Analysis of \(\Omega _c(3000)\) , \(\Omega _c(3050)\) , \(\Omega _c(3066)\) , \(\Omega _c(3090)\) and \(\Omega _c(3119)\) with QCD sum rules

The European Physical Journal C, May 2017

In this article, we assign \(\Omega _c(3000)\), \(\Omega _c(3050)\), \(\Omega _c(3066)\), \(\Omega _c(3090)\) and \(\Omega _c(3119)\) to the P-wave baryon states with \(J^P={\frac{1}{2}}^-\), \({\frac{1}{2}}^-\), \({\frac{3}{2}}^-\), \({\frac{3}{2}}^-\) and \({\frac{5}{2}}^-\), respectively, and study them with the QCD sum rules by introducing an explicit relative P-wave between the two s quarks. The predictions support assigning \(\Omega _c(3050)\), \(\Omega _c(3066)\), \(\Omega _c(3090)\) and \(\Omega _c(3119)\) to the P-wave baryon states with \(J^P={\frac{1}{2}}^-\), \({\frac{3}{2}}^-\), \({\frac{3}{2}}^-\) and \({\frac{5}{2}}^-\), respectively, where the two s quarks are in relative P-wave, while \(\Omega _c(3000)\) can be assigned to the P-wave baryon state with \(J^{P}={\frac{1}{2}}^-\), where the two s quarks are in relative S-wave.

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Analysis of \(\Omega _c(3000)\) , \(\Omega _c(3050)\) , \(\Omega _c(3066)\) , \(\Omega _c(3090)\) and \(\Omega _c(3119)\) with QCD sum rules

Eur. Phys. J. C Zhi-Gang Wang 0 respectively 0 where the two s quarks are in 0 relative P-wave 0 while 0 ) can be assigned to the P- wave baryon state with J P = 0 where the two s quarks are in relative S-wave. 0 0 Department of Physics, North China Electric Power University , Baoding 071003 , People's Republic of China In this article, we assign c(3000), c(3050), c(3066), c(3090) and c(3119) to the P-wave baryon states with J P = 21 −, 21 −, 23 −, 23 − and 25 −, respectively, and study them with the QCD sum rules by introducing an explicit relative P-wave between the two s quarks. The predictions support assigning c(3050), c(3066), c(3090) and c(3119) to the P-wave baryon states with J P = 21 −, - c(3050), c(3066), c(3090) and c(3119) 1 Introduction In the past years, several new charmed baryon states have been observed, and the spectroscopy of the charmed baryon states have re-attracted much attention [1], the QCD sum rules plays an important roles in assigning those new baryon states. The masses of the heavy baryon states with J P = 21 ±, 23 ±, 5 ± have been studied with the full QCD sum rules [2– 2 18] or the QCD sum rules combined with the heavy quark effective theory [19–28]. Recently, the LHCb collaboration studied the c+ K − mass spectrum with a sample of pp collision data corresponding to an integrated luminosity of 3.3 fb−1 collected by the LHCb experiment, and one observed five new narrow excited c0 states, c(3000), c(3050), c(3066), c(3090), c(3119) [29]. The measured masses and widths are c(3000) : M = 3000.4 ± 0.2 ± 0.1 MeV, = 4.5 ± 0.6 ± 0.3 MeV, = 0.8 ± 0.2 ± 0.1 MeV, c(3050) : M = 3050.2 ± 0.1 ± 0.1 MeV, c(3066) : M = 3065.6 ± 0.1 ± 0.3 MeV, = 3.5 ± 0.4 ± 0.2 MeV, c(3090) : M = 3090.2 ± 0.3 ± 0.5 MeV, = 8.7 ± 1.0 ± 0.8 MeV, c(3119) : M = 3119.1 ± 0.3 ± 0.9 MeV, = 1.1 ± 0.8 ± 0.4 MeV. There have been several assignments for those new charmed states. In Ref. [30], c(3066) and c(3119) are assigned to the 2S c0 states with J P = 21 + and 23 +, respectively. In Ref. [31], possible assignments of those c0 states to the P-wave baryon states with J P = 21 −, 23 − and 25 − are discussed. In Refs. [32–34], the c(3000), c(3050), c(3066), c(3090) and c(3119) are assigned to the Pwave baryon states with J P = 21 −, 21 −, 23 −, 23 − and 25 −, respectively. In Refs. [35,36], those c0 states are assigned to the pentaquark states or molecular pentaquark states with J P = 21 −, 23 − or 25 −. In Ref. [37], c(3000), c(3050), c(3066) and c(3090) are assigned to the P-wave baryon states with J P = 21 −, 23 −, 3 − and 21 −, respectively. In Ref. [38], c(3090) and c(31219) are assigned to the 2S c0 states with J P = 21 + and 23 +, respectively, while c(3000), c(3066) and c(3050) are assigned to the P-wave baryon states with J P = 21 −, 23 − and 25 −, respectively. In this article, we tentatively assign c(3000), c(3050), c(3066), c(3090) and c(3119) to the P-wave baryon states with J P = 21 −, 21 −, 23 −, 23 − and 25 −, respectively, and study their masses and pole residues with the QCD sum rules in detail. The ground state quarks have the spin-parity 21 +, two quarks can form a scalar diquark or an axialvector diquark with the spin-parity 0+ or 1+, the diquark then combines with a third quark to form a positive parity baryon with spin 21 or 3 . We can construct the baryon currents η and ημ with pos2 itive parity without introducing additional P-wave. As multiplying i γ5 to the baryon currents changes their parity, the currents i γ5η and i γ5ημ couple potentially to the negative parity heavy baryon states. In Refs. [17,18], we construct the currents without introducing relative P-wave to study the negative parity heavy, doubly heavy and triply heavy baryon states, and obtain satisfactory results. The predictions M = 2.98 ± 0.16 GeV for the c0 states with J P = 21 −, 23 − are consistent with the masses of c(3000), c(3050), c(3066), c(3090) from the LHCb collaboration [17]. In Ref. [39], we construct the interpolating currents by introducing the relative P-wave explicitly, study the negative parity charmed baryon states c(2625) and c(2815) with the full QCD sum rules, and reproduce the experimental values of the masses. In this article, we extend our previous work to study c(3000), c(3050), c(3066), c(3090) and c(3119) with QCD sum rules by introducing the relative P-wave explicitly. The article is arranged as follows: we derive the QCD sum rules for the masses and pole residues of the c0 states in Sect. 2; in Sect. 3, we present the numerical results and discussions; and Sect. 4 is reserved for our conclusions. 2 QCD sum rules for the In the following, we write down the two-point correlation functions ( p), μν ( p), μναβ ( p) in the QCD sum rules, ( p) = i d4x ei p·x 0|T J (x ) J¯(0) |0 , + siT (x )C γμ∂ν s j (x ) ck (x ), gμν = gμν − 41 γμγν , i , j , k are color indices, C is the charge conjugation matrix. We construct the currents with the light diquarks Sμiν = εi jk [∂μsiT C γν s j + siT C γν ∂μs j ]. The Sμiν have two Lorentz indices μ and ν, but they are neither symmetric nor anti-symmetric when interchanging the indices μ and ν. The scalar components Sμiν gμν and Sμiν σ μν couple potentially to the spin-0 diquarks. The Dirac matrices gαμγ ν − gαν γ μ and gαμγ ν + gαν γ μ − 21 gμν γ α are antisymmetric and symmetric, respectively, when interchanging the indices μ and ν, the vector components Sμiν (gαμγ ν − gαν γ μ) and Sμiν (gαμγ ν + gαν γ μ − 21 gμν γ α) couple potentially to the spin-1 diquarks. The symmetric components Sμiν + Sνiμ couple potentially to the spin-0 and 2 diquarks. So we choose the currents J (x ), Jμ(x ) and Jμν (x ) to study the spin- 21 , 23 and 25 baryon states, respectively. The currents J (0), Jμ(0) and Jμν (0) couple potentially to the 21 −, 21 +, 3 − and 21 −, 23 +, 5 − charmed baryon states B−, 2 2 21 B +1, B −3 and B −1, B +3, B −5, respectively, 2 2 2 2 2 0| J (0)|B −1( p) = λ −1U −( p, s), 2 2 0| Jμ(0)|B +1( p) = f 1+ pμU +( p, s), 2 2 0| Jμ(0)|B −3( p) = λ −3Uμ−( p, s), 2 2 0| Jμν (0)|B −1( p) = g −1 pμ pνU −( p, s), 2 2 0| Jμν (0)|B +3( p) = f 3+ pμUν+( p, s) + pνUμ+( p, s) , 2 2 0| Jμν (0)|B −5( p) = λ −5Uμ−ν ( p, s). 2 2 tially to the 21 +, 21 −, 23 + and 21 +, 23 −, 25 + charmed baryon states B +1, B−, B +3 and B +1, B−, B +5, respectively [42–44], 2 21 2 2 23 2 0| J (0)|B +1( p) = λ +1i γ5U +( p, s), (7) 2 2 0| Jμ(0)|B −1( p) = f 1− pμi γ5U −( p, s), 2 2 0| Jμ(0)|B +3( p) = λ +3i γ5Uμ+( p, s), (8) 2 2 0| Jμν (0)|B +1( p) = g +1 pμ pν i γ5U +( p, s), 2 2 0| Jμν (0)|B −3( p) = f 3−i γ5 pμUν−( p, s) + pνUμ−( p, s) , 2 2 0| Jμν (0)|B +5( p) = λ +5i γ5Uμ+ν ( p, s). (9) 2 2 The spinors U ±( p, s) satisfy the Dirac equations ( p − M±) U ±( p) = 0, while the spinors Uμ±( p, s) and Uμ±ν ( p, s) satisfy the Rarita–Schwinger equations ( p − M±)Uμ±( p) = 0 and ( p − M±)Uμ±ν ( p) = 0, and the relations γ μUμ±( p, s) = 0, pμUμ±( p, s) = 0, γ μUμ±ν ( p, s) = 0, pμUμ±ν ( p, s) = 0, Uμ±ν ( p, s) = Uν±μ( p, s). The λ ±21/ 23 / 25 , f 21±/ 23 and g ±21 are the pole residues or current-baryon coupling constants. At the phenomenological side, we insert a complete set of intermediate charmed baryon states with the same quantum numbers as the current operators J (x ), i γ5 J (x ), Jμ(x ), i γ5 Jμ(x ), Jμν (x ) and i γ5 Jμν (x ) into the correlation functions ( p), μν ( p) and μναβ ( p) to obtain the hadronic representation [40,41]. After isolating the pole terms of the lowest states of the charmed baryon states, we obtain the following results: ( p) = λ −212 Mp −2+−Mp−2 + λ +212 Mp +2−−Mp+2 + . . . , 2 M −2 − p2 2 M +2 − p2 2 M +2 − p+2 pμ pν + f 1−2 p − M 2 M −2 − p−2 pμ pν + . . . , 2 M+2 − p+2 pμ pα −gνβ + 2 M−2 − p−2 pμ pα −gνβ + 2 M−2 − p−2 pμ pν pα pβ + g +12 p − M 2 M+2 − p+2 pμ pν pα pβ + . . . , U U = ( p + M±) , where gμν = gμν − pμp2pν . In calculations, we have used the following summations [45]: and p2 = M 2 on the mass shell. ± andWeμcνaαnβ (repw)riintteotthhee cfoorllroewlaitniognfofurmncaticocnosrdin(gp)to, Loμrνe(nptz) covariance: ( p) = μναβ ( p) = 25 ( p2) gμα gνβ +2 gμβ gνα + . . . . (18) In this article, we choose the tensor structures gμν and gμα gνβ + gμβ gνα for analysis, and separate the contributions of the 3 ± and 25 ± charmed baryon states unambiguously. For 2 a detailed discussion of this subject, one can consult Ref. [44]. We obtain the hadronic spectral densities at phenomenological side through the dispersion relation, Im j (s) = p[λ −j2δ(s − M −2) + λ +j2δ(s − M 2 ) + ] +[M−λ −j2δ(s − M −2) − M+λ +j2δ(s − M 2 ) , + ] = p ρ 1j,H (s) + ρ 0j,H (s), (19) where j = 21 , 23 , 25 , the subscript H denotes the hadron side, then we introduce the weight function exp(− Ts2 ) to obtain the QCD sum rules at the phenomenological side, s0 s √sρ 1j,H (s) + ρ 0j,H (s) exp − T 2 where the s0 are the continuum thresholds and the T 2 are the Borel parameters [44]. At the QCD side, we calculate the light quark parts of the correlation functions ( p), μν ( p), μναβ ( p) with the full light quark propagators in the coordinate space and take the momentum space expression for the full c-quark propagator. It is straightforward but tedious to compute the integrals both in the coordinate and momentum spaces to obtain the correlation functions j ( p2), therefore we obtain the QCD spectral densities through the dispersion relation, = p ρ 1j,QC D(s) + ρ j,QC D(s), 0 We derive Eq. (22) with respect to T12 , then eliminate the pole residues λ −j and obtain the QCD sum rules for the masses of the charmed baryon states, M−2 = − d(1/dT 2) ms0c2 ds √sρ 1j,QC D(s) + ρ 0j,QC D(s) exp − Ts2 ms0c2 ds √sρ 1j,QC D(s) + ρ 0j,QC D(s) exp − Ts2 3 Numerical results and discussions In the article, we take the M S masses mc(mc) = (1.275 ± 0.025) GeV and ms (μ = 2 GeV) = (0.095 ± 0.005) GeV from the particle data group [1], and take into account the energy-scale dependence of the M S masses from the renormalization group equation, where t = log μ22 , b0 = 331−22πn f , b1 = 1532−4π192n f , b2 = 2857− 51093238nπf3+ 32275 n2f , = 213, 296 and 339 MeV for the flavors n f = 5, 4 and 3, respectively [1]. In Refs. [47–51], we study the acceptable energy scales of the QCD spectral densities for the hidden-charm (bottom) tetraquark states and molecular states in the QCD sum rules for the first time, and we suggest the empirical formula μ = M X2/Y/Z − (2MQ )2 to determine the optimal energy scales, where X , Y , Z denote the four-quark states, and MQ is the effective heavy quark mass. The empirical energy-scale formula also works well in studying the hidden-charm pentaquark states [44]. In Ref. [39], we use the diquark–quark model to construct the interpolating currents, and take the analogous formula μ = M 2 c/ c − Mc2 to determine the energy scales of the QCD spectral densities of the QCD sum rules for the charmed baryon states c(2625) and c(2815), and obtain satisfactory results. In this article, we use the formula μ = M 2 c − Mc2 to determine the energy scales of the QCD spectral densities. If we take the updated value Mc = 1.82 GeV [52], then μ ≈ 2.5 GeV. In calculations, we set the energy scales of the QCD spectral densities to be μ = 2.5 GeV. Now we search for the Borel parameters T 2 and continuum threshold parameters s0 to satisfy the following three criteria: 1. pole dominance at the phenomenological side; 2. convergence of the operator product expansion; 3. appearance of the Borel platforms. In calculations, we observe that no stable QCD sum rules can be obtained for the current J 2(x ). The resulting Borel parameters T 2, continuum threshold parameters s0, pole contributions and perturbative contributions (per) are shown explicitly in Table 1, where the perturbative contributions are defined by per = Table 1 The Borel parameters T 2, continuum threshold parameters s0, pole contributions (pole) and perturbative contributions (perturbative) T 2 (GeV2) √s0 (GeV) ρper(s) and ρtot(s) denote the perturbative and total QCD spectral densities, respectively. From the table, we can see that the criteria 1 and 2 can be satisfied. We take into account all uncertainties of the relevant parameters, and we obtain the values of the masses and pole residues of the c0 baryon states, which are shown in Figs.1, 2 and Table 2. In Figs.1, 2, we plot the masses and pole residues with variations of the Borel parameters at much larger intervals than the Borel windows shown in Table 1. In the Borel windows, the uncertainties originating with the Borel parameters in the Borel windows are very small, δ M c /M c = (1.2 − 1.6)%, the criterion 3 is also satisfied. The three criteria are all satisfied, we expect to make reliable predictions. In Figs. 1 and 2 and Table 2, we also present the possible assignments of the c0 states according to the masses. In Ref. [17], we choose the currents without introducing the relative P-wave to study the negative parity heavy and doubly heavy baryon states, and we obtain the predictions M = 2.98 ± 0.16 GeV for the c0 states with J P = 21 −, 23 −, where the diquark constituent εi jk s Tj C γμsk is taken to construct the currents. Multiplying i γ5 to the baryon currents changes their parity, we can choose currents without introducing relative P-wave to study the P-wave baryon states. The current εi jk s Tj C γμsk γ μci couples potentially to the c0 state with J P = 21 − [17], the mass of the c(3000) is in excellent agreement with the prediction M = 2.98 ± 0.16 GeV [17] or the prediction M = 2.990 ± 0.129 GeV based on a more general interpolating current with additional parameter [53], the c(3000) can be assigned to the P-wave charmed baryon state with J P = 21 −, where two s quarks are in relative S-wave. In Table 3, we present some predictions for the masses of the P-wave c0 baryon states from the full QCD sum rules [17, 53, 54] and potential quark models [55–58]. Table 2 The masses M, pole residues λ and possible assignments of the charmed baryon states, where jl denotes the total angular momentum of the light degree of freedom 3.05 ± 0.11 3.06 ± 0.11 3.06 ± 0.10 3.11 ± 0.10 Table 3 The masses of the P-wave c baryon states, where the unit is GeV, jl denotes the total angular momentum of the light degree of freedom. We neglect the mixing effects of the 2 0 − 21 1− and 23 1− − 23 2− in the 1 − potential quark models for simplicity 2.34 ± 0.50 1.03 ± 0.23 2.47 ± 0.47 1.07 ± 0.17 c(3066/3090) c(3066/3090) 3.05 ± 0.11 3.06 ± 0.11 3.06 ± 0.10 3.11 ± 0.10 2.98 ± 0.16 2.98 ± 0.16 2.990 ± 0.129 3.056 ± 0.103 3.08 ± 0.12 We cannot identify a baryon state unambiguously with the mass alone; it is necessary to study the decay widths of those P-wave baryon states with the QCD sum rules. In Ref. [53], Agaev, Azizi and Sundu study the masses and widths of the 1P 21 −, 23 − and 2S 21 +, 23 + c0 baryon states with the full QCD sum rules, and they assign c(3000), c(3050) and c(3119) to the c0 baryon states with the quantum numbers (1P, 21 −), (1P, 23 −) and (2S, 23 +), respectively, and assign the c(3066) or c(3090) to the c0 baryon state with the quantum numbers (2S, 21 +). 4 Conclusion In this article, we assign c(3000), c(3050), c(3066), c(3090) and c(3119) to the P-wave charmed baryon states with J P = 21 −, 21 −, 23 −, 23 − and 25 −, respectively, and we study their masses and pole residues with the QCD sum rules in detail by introducing an explicit relative P-wave between the two constituents of the light diquarks. The predictions support assigning c(3050), c(3066), c(3090) and c(3119) to the P-wave baryon states with J P = 21 −, 23 −, 3 − and 25 −, respectively, where the two constituents of 2 the light diquark are in relative P-wave; while the c(3000) can be assigned to the P-wave charmed baryon state with J P = 21 −, where the two constituents of the light diquark are in relative S-wave. Acknowledgements This work is supported by National Natural Science Foundation, Grant Number 11375063. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3. 1. K.A. Olive et al., Chin. Phys. C 38 , 090001 ( 2014 ) 2. E. Bagan , M. Chabab , H.G. Dosch , S. Narison , Phys. Lett . B 278 , 367 ( 1992 ) 3. E. Bagan , M. Chabab , H.G. Dosch , S. Narison , Phys. Lett . B 287 , 176 ( 1992 ) 4. F.O. Duraes , M. Nielsen , Phys. Lett . B 658 , 40 ( 2007 ) 5. Z.G. Wang , Eur. Phys. J. C 54 , 231 ( 2008 ) 6. J.R. Zhang , M.Q. Huang , Phys. Rev. D 77 , 094002 ( 2008 ) 7. J.R. Zhang , M.Q. Huang , Phys. Rev. D 78 , 094015 ( 2008 ) 8. Z.G. Wang , Eur. Phys. J. C 61 , 321 ( 2009 ) 9. M. Albuquerque , S. Narison , M. Nielsen , Phys. Lett . B 684 , 236 ( 2010 ) 10. T.M. Aliev , K. Azizi , M. Savci , Nucl. Phys. A 895 , 59 ( 2012 ) 11. T.M. Aliev , K. Azizi , M. Savci , JHEP 1304 , 042 ( 2013 ) 12. T.M. Aliev , K. Azizi , T. Barakat , M. Savci , Phys. Rev. D 92 , 036004 ( 2015 ) 13. T. M. Aliev , K. Azizi and M. Savci . arXiv:1504.00172 14. Z.G. Wang , Phys. Lett . B 685 , 59 ( 2010 ) 15. Z.G. Wang , Eur. Phys. J. C 68 , 459 ( 2010 ) 16. Z.G. Wang , Eur. Phys. J. A 45 , 267 ( 2010 ) 17. Z.G. Wang , Eur. Phys. J. A 47 , 81 ( 2011 ) 18. Z.G. Wang , Commun. Theor. Phys. 58 , 723 ( 2012 ) 19. E.V. Shuryak , Nucl. Phys . B 198 , 83 ( 1982 ) 20. A.G. Grozin , O.I. Yakovlev , Phys. Lett . B 285 , 254 ( 1992 ) 21. E. Bagan , M. Chabab , H.G. Dosch , S. Narison , Phys. Lett . B 301 , 243 ( 1993 ) 22. Y.B. Dai , C.S. Huang , C. Liu , C.D. Lu , Phys. Lett . B 371 , 99 ( 1996 ) 23. Y.B. Dai , C.S. Huang , M.Q. Huang , C. Liu , Phys. Lett . B 387 , 379 ( 1996 ) 24. C.S. Huang , A.L. Zhang , S.L. Zhu , Phys. Lett . B 492 , 288 ( 2000 ) 25. D.W. Wang , M.Q. Huang , C.Z. Li , Phys. Rev. D 65 , 094036 ( 2002 ) 26. D.W. Wang , M.Q. Huang , Phys. Rev. D 68 , 034019 ( 2003 ) 27. H.X. Chen , W. Chen , Q. Mao , A. Hosaka , X. Liu , S.L. Zhu , Phys. Rev. D 91 , 054034 ( 2015 ) 28. Q. Mao , H.X. Chen , W. Chen , A. Hosaka , X. Liu , S.L. Zhu , Phys. Rev. D 92 , 114007 ( 2015 ) 29. R. Aaij et al. arXiv:1703.04639 30. S. S. Agaev , K. Azizi , H. Sundu . arXiv:1703.07091 31. H.X. Chen , Q. Mao , W. Chen , A. Hosaka , X. Liu , S.L. Zhu . arXiv:1703.07703 32. M. Karliner , J.L. Rosner. arXiv:1703.07774 33. W. Wang , R.L. Zhu . arXiv:1704.00179 34. M. Padmanath , N. Mathur . arXiv:1704.00259 35. G. Yang , J. Ping. arXiv:1703.08845 36. H. Huang , J. Ping , F. Wang . arXiv:1704.01421 37. K.L. Wang , L.Y. Xiao , X.H. Zhong , Q. Zhao . arXiv:1703.09130 38. H.Y. Cheng , C.W. Chiang . arXiv:1704.00396 39. Z.G. Wang , Eur. Phys. J. C 75 , 359 ( 2015 ) 40. M.A. Shifman , A.I. Vainshtein , V.I. Zakharov , Nucl. Phys . B 147 ( 385 ), 448 ( 1979 ) 41. L.J. Reinders , H. Rubinstein , S. Yazaki , Phys. Rep. 127 , 1 ( 1985 ) 42. Y. Chung , H.G. Dosch , M. Kremer , D. Schall , Nucl. Phys . B 197 , 55 ( 1982 ) 43. D. Jido , N. Kodama , M. Oka , Phys. Rev. D 54 , 4532 ( 1996 ) 44. Z.G. Wang , Eur. Phys. J. C 76 , 70 ( 2016 ) 45. S.-Z. Huang , Free Particles and Fields of High Spins (in Chinese) (Anhui peoples Publishing House , Hefei ( 2006 ) 46. P. Colangelo , A. Khodjamirian . arXiv:hep-ph/0010175 47. Z.G. Wang , T. Huang , Phys. Rev. D 89 , 054019 ( 2014 ) 48. Z.G. Wang , Eur. Phys. J. C 74 , 2874 ( 2014 ) 49. Z.G. Wang , T. Huang , Nucl. Phys. A 930 , 63 ( 2014 ) 50. Z.G. Wang , T. Huang , Eur. Phys. J. C 74 , 2891 ( 2014 ) 51. Z.G. Wang , Eur. Phys. J. C 74 , 296 ( 2014 ) 52. Z.G. Wang , Eur. Phys. J. C 76 , 387 ( 2016 ) 53. S. S. Agaev , K. Azizi , H. Sundu . arXiv:1704.04928 54. K. Azizi , H. Sundu , Eur. Phys. J. Plus 132 , 22 ( 2017 ) 55. Z. Shah , K. Thakkar , A.K. Rai , P.C. Vinodkumar , Chin. Phys . C 40 , 123102 ( 2016 ) 56. W. Roberts , M. Pervin , Int. J. Mod. Phys. A 23 , 2817 ( 2008 ) 57. A. Valcarce , H. Garcilazo , J. Vijande , Eur. Phys. J. A 37 , 217 ( 2008 ) 58. D. Ebert , R.N. Faustov , V.O. Galkin , Phys. Rev. D 84 , 014025 ( 2011 )


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Zhi-Gang Wang. Analysis of \(\Omega _c(3000)\) , \(\Omega _c(3050)\) , \(\Omega _c(3066)\) , \(\Omega _c(3090)\) and \(\Omega _c(3119)\) with QCD sum rules, The European Physical Journal C, 2017, 325, DOI: 10.1140/epjc/s10052-017-4895-5