cð2940Þþ is a JP ¼
1=2þ state. To some extent, the contribution of the inter-
mediate �cð2940Þþ of JP ¼ 1=2� to p �p ! ��cD0p is
immersed in the background.The Dalitz plot is a very useful tool for the data analysis
since much information is exposed by the plot. With the
help of the FOWL code, we present the Dalitz plot for the
p �p ! ��cD0p process and the pD0 invariant mass spec-
trum m2pD0 in Figs. 7–9.
Just as shown in Fig. 7, the shape of the distributions,
where peaks appear at certain locations, are not the Breit-
Wigner types. This is mainly due to an interference be-
tween the amplitudes of p �p ! �c��c ! ��cD
0p and
p �p ! �cð2940Þþ ��c ! ��cD0p, which also implies that
p �p ! �c��c ! ��cD
0p forms the dominant background
for p �p ! ��cD0p.
With JP ¼ 3=2� or 5=2� assignments to �cð2940Þþ,we find that there exist explicit cusp structures correspond-
ing to �cð2940Þþ in the pD0 invariant mass spectrum,
which can be described by the Breit-Wigner formalism.
The Dalitz plot analysis indicates that �cð2940Þþ signal
can be well distinguished from the background in the
p �p ! ��cD0p process. That is due to the fact that the
contribution of p �p ! �c��c ! ��cD
0p is far smaller
than that of p �p ! �cð2940Þþ ��c ! ��cD0p as shown in
Figs. 5 and 6.
FIG. 8 (color online). The Dalitz plot and invariant mass spectra for p �p ! ��cD0p at
ffiffiffis
p ¼ 5:32 GeV and with J ¼ 3=2 assignmentto �cð2940Þþ. Here, the left or right column corresponds to the numerical result of the production of �cð2940Þþ with positive ornegative parity.
JUN HE et al. PHYSICAL REVIEW D 84, 114010 (2011)
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V. DISCUSSION AND CONCLUSION
In this work we investigate the production rate of�cð2940Þþ in the future experiments at PANDA. We findif the branching ratio of�cð2940Þþ decaying intoD0p is atthe order 0.1, at least 104 events of �cð2940Þþ per day canbe produced at PANDA.Here, let us briefly discuss dependence of the numerical
result on the phenomenologically introduced parameter �used in this work. The cutoff � ¼ 3 GeV is adopted assuggested in Ref. [30]. If the cutoff� decreases to 2.5 GeV,both the production rate of �cð2940Þþ and the backgroundwould increase about one order. The number of events isstill large enough for investigating behaviors of�cð2940Þþin the proton and antiproton collision. In our numericalcomputations we adopt the same cutoff � value as that inRef. [30].We would like to specify an important issue, which was
discussed in the literature and may affect our theoreticalestimate of the production rate. It is noted that the initialstate interaction (ISI) effect is included in the numericalresult presented in Secs. III and IV. The ISI is an important
FIG. 9 (color online). The Dalitz plot and invariant mass spectra for p �p ! ��cD0p at
ffiffiffis
p ¼ 5:32 GeV and with J ¼ 5=2 assignmentto �cð2940Þþ. Here, the left or right column corresponds to the numerical result of the production of �cð2940Þþ with positive ornegative parity.
FIG. 10 (color online). The total cross section and invariantmass spectrum for p �p ! ���þþ
c���c at
ffiffiffis
p ¼ 5:35 GeV. Here,we consider the ISI effect just discussed in Sec. V.
PRODUCTION OF THE CHARMED BARYON . . . PHYSICAL REVIEW D 84, 114010 (2011)
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effect for studying meson production in nucleon-nucleoncollisions as the transition occurs near the threshold. Thateffect was first observed by the authors of Refs. [32,33]that the ISI makes the cross section to be reduced by anoverall factor, which is slightly energy-dependent. In
studying p �p ! ��c�c process, the authors of Ref. [30]also took into account the ISI effect, which reduces the
cross section of p �p ! ��c�c by a factor 10. The ISI may beinduced by complicated interaction processes among theingredients inside the colliding p and �p, which may bevalence quarks or even gluons and sea quarks. It is believedthat such processes are governed by the nonperturbativeQCD effects, thus not calculable so far. Interesting tonote that for high energy p �p or pp collisions, one canuse the parton distribution function (PDF) due to theasymptotic freedom of QCD, but for lower energy colli-sions, we do not know how to correctly deal with the ISIeffects. Therefore, as suggested by previous research[32,33], we would retain a phenomenological factor inthe numerical estimate of the production rate to take care
of the ISI effect on p �p ! ��c�cð2940Þþ. Thus, an extrafactor is introduced to reflect the ISI effect, which makes
the cross section of p �p ! ��c�cð2940Þþ correspondingto Eq. (12) suppressed by 1 order of magnitude (the ISIeffect is considered in the numerical results presented inFigs. 2–10). With above consideration, we can roughlyestimate the production events of �cð2940Þþ at PANDAand the results are presented in Fig. 3. The designedluminosity of PANDA is about 2� 1032 cm�2=s, so theintegrated luminosity in 1 d run is about 104 nb�1.Assuming we have a 50% overall efficiency, we mayexpect 104–108 events of �cð2940Þþ per day produced atPANDA. In addition, we also would like to emphasize thatthe qualitative conclusion, which is made via the back-ground analysis and Dalitz plot, is not affected by whetherincluding the ISI effect.
Furthermore, the line shape of the cross section andinvariant mass spectrum without taking in the backgroundis independent of the coupling constant g�cð2940ÞþD0p. If the
branching ratio of �cð2940Þþ ! D0p is about 10%, thereis a large final-state phase space for the production of
p �p ! �c��c ! ��cD
0p. As 104–108 of �cð2940Þþ perday can be produced, one can carefully study the properties
of �cð2940Þþ via the channel of p �p ! �cð2940Þ þ ��c !D0pþ �D0 �p in the future PANDA experiments. In thesecond subprocess, �c decays into �D0 þ �p which is easy
to be experimentally observed and the constructed invari-ant mass can accurately identify �c.Since the Belle Collaboration confirmed �cð2940Þþ
in the �cð2455Þ0;þþ�þ;� channels [2], we also study
the �cð2940Þþ production in p �p ! ���þþ ���c , where
p �p ! ��c�c ! ���c �
��þþc and p �p ! ��c�cð2940Þþ !
��c���þþ
c compose the background and signal for the�cð2940Þþ production, respectively. In the former channel,because of constraint from the phase space, the �c canonly be an off-shell intermediate state for the final state��c, so due to the Breit-Wigner structure, such a subpro-cess is relatively suppressed in comparison with the‘‘signal.’’ The cross section and the invariant mass
spectrum of p �p ! ��c���þþ with
ffiffiffis
p ¼ 5:35 GeV andBð�cð2940Þþ ! ���þþ
c Þ � 10% is presented in Fig. 10.Here, we take the coupling constant as g�c�c� ¼ 3:9,
which results in a weaker background. The signals of�cð2940Þþ can be distinguished from the backgroundeasily as shown in Fig. 10. Thus, one can conclude that
the channel p �p ! ���þþc
��c is also a suitable channel tostudy �cð2940Þþ.Based on the analysis above, it is optimistic to inves-
tigate�cð2940Þþ in the future experiment of PANDA, eventhough the cross section is not as large as for thecharminium-like states, such as Xð3872Þ [17].In addition, it is very interesting to notice the observa-
tion potential at BelleII [34,35] and the SuperB factory[36], which will produce a large database of �ð4SÞ. As�ð4SÞ may have a sizable branching ratio to decay into
�cð2940Þ þ ��cð2940Þð ��cÞ, thus comparing the data ob-tained at PANDA with that from the B-factory wouldmake more sense and help eventually to pin down thespin-parity assignment of �cð2940Þþ.
ACKNOWLEDGMENTS
This project is supported by the National NaturalScience Foundation of China under GrantsNo. 11175073, No. 10905077, No. 11005129,No. 11035006, No. 11075079; the Ministry of Educationof China (FANEDD under Grant No. 200924, DPFIHEunder Grant No. 20090211120029, NCET under GrantNo. NCET-10-0442); the project sponsored by SRF forROCS, SEM under Grant No. HGJO90402 and theSpecial Foundation of President Support by the ChineseAcademy of Sciences under Grant No. YZ080425.
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