# Search for the Charmed Baryonium and Dibaryon Structures via the QCD Sum Rules

Authors: Xiu-Wu Wang; Zhi-Gang Wang
Journal: Advances in High Energy Physics
 (2022)

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## Abstract

In the present work, we construct eight six-quark currents to study theΣcΣ¯c baryonium and ΣcΣc dibaryon states via the QCD sum rules. For either ΣcΣ¯c baryonium or ΣcΣc dibaryon states, we construct four currents with the JP=1−,1+,0+ and 0−. Except the current 1+ of ΣcΣc, we find the Borel windows for the other seven. There are two possible ΣcΣ¯c molecular states or compact six-quark states with the JP=1− and 0−. The results of the current 0+ of ΣcΣc show a possible ΣcΣc molecular state with 20 MeV binding energy. We find two ΣcΣ¯c baryonium resonances states with the JP=1+,0+ and two ΣcΣc dibaryon resonances states with the JP=0−,1−, respectively. Pole residues of the seven states are also calculated.


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## Body

## 1. Introduction

The dibaryon is composed of two baryons, and the baryonium is formed by a baryon and antibaryon. In 1980s, the research of the interaction between the two baryons caused great attention both theoretically and experimentally [1]. The first known dibaryon state discovered in 1932 has been the deuteron, the bound state of proton and neutron [2]. Except for the deuteron, another genuine dibaryon resonance observed in experiment is the d∗2380 [3–5]. The baryon consists of three quarks, six quarks for the dibaryon or baryonium, it is natural to extend the concept of hexaquarks for which the quarks sitting in a common quark bag. The data of the electromagnetic form factors of the state are possible to differentiate whether it is a molecular type or a compact six-quark entity. For the deuteron, its charge radius is 2.1 fm, the proton and the neutron inside the deuteron are on average 4 fm apart from each other and do not overlap [6, 7], these data depict a clear physical picture of the hadronic molecule for the deuteron. One could also make the differentiation via the decay branching; in Ref. [8], the decay width of d∗2380 is considered via the chiral quark model; it is proposed that d∗2380 spends 2/3 of its time as a six-quark and the rest as a ΔΔ molecule. Theoretically and experimentally, the ways which may find the difference are there; however, seldom work has been done yet for both the ΣcΣc dibaryon and ΣcΣ¯c baryonium in this aspect. At present, it is too hard for us to differentiate ΣcΣc dibaryon or ΣcΣ¯c baryonium from the compact six-quark state. We now could only say: it may be the molecular state or compact six-quark state if the mass is below the threshold of the two baryon constituents (bound state); as for the dibaryon resonance state, its mass is above the threshold of the two baryon constituents.The oldest prediction of the existence of dibaryon with nearly 100 MeV binding energy based on SU(6) symmetry was done by Dyson and Xuong [9] which is in good agreement with the experimental observations of d∗2380 [3–5]. Although the insufficient experimental data for the solid observations of the dibaryon and baryonium states, lots of theoretical calculations have been done in search of them. In recent years, several QCD-inspired models are applied to study the dibaryons and baryoniums, such as the quark delocalization color screening model [10, 11], solving the Bethe-Salpeter equation via effective Lagrangians [12, 13], constituent quark model [14, 15], lattice QCD [16, 17], and the QCD sum rules [18–21]. Especially, in Refs. [22, 23], the authors study the charmed hadrons to investigate the mutual interactions between them and search for poles by solving the Bethe-Salpeter equation. It is natural to ask: what are the predictions of the interactions of these charmed hadrons in the framework of the QCD sum rules? In Ref. [24], the scalar and axialvector ΞccΣc dibaryon states are studied in consideration of two-baryon scattering states. It is proposed that the two-baryon scattering states cannot saturate the QCD sum rules and their contributions can be neglected. We follow this idea and do not consider the two-baryon scattering states. The earlier study of the hidden-charm tetraquark molecular states has previously been published in a preprint [25]. In this article, we construct eight six-quark local interpolating currents to study both the ΣcΣ¯c baryoniums with the JP=1−,1+,0+, 0− and the ΣcΣc dibaryons with the JP=0+,0−,1+, 1−, respectively.The article is arranged as follows: we derive the QCD sum rules of the dibaryon and baryonium states in Section2. We present the numerical results and discussions in Section 3. Section 4 is reserved for our conclusions.


## 2. The QCD Sum Rules for the Baryonium and Dibaryon States

Now, let us write down the corresponding two-point correlation functions from the eight constructed currents:(1)Π1;αβp=i∫d4xeip·x0J1,αxJ1,β†00,Π2;αβp=i∫d4xeip·x0J2,αxJ2,β†00,Π3p=i∫d4xeip·x0J3xJ3†00,Π4p=i∫d4xeip·x0J4xJ4†00,Π5p=i∫d4xeip·x0J5xJ5†00,Π6p=i∫d4xeip·x0J6xJ6†00,Π7;αβp=i∫d4xeip·x0J7,αxJ7,β†00,Π8;αβp=i∫d4xeip·x0J8,αxJ8,β†00,where
(2)J1,α=J¯ΣγαJΣ,J2,α=J¯Σγ5γαJΣ,J3=J¯ΣJΣ,J4=J¯Σγ5JΣ,J5=JΣTCγ5JΣ,J6=JΣTCJΣ,J7,α=JΣTCγαJΣ,J8,α=JΣTCγ5γαJΣ,JΣ=εijkuiTCγμdjγμγ5ck,the superscripts i,j,k are color indices and C represents the charge conjugation matrix. The parities of these currents are shown as
(3)P^J1,αxP∧−1=J1αx~,P^J2,αxP∧−1=−J2αx~,P^J3xP∧−1=J3x~,P^J4xP∧−1=−J4x~,P^J5xP∧−1=J5x~,P^J6xP∧−1=−J6x~,P^J7,αxP∧−1=−J7αx~,P^J8,αxP∧−1=J8αx~,where P^ is the parity operator, x=x0,x1,x2,x3 and x~=x0,−x1,−x2,−x3. A complete set of intermediate hadronic states are inserted into each JixJi†0 in the above correlation functions. The correlation functions at the hadron sides are simplified as
(4)Π1,2,7,8;αβp=A1,2,7,8p−gαβ+pαpβp2+⋯,Π3,4,5,6p=λ3,4,5,62M3,4,5,62−p2+⋯,where
(5)A1,2,7,8p=λ1,2,7,82M1,2,7,82−p2+⋯,0J1,2,7,8;α0Z1,2,7,8=λ1,2,7,8εα,0J3,4,5,60Z3,4,5,6=λ3,4,5,6,Zi〉 denote the ground states which have the same JP as Ji, the εα are the polarization vectors and λi are the pole residues which show the coupling of the currents Ji to the states (i=1,2,⋯,8).For the QCD sides of the correlation functions, we contract the quark fields via the Wick theorem and express the correlation functions in terms of full quark propagators. After the detailed calculations, we findΠ7;αβp≡0 which means the net contribution of all the Feynman diagrams of this state including the leading order, perturbation terms and all kinds of condensates is zero. Except for this term, the others are given by
(6)Π1;αβp=−εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γμγαγτγ5Bnk′xγ5γμ′γβγτ′γ5Bn′k−xTrγτ′Qm′j−xγμCQl′iT−xCTrγτQmj′xγμ′CQli′TxC,Π2;αβp=−εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γμγ5γαγτγ5Bnk′xγ5γμ′γ5γβγτ′γ5Bn′k−xTrγτ′Qm′j−xγμCQl′iT−xCTrγτQmj′xγμ′CQli′TxC,Π3p=−εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γμγτγ5Bnk′xγ5γμ′γτ′γ5Bn′k−xTrγτ′Qm′j−xγμCQl′iT−xCTrγτQmj′xγμ′CQli′TxC,Π4p=−εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γμγ5γτγ5Bnk′xγ5γμ′γ5γτ′γ5Bn′k−xTrγτ′Qm′j−xγμCQl′iT−xCTrγτQmj′xγμ′CQli′TxC,Π5p=−2εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γτγ5γμγ5Bkk′xγ5γμ′γ5γτ′γ5CBnn′TxCTrγμQjj′xγμ′CQii′TxCTrγτQmm′xγτ′CQll′TxC+Trγ5γτγ5γμγ5Bkn′xγ5γμ′γ5γτ′γ5CBnk′TxCTrγμQjj′xγτ′CQii′TxCTrγτQmm′xγμ′CQll′TxC−2Trγ5γτγ5γμγ5Bkk′xγ5γμ′γ5γτ′γ5CBnn′TxCTrγμQjj′xγμ′CQli′TxCγτQmm′xγτ′CQil′TxC,Π6p=2εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γτγμγ5Bkk′xγ5γμ′γτ′γ5CBnn′TxCTrγμQjj′xγμ′CQii′TxCTrγτQmm′xγτ′CQll′TxC+Trγ5γτγμγ5Bkn′xγ5γμ′γτ′γ5CBnk′TxCTrγμQjj′xγτ′CQii′TxCTrγτQmm′xγμ′CQll′TxC−2Trγ5γτγμγ5Bkk′xγ5γμ′γτ′γ5CBnn′TxCTrγμQjj′xγμ′CQli′TxCγτQmm′xγτ′CQil′TxC,Π8;αβp=2εijkεlmnεi′j′k′εl′m′n′i∫d4xeip·xTrγ5γτγ5γαγμγ5Bkk′xγ5γμ′γ5γβγτ′γ5CBnn′TxCTrγμQjj′xγμ′CQii′TxCTrγτQmm′xγτ′CQll′TxC+Trγ5γτγ5γαγμγ5Bkn′xγ5γμ′γ5γβγτ′γ5CBnk′TxCTrγμQjj′xγτ′CQii′TxCTrγτQmm′xγμ′CQll′TxC−2Trγ5γτγ5γαγμγ5Bkk′xγ5γμ′γ5γβγτ′γ5CBnn′TxCTrγμQjj′xγμ′CQli′TxCγτQmm′xγτ′CQil′TxC,where Qabx and Babx are the full light and heavy quark propagators, respectively, under the operator product expansion at the quark level, they are expressed as
(7)Qabx=ix/δab2π2x4−δab12q¯q−δabx2192q¯gsσGq−iδabx2x/gs2q¯q27776−tnabx/σαβ+σαβx/i32π2x2gsGαβn−δabx4q¯qGG27648−18q¯bσαβqaσαβ−14q¯bγμqaγμ+⋯,Babx=i2π4∫d4ke−ik·xδabk/−mc−gsGαβhtabh4σαβk/+mc+k/+mcσαβk2−mc22+gsDαGβλhtabhfλβα+fλαβ3k2−mc24+⋯,fλαβ=k/+mcγλk/+mcγαk/+mcγβk/+mc,where tn=λn/2, λn are the Gell-Mann matrices (n=1,2,⋯,8) and Dα=∂α−igsGαhth [26–28].Consider the Feynman graphes of the leading orders of these nonzero correlation functions, each one contains two heavy quark lines and four light quark lines. If each heavy quark line emits a gluon and each light quark line contributes quark-antiquark pair, they form the quark-gluon operatorgsGαβgsGητq¯qq¯qq¯qq¯q with dimension 16. This operator lead to vacuum condensates αs/πGGq¯q4 and q¯gsσGq2q¯q2. So, the highest dimension of the considered condensates is up to 16 in the present work. As for the truncation of the order Oαsk, the contributions of the related vacuum condensates are tiny while k≥3/2; it is accurate enough for us to calculate terms for k≤1 [29]. Detailed calculations show that the vacuum condensates q¯q and q¯gsσGq have no contribution for all the considered states in this paper. Thus, the chosen vacuum condensates of the operator product expansions are αs/πGG, q¯q2, q¯gsσGqq¯q, q¯gsσGq2, αs/πGGq¯q2, q¯q4, q¯gsσGqq¯q3, q¯gsσGq2q¯q2, and αs/πGGq¯q4.After the calculations of the integrals in the coordinate space for the light quarks and momentum space for heavy quarks of the correlation functions, we perform the Borel transforms for both the hadronic sides and the QCD sides, we get the QCD sum rules,(8)λi2exp−Mi2T2=∫Δ2s0dsρisexp−sT2,where ρis are the QCD spectral densities of Ji, Δ2=4mc2. As for the continuum threshold parameters s0, we take the experiential values [24, 29, 30],
(9)s0=MZ+0.5~0.7GeV,where MZ are the masses of the ground states.We differentiate the Equation (8) with respect to τ=1/T2 and eliminate the pole residues, the extracted masses are shown as
(10)Mi2=−d/dτ∫Δ2s0dsρisexp−sτ∫Δ2s0dsρisexp−sτ.


## 3. Numerical Results and Discussions

We apply the standard values of the vacuum condensatesq¯q=−0.24±0.01GeV3, q¯gsσGq=m02q¯qGeV2, m02=0.8±0.1GeV2, αs/πGG=0.33GeV4 at the energy scale μ=1GeV [26, 31], and choose the MS¯ mass mcmc=1.275±0.025GeV [32]. Consider the energy-scale dependence for the above condensates,
(11)q¯qμ=q¯q1GeVαs1GeVαsμ12/33−2nf,q¯gsσGqμ=q¯gsσGq1GeVαs1GeVαsμ12/33−2nf,mcμ=mcmcαsμαsmc12/33−2nf,αsμ=1b0t1−b1b02logtt+b12log2t−logt−1+b0b2b04t2,where t=logμ2/ΛQCD2, b0=33−2nf/12π, b1=153−19nf/24π2, b2=2857−5033/95033/9nf+325/27325/27nf2/128π3, and ΛQCD=213 MeV, 296 MeV, and 339 MeV for the flavors nf=5,4,3, respectively [32–34]. In this paper, we choose the flavor number nf=4 for all the states. Compared with the heavy quarks, the masses of the light quarks are too small to make effective difference. So, we ignore the masses of the light quarks. The masses of the baryon and anti-baryon MΣc=MΣ¯c=2.455 GeV are from the particle data group [32]. We abandon the expressions of the lengthy spectral densities of these currents which are dozens of pages, one can contact us via the email. Note that Equation (10) depends on the energy scale μ [19, 35], we apply the energy scale formula to determine the best energy scales of the QCD spectral densities [27],
(12)μ=MX/Y/Z2−4Mc2,where Mc is the effective charm quark mass, we choose the value Mc=1.84±0.01 GeV [36]. Interestingly, in Ref. [29], for the vector current Jμ=J¯ΛγμJΛ, if we set Mc=1.84 GeV, the central value of the mass of ΛcΛ¯c with the JP=1− is 4.57 GeV with s0=2mΛ+0.66 GeV and PC=39%−53% which indicates a possible bound ΛcΛ¯c baryonium state, where mΛ=2.29 GeV is the mass of Λc [32]. As part of the systematic study for the dibaryons formed by the charmed baryons, the detailed results of Ref. [29] are also shown in Table 1. From Equatio (10), we find that MZ relies on the threshold parameter s0 and Borel parameter T2. Of course, at first, we do not know the suitable energy scale, so we try and adjust the value of μ via trial and error. From the energy scale formula Equation (12), one can determine that MZ increases with the parameter μ; however, numerical results show that mass derived from Equation (10) decreases with the increment of the parameter μ, so we can always find the best energy scale and determine the mass which satisfies the energy scale formula. As for the values of s0 and T2, we search for the best Borel window which satisfies the following two principles, firstly, the pole dominance criterion; here, we define the pole contributions (PC) of the QCD sum rules as
(13)PC=∫4mc2s0dsρQCDsexp−s/T2∫4mc2∞dsρQCDsexp−s/T2,secondly, the convergence of the contribution of operator product expansion, for which, we define the contributions of the vacuum condensates of dimension n as
(14)Dn=∫4mc2s0dsρQCD;nsexp−s/T2∫4mc2s0dsρQCDsexp−s/T2.Table 1
The related numerical results extracted from the Borel windows of the seven currents.
JiJPT2 (GeV2)s0 (GeV)μ (GeV)M (GeV)PCλ10−3GeV8ΣcΣ¯cJ11−3.6~4.05.60±0.13.24.88−0.08+0.0954~41%3.23−0.43+0.46ΣcΣ¯cJ21+3.6~4.05.90±0.13.85.31−0.07+0.0754~42%4.74−0.64+0.72ΣcΣ¯cJ30+3.4~3.85.80±0.13.75.23−0.07+0.0755~43%4.19−0.59+0.67ΣcΣ¯cJ40−3.6~4.05.60±0.13.24.88−0.08+0.0853~40%3.34−0.45+0.48ΣcΣcJ50+3.3~3.75.55±0.13.24.89−0.10+0.1156~42%4.09−0.56+0.61ΣcΣcJ60−3.6~4.05.90±0.13.95.37−0.08+0.0852~40%6.65−0.93+1.03ΣcΣcJ81−3.3~3.75.85±0.13.75.23−0.06+0.0657~43%4.66−0.63+0.71ΛcΛcJ10+3.4~3.85.70±0.13.65.12−0.12+0.1554~42%1.81−0.27+0.31ΛcΛ¯cJ20−3.2~3.65.30±0.12.84.66−0.09+0.1054~41%0.64−0.09+0.10ΛcΛ¯cJ31+3.4~3.85.60±0.13.45.00−0.09+0.1055~42%0.64−0.09+0.10ΛcΛ¯cJ41−3.2~3.65.25±0.12.74.57−0.09+0.0953~39%0.52−0.08+0.09Due to the uncertainties of the input parameters, the uncertainties of the extracted masses and pole resides are determined by the formula,(15)δ=∑i∂f∂xi2xi=x¯ixi−x¯i2,where f represent the masses or the pole resides, xi are the input parameters q¯q, q¯gsσGq, ⋯, x¯i denote the central values of these parameters. Since it is difficult to find the analytic expressions of the partial derivatives ∂f/∂xi, we carry out the approximate numerical calculations for the uncertainties via,
(16)∂f∂xi2xi−x¯i2≈fx¯i±Δxi−fx¯i2.ExceptJ7, we find the Borel windows for the other seven currents. Their numerical results are shown in Figures 1–7, respectively. In each figure, we show the masses, dimensional contributions of vacuum condensates and pole residues of each current on M−T2, Dn−T2, and λ−T2 graphs, respectively. Currents J1, J2, J3, and J4 are related to the ΣcΣ¯c baryonium structures. For the vector current J1, the extracted mass of the corresponding ΣcΣ¯c state with the JP=1− is 4.88 GeV with the upper uncertainty being 0.09 GeV. Since the threshold of the two Σc and Σ¯c baryon constituents is 4.91 GeV, so, we could not say for sure whether it is a molecular state formed by the two baryons or not. On the safe side, it is a possible molecular or compact six-quark state. In the same way, ΣcΣ¯c with the JP=0− is also a possible molecular or compact six-quark state. As for axial-vector current J2 and scalar current J3, their extracted masses of the corresponding states with the JP=1+ and 0+ are 5.31 GeV and 5.23 GeV, respectively. They are all above the thresholds of the two Σc and Σ¯c baryon constituents even if we take into the account of the lower bounds of uncertainties of the extracted masses. Both these two are the baryonium resonance states.Figure 1
The numerical results ofJ1: M1−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D1n−T2 for (b); λ1−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 2
The numerical results ofJ2: M2−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D2n−T2 for (b); λ2−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 3
The numerical results ofJ3: M3−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D3n−T2 for (b); λ3−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 4
The numerical results ofJ4: M4−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D4n−T2 for (b); λ4−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 5
The numerical results ofJ5: M5−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D5n−T2 for (b); λ5−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 6
The numerical results ofJ6: M6−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D6n−T2 for (b); λ6−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.Figure 7
The numerical results ofJ8: M8−T2 for (a), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values; D8n−T2 for (b); λ8−T2 for (c), dashed curve is drawn from the upper values of the input parameters and dotted curve is from the lower values.CurrentsJ5, J6, J7, and J8 are related to the ΣcΣc dibaryon states. For the current J7,α=JΣTCγαJΣ, its related correlation function Π7;αβp≡0. It indicates that there is no such ΣcΣc dibaryon state with the JP=1+. The extracted mass from J5 is 4.89 GeV which is 20 MeV below the the threshold of the two Σc baryon constituents. Due to the uncertainties of input parameters, the related uncertainty of the mass of this state is up to 0.1 GeV, it is also a possible ΣcΣc molecular or a compact six-quark state with the JP=0+. We also get the masses of J6 and J8, they are all above the thresholds of the two baryon constituents. The detailed results of each states are listed in Table 1.For all these seven currents, it is clear to be seen from theDin−T2 curves in each titled figures, the most important items are the leading order, q¯q2 and q¯gsσGqq¯q. We find that the higher dimensional vacuum condensates n≥10 play the less important roles. So, the convergence of the operator product expansion holds very well. It is worth mentioning that condensate q¯q2 plays a dominant role for the current J4, what is more, the leading order of J8 contributes the most important part for both the mass and pole residue of the corresponding state.In 2017, the LHCb has observed the doubly-charmed baryonΞcc++ with mass of 3621.40±0.78 MeV [37]. It is proposed that there is large binding energy Bcc=129 MeV of the two heavy c-quarks in a baryon [38]. In Ref. [39], the quark-level analogue of nuclear fusion for the two Λc baryons was discussed. In a similar way, we also consider the quark-rearrangement reaction, the possible decays of ΣcΣc dibaryon states are given by
(17)ΣcΣc⟶Ξcc++n,cudcud⟶ccuddu.Since theJP of Ξcc++ is unknown yet, thus, it is also impossible for us to determine the JP of the produced neutron after the decay. We can only estimate the upper values of the exothermic energy Qupper of each ΣcΣc quark-rearrangement reaction by setting the minimum mass of the neutron as mn=1440 MeV. For ΣcΣc with the JP=0+, it is impossible to have such kind of decay since its mass is less than the sum of mΞcc++ and mn. As for 0− and 1−, the corresponding Qupper are 310 MeV and 170 MeV, respectively.


## 4. Conclusions

In this article, we construct the eight interpolating currents to study theΣcΣ¯c baryonium and ΣcΣc dibaryon states via the QCD sum rules. The correlation function of J7 is zero which indicates that there is no such ΣcΣc dibaryon state with the JP=1+. We find two possible ΣcΣ¯c molecular or compact six-quark states with the JP=1− and 0−. Their masses are 4.88−0.08+0.09 GeV and 4.88−0.08+0.08 GeV, respectively. For the currents J2, J3, J6, and J8, the extracted masses of these four states are 5.31−0.07+0.07 GeV, 5.23−0.07+0.07 GeV, 5.37−0.08+0.08 GeV, and 5.23−0.06+0.06 GeV, respectively. Both the four are above the the thresholds of the two baryon constituents. We conclude that ΣcΣ¯c with the JP=1+ and 0+ are baryonium resonances states and ΣcΣc with the JP=0− and 1− are dibaryon resonances states. We find the central value of the mass of the state with the JP=0+ is just 20 MeV below the threshold of the two Σc baryon constituents. Considering the uncertainty, ΣcΣc dibaryon with the JP=0+ is also a possible molecular state. For all the bound states related to ΣcΣ¯c and ΣcΣc, we need more data, such as the electromagnetic form factors, to differentiate whether the bound dibaryon or baryonium is a molecular state or a compact six-quark entity. This is also the task of our further work. The possible decays, the quark-rearrangement reactions of each ΣcΣc states are discussed. The upper values of the exothermic energy are calculated for these decays which may be experimentally verified in the future.



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