# Reanalysis ofΩc→Ξc+K- Decay in QCD

Authors: T. M. Aliev; S. Bilmis; M. Savci
Journal: Advances in High Energy Physics
 (2018)

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## Abstract

The strong coupling constants of newly observedΩc0 baryons with spins J=1/2 and J=3/2 decaying into Ξc+K- are estimated within light cone QCD sum rules. The calculations are performed within two different scenarios on quantum numbers of Ωc baryons: (a) all newly observed Ωc baryons are negative parity baryons; that is, the Ωc(3000), Ωc(3050), Ωc(3066), and Ωc(3090) have quantum numbers JP=1/2- and JP=3/2- states, respectively; (b) the states Ωc(3000) and Ωc(3050) have quantum numbers JP=1/2- and JP=1/2+, while the states Ωc(3066) and Ωc(3090) have the quantum numbers JP=3/2- and JP=3/2+, respectively. By using the obtained results on the coupling constants, we calculate the decay widths of the corresponding decay. The results on decay widths are compared with the experimental data of LHC Collaboration. We found out that the predictions on decay widths within these scenarios are considerably different from the experimental data; that is, both considered scenarios are ruled out.


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## Body

## 1. Introduction

Lately, in the invariant mass spectrum ofΞc+K-, very narrow excited Ωc states (Ωc(3000), Ωc(3050), Ωc(3066), Ωc(3090), and Ωc(3119)) have been observed at LHCb [1]. Quantum numbers of these newly observed states have not been determined in the experiments yet. Hence, various possibilities about the quantum numbers of these states have been speculated in recent works. In [2], the states Ωc(3050) and Ωc(3090) are assigned as radial excitation of ground state Ωc(3000) and Ω∗(3066) baryons with the JP=1/2+ and 3/2+, respectively. On the other hand, in [3–7] these new states are assumed as the P-wave states with JP=1/2-,1/2-,3/2-,3/2-, and 5/2-, respectively. Moreover the new states are assumed as pentaquarks in [8]. Similar quantum numbers of these new states are assigned in [9]. Analysis of these states is also studied with lattice QCD, and the results indicated that most probably these states have JP=1/2-,3/2-,5/2- quantum numbers [3]. Another set of quantum number assignments, namely, 3/2-, 3/2-, 5/2-, and 3/2+, is given in [4]. In [10], it is obtained that the prediction on mass supports assigning Ωc(3000) as JP=1/2-, Ωc(3090) as JP=3/2- or the 2S state with JP=1/2+, and Ωc(3119) as JP=3/2+.In this work, we estimate the strong coupling constants ofΩc0→Ξc+K- in the framework of light cone QCD sum rules. In our calculations, two different possibilities on quantum numbers of Ωc baryons are explored:(a)
All newly observedΩc states have negative parities. More precisely, Ωc(3000) and Ωc(3050) have quantum numbers JP=1/2-, Ωc(3066), and Ωc(3090) have 3/2-, and Ωc(3119) has quantum numbers 5/2-.(b)
Part of newly observedΩc baryons have negative parity, and another part represents a radial excitations of ground state baryons; that is, Ωc(3000) has JP=1/2-, Ωc(3050) has JP=1/2+, and Ωc(3066) and Ωc(3090) states have quantum numbers JP=3/2- and 3/2+, respectively.Note that the strong coupling constants ofΩc→Ξc+K- decay within the same framework are studied in [11] and in chiral quark model [12], respectively. However, the analysis performed in [11] is incomplete. First of all, the contribution of negative parity Ξc baryons is neglected entirely. Second, in our opinion the numerical analysis presented in [11] is inconsistent.The article is organized as follows. In Section2 the light cone sum rules for the coupling constants of Ωc→Ξc+K- decay are derived. Section 3 is devoted to the analysis of the sum rules obtained in the previous section. In this section, we also estimate the widths of corresponding decay, and comparison with the experimental data is presented.


## 2. Light Cone Sum Rules for the Strong Coupling Constants ofΩc→Ξc+K- Transitions

For the calculation of the strong coupling constants ofΩc→Ξc+K- transitions we consider the following two correlation functions in both pictures:(1)Π=i∫d4xeipxKqηΞcxη-Ωc00,Πμ=i∫d4xeipxKqηΞcxη-Ωc∗μ00,where ηΞc(ηΩc) is the interpolating current of Ξc(Ωc) baryon and ηΩc∗μ is the interpolating current of JP=3/2Ωc∗ baryon:(2)ηΞc=16ϵabc2uaTCsbγ5cc+2βuaTCγ5sbcc+uaTCcbγ5sc+βuaTCγ5cbsc+caTCsbγ5uc+βcaTCγ5sbuc(3)ηΩc=ηΞcu⟶s(4)ηΩc∗μ=13ϵabcsaTCγμsbcc+saTCγμcbsc+caTCγμsbsc,where a,b, and c are color indices, C is the charge conjugation operator, and β is arbitrary parameter.We calculateΠ (Πμ) employing the light cone QCD sum rules (LCSR). According to the sum rules method approach, the correlation functions in (1) can be calculated in two different ways:(i)
In terms of hadron parameters.(ii)
In terms of quark-gluons in the deep Euclidean domain.These two representations are then equated by using the dispersion relation, and we get the desired sum rules for corresponding strong coupling constant. The hadronic representations of the correlation functions can be obtained by saturating (2) and (3) with corresponding baryons.Here we would like to note that the currentsηΞc, ηΩc, and ηΩc∗ interact with both positive and negative parity baryons. Using this fact for the correlation functions from hadronic part we get(5)Πhad=∑i=+,-j=+,-0ηΞcΞcjpKqΞcjpΩcip+qΩcip+qη-Ωc0p2-mΞcj2p+q2-mΩci2,Πμhad=∑i=+,-j=+,-0ηΞcΞcjpKqΞcjpΩc∗ip+qΩc∗ip+qη-Ωcμ0p2-mΞcj2p+q2-mΩc∗i2.The matrix elements in (5) are determined as(6)0ηBB+p=λ+up,0ηBB-p=λ-up,KqBpBp+q=gu-piΓup+q,KqBpB∗p+q=g∗u-pΓ′uμp+qqμ,where(7)Γ=γ5for-+⟶-+1for-+⟶+-transitions,Γ′=1for-+⟶-+γ5for-+⟶+-transitions,g is strong coupling constant of the corresponding decay, λB(i) are the residues of the corresponding baryons, and uμ is the Rarita-Schwinger spinors. Here the sign +(-) corresponds to positive (negative) parity baryon. In further discussions, we will denote the mass and residues of ground and excited states of Ωc(Ωc∗) baryons as m0,λ0(m0∗,λ0∗), m1,λ1(m1∗,λ1∗), and m2,λ2(m2∗,λ2∗) for scenario (a) and for scenario (b); the same notation is used as in previous case by just replacing m2,λ2(m2∗,λ2∗) to m3,λ3(m3∗,λ3∗). Moreover, the mass and residues of Ξc baryons are denoted as m0′, λ0′, and m1′,λ1′. Using the matrix elements defined in (6) for the correlation functions given in (1) we get (for case (a))(8)Π=iA1p+m0′γ5p+q+m0+iA2p+m0′p+q+m1-γ5+iA3γ5p+m1′p+q+m0+iA4γ5p+m1′γ5p+q+m1-γ5+iA5p+m0′p+q+m2-γ5+iA6γ5p+m1′γ5p+q+m2-γ5(9)Πμ=+A1∗p+m0′p+q+m0∗-qμ+A2∗p+m0′γ5p+q+m1∗-γ5-qμ+A3∗γ5p+m1′γ5p+q+m0∗-qμ+A4∗γ5p+m1′p+q+m1∗-γ5-qμ+A5∗p+m0′γ5p+q+m2∗-γ5-qμ+A6∗γ5p+m1′p+q+m2∗-γ5-qμ+otherstructures,where(10)A1∗=λ0∗λ0′g1∗m0′2-p2m0∗2-p+q2A2∗=A1m0∗⟶m1∗,g1∗⟶g2∗,λ0∗⟶λ1∗A3∗=A1m0′⟶m1′,g1∗⟶g3∗,λ0′⟶λ1′A4∗=A3m0∗⟶m1∗,g3∗⟶g4∗,λ0∗⟶λ1∗A5∗=A2m1∗⟶m2∗,g2∗⟶g5∗,λ1∗⟶λ2∗A6∗=A5m0′⟶m1′,g5∗⟶g6∗,λ0′⟶λ1′.The result for scenario (b) can be obtained from (8) and (9) by following replacements:(11)A5p+m0′p+q+m2-γ5⟶A~5p+m0′iγ5p+q+m3A6γ5p+m1′γ5p+q+m2-γ5⟶A~6γ5p+m1′p+q+m3A5∗p+m0′γ5qαp+q+m2∗-γ5-gμα⟶A~5p+m0′qαp+q+m3∗-gμαA6∗γ5p+m1′qαp+q+m2∗-gμα-γ5⟶A~6γ5p+m1′qαγ5p+q+m3∗-gμα.Note that to derive (9), we used the following formula for performing summation over spins of Rarita-Schwinger spinors:(12)∑uαpu-βp=-p+mgαβ-γαγβ3+2pαpβ3m2+pαγβ-pβγα3m,and in principle one can obtain the expression for the hadronic part of the correlation function. At this stage two problems arise. One of them is dictated by the fact that the current ημ interacts not only with spin 3/2 but also with spin 1/2 states. The matrix element of the current ημ with spin 1/2 state is defined as(13)0ημ12=Aγμ-4mpμup;that is, the terms in the RHS of (12) ~γμ and the right end (p+q)μ contain contributions from 1/2 states, which should be removed. The second problem is related to the fact that not all structures appearing in (9) are independent. In order to cure both these problems we need ordering procedure of Dirac matrices. In present work, we use ordering of Dirac matrices as pqγμ. Under this ordering, only the term ~gμα contains contributions solely from spin 3/2 states. For this reason, we will retain only gμα terms in the RHS of (9).In order to find sum rules for the strong coupling constants ofΩc→Ξc+K- transitions we need to calculate Π and Πμ from QCD side in the deep Euclidean region, p2→-∞, (p+q)2→-∞. The correlation from QCD side can be calculated by using the operator product expansion.Now let us demonstrate steps of calculation of the correlation function from QCD side. As an example let us consider one term of correlationΠμ; that is, consider(14)Πμ~ϵabcϵa1b1c1∫d4xeipxKq162uaTCγ5sb1cc1xc-0c1s-b10γμCs-a1T0.By using Wick’s theorem, this term can be written as(15)Πμ~ϵabcϵa1b1c1∫d4xeipxKqs-1a1γμCTSsbb1TxCTua1xγ5Sccc1x-s-b10γμCSsba1TCTuaγ5Sccc1x0.From this formula, it follows that, to obtain the correlation function(s) from QCD side, first of all we need the expressions of light and heavy quark propagators. The expressions of the light quark propagator in the presence of gluonic and electromagnetic background fields are derived in [13](16)Sx=ix2π2x4-mq4πx2-igs16π2∫duu-xσαβ+uσαβxx2gsGαβux+eqFαβ-imq2gsGμνσμν+eqFμνσμνln-x2Λ24+2γE.The heavy quark propagator is given as(17)SQ=∫d4k2π4e-ikxik+mQk2-mQ2-igs∫d4k2π4i∫01duk+mQ2mQ2-k22Gμνuxσμν+ixμmQ2-k2Gμνuxγν,where γE is the Euler constant.For calculation of the correlator function(s) we need another ingredient of light cone sum rules, namely, the matrix elements of nonlocal operatorsq-(x)Γq(y) and q-(x)ΓGμνq(y) between vacuum and the K-meson, that is, Kqq-(x)Γq(y)|0〉 and 〈K(q)|q-(x)ΓGμνq(y)|0〉. Here Γ is the any Dirac matrix, and Gμν is the gluon field strength tensor, respectively. These matrix elements are defined in terms of K-meson distribution amplitudes (DAs). The DAs of K meson up to twist-4 are presented in [12].From (8) and (9) it follows that the different Lorentz structures can be used for construction of the relevant sum rules. Among of six couplings, we need only A2(A2∗) and A5(A5∗) and A2(A2∗) and A~5(A~5∗) for cases (a) and (b), respectively. For determination of these coupling constants, we need to combine sum rules obtained from different Lorentz structures. From (8) and (9) (for case (a)) it follows that the Lorentz structures pqγ5, pγ5, qγ5, γ5 and pqqμ, pqμ, qqμ, and qμ appear. We denote the corresponding invariant functions Π1,Π2,Π3,Π4 and Π1∗,Π2∗,Π3∗, and Π4∗, respectively. Explicit expressions of the invariant functions Πi and Πi∗ are very lengthy, and therefore we do not present them in the present study.The sum rules for the corresponding strong coupling constants are obtained by choosing the coefficients aforementioned structures and equating to the corresponding results from hadronic and QCD sides. Performing doubly Borel transformation with respect to variablep2 and (p+q)2 in order to suppress the contributions of higher states and continuum we get the following four equations (for each transition):(18)Π1B=-A1B-A2B+A3B+A4B-A5B+A6B,Π2B=A1Bm0-m0′+A2B-m1-m0′+A3B-m0-m1′+A4Bm1-m1′+A5B-m2-m0′+A6Bm2-m1′Π3B=A1B-m0′+A2B-m0′+A3B-m1′+A4B-m1′+A5B-m0′+A6B-m1′Π4B=A1Bm0m0′-m0′2+A2B-m0′m1-m0′2+A3Bm0m1′+m1′2+A4B-m1′m1+m1′2+A5B-m0′m2-m0′2+A6B-m2m1′+m1′2Π1∗B=-A1∗B+A2∗B-A3∗B-A4∗B+A5∗B-A6∗B,Π2∗B=-A1∗Bm0∗+m0′+A2∗Bm0′-m1∗+A3∗B-m0∗+m1′+A4∗Bm0∗+m1′+A5B-m2∗+m0′+A6Bm1′+m2∗Π3∗B=-A1∗Bm0′+A2∗Bm0′+A3∗Bm1′+A4∗Bm1′+A5∗Bm0′+A6∗Bm1′Π4∗B=-A1∗Bm0∗m0′+m0′2+A2∗Bm0′2-m1∗m0′+A3∗B-m1′2+m1′m0∗+A4∗B-m1′2-m1′m1∗+A5∗Bm0′2-m0′m2∗+A6∗B-m1′2-m1′m2∗,where superscript B means Borel transformed quantities,(19)AαB∗=gα∗λiλj′e-mi2/M12-mj2/M22.The masses of the initial and final baryons are close to each other; hence in the next discussions, we setM12=M22=2M2. In order to suppress the contributions of higher states and continuum we need subtraction procedure. It can be performed by using quark-hadron duality; that is, starting some threshold the spectral density of continuum coincides with spectral density of perturbative contribution. The continuum subtraction can be done using formula(20)M2ne-mc2/M2⟶1Γn∫m2s0dse-sM2s-mc2n-1.For more details about continuum subtraction in light cone sum rules, we refer readers to work [14].As we have already noted in case (a) we need to determine two coupling constantsg2(g2∗) and g5(g5∗) for each class of transitions. From (18) it follows that we have six unknown coupling constants but have only four equations. Two extra equations can be obtained by performing derivative over (1/M2) of the any two equations. In result, we have six equations and six unknowns and the relevant coupling constants g2(g2∗) and g5(g5∗) can be determined by solving this system of equations.The results for scenario (b) can be obtained from the results for scenario (a) with the help of aforementioned replacements.From (18), it follows that, to estimate strong coupling constants g2(g2∗) and g5(g5∗) responsible for the decay of Ωc→ΞcK and Ωc∗→ΞcK, we need the residues of Ωc and Ξc baryons. For calculation of these residues for Ωc, we consider the following two point correlation functions:(21)Πp=∫d4xeipx0TηΩcxη-Ωc00,Πμνp=∫d4xeipx0TηΩcμxη-Ωcν00.The interpolating currentsηΩc and ημΩc couple not only to ground states, but also to negative (positive) parity excited states; therefore their contributions should be taken into account. In result, for physical parts of the correlation functions we get(22)Πp=0ηΩcp,sΩcp,sη-00-p2+m02+0ηΩ1cp,sΩ1cp,sη-00-p2+m12+0ηΩ23cp,sΩ23cp,sη-00-p2+m22+⋯,Πμν=0ημΩc∗p,sΩc∗p,sη-ν00m0∗2-p2+0ημΩ1c∗p,sΩ1c∗p,sη-ν00m1∗2-p2+0ημΩ23c∗p,sΩ23c∗p,sη-ν00m2∗2-p2+⋯,where the dots denote contributions of higher states and continuum. The matrix elements in these expressions are defined as(23)0ηΩcp,s=λ0up,0ηΩ12cp,s=λ12γ5up0ηΩc∗p,s=λ0∗uμp,0ηΩ12cp,s=λ12∗γ5uμp.As we already noted, only the structuregμν describes the contribution coming from 3/2 baryons. Therefore we retain only this structure.For the physical parts of the correlation function, we get(24)Πphy=p+m0λ02m02-p2+p-m1λ12m12-p2+p∓m23λ232m232-p2Πμνphy=p+m0∗gμνλ0∗2m0∗2-p2+p-m1∗gμνλ1∗2m1∗2-p2+p∓m23∗λ232m23∗2-p2.Here in the last term, upper (lower) sign corresponds to case (a) (case (b)).Denoting the coefficients of the Lorentz structuresp and I operators Π1, Π2 and pgμν, gμν as Π1∗, Π2∗, respectively, and performing Borel transformations with respect to -p2, for spin 1/2 case, we find(25)Π1B=λ02e-m02/M2+λ12e-m12/M2+λ232e-m22/M2,Π2B=λ02m0e-m02/M2-λ12m1e-m12/M2∓λ232m23e-m232/M2.The expressions for spin3/2 case formally can be obtained from these expressions by replacing λ→λ∗, m→m∗, and Π→Π∗. The invariant functions Πi, Πi∗ from QCD side can be calculated straightforwardly by using the operator product expansion. Their expressions are presented in [15] (see also [5]).Similar to the determination of the strong coupling constant, for obtaining the sum rule for residues we need the continuum subtraction. It can be performed in following way. In terms of the spectral densityρ(s) the Borel transformed ΠB can be written as(26)ΠiB=∫mc2∞ρise-s/M2ds.The continuum subtraction can be done by using the quark-hadron duality and for this aim it is enough to replace(27)∫mc2∞ρise-s/M2ds⟶∫mc2s0ρise-s/M2ds.It follows from the sum rules that we have only two equations, but six (three masses and three residues) are unknowns. In order to simplify the calculations, we take the masses ofΩc as input parameters. Hence, in this situation, we need only one extra equation, which can be obtained by performing derivatives over (-1/M2) on both sides of the equation. Note that the residues of Ξc baryons are calculated in a similar way.


## 3. Numerical Analysis

In this section we present our numerical results of the sum rules for the strong coupling constants responsible forΩc(3000)→Ξc+K- and Ωc(3066)→Ξc+K- decay derived in previous section. The Kaon distribution amplitudes are the key nonperturbative inputs of sum rules whose expressions are presented in [12]. The values of other input parameters are(28)fK=0.16GeV,m02=0.8±0.2GeV2,q-q=-0.240±0.0013GeV3,s-s=0.8q-q.The sum rules forg-+ and g-+∗ contain the continuum threshold s0, Borel variable M2, and parameter β in interpolating current for spin 1/2 particles. In order to extract reliable values of these constants from QCD sum rules, we must find the working regions of s0, M2, and β in such a way that the result is insensitive to the variation of these parameters. The working region of M2 is determined from conditions that the operator product expansion (OPE) series is convergent and higher states and continuum contributions should be suppressed. More accurately, the lower bound of M2 is obtained by demanding the convergence of OPE and dominance of the perturbative contributions over the nonperturbative one. The upper bound of M2 is determined from the condition that the pole contribution should be larger than the continuum and higher states contributions. We obtained that both conditions are satisfied when M2 lies in the range(29)2.5GeV2≤M2≤5GeV2.The continuum threshold s0 is not arbitrary and related to the energy of the first excited state; that is, s0=mground+δ2. Analysis of various sum rules shows that δ varies between 0.3 and 0.8 GeV, and in this analysis δ=0.4GeV is chosen. As an example, in Figures 1 and 2 we present the dependence of the residues of Ωc(3000) and Ωc(3050) on cos⁡θ for the scenario (a) at s=11GeV2 and several fixed values of M2, respectively. From these figures, we obtain that when cos⁡θ lies between -1 and -0.5 the residues exhibit good stability with respect to the variation of cos⁡θ and the results are practically insensitive to the variation of M2. And we deduce the following results for the residues:(30)λ1=0.08±0.03GeV3,λ2=0.11±0.04GeV3.Figure 1
The dependence of residue forΩc(3000) on cos⁡θ at s0=11GeV2 and at various fixed values of M2 for scenario (a).Figure 2
Same as in Figure1, but for Ωc(3050).Performing similar analysis forΩc baryons in scenario (b) we get (Figures 3 and 4)(31)λ1=0.030±0.001GeV3,λ3=0.04±0.01GeV3.The detailed numerical calculations lead to the following results for spin 3/2Ωc baryon residues:(32)λ1∗=0.18±0.02GeV3,λ2∗=0.17±0.02GeV3,λ1∗=0.024±0.002GeV3,λ3∗=0.05±0.01GeV3.Figure 3
Same as in Figure1, but for scenario (b).Figure 4
Same as in Figure2, but for scenario (b).From these results we observe that the residues ofΩc baryons in scenario (a) are larger than that one for the scenario (b). This leads to the larger strong coupling constants for scenario (b) because it is inversely proportional to the residue.Having obtained the values of the residues, our next problem is the determination of the corresponding coupling constants using the values ofM2 and s0 in their respective working regions which are determined from mass sum rules. In Figures 5, 6, 7, and 8, we studied the dependence of the strong coupling constants for Ωc∗→ΞcK0 transitions for the scenarios (a) and (b) on cos⁡θ, respectively. We obtained that when M2 varies in its working region the strong coupling constant demonstrates weak dependence on M2, and the results for the spin-3/2 states also practically do not change with the variation of s0. Our results on the coupling constants are as follows:For scenario (a),(33)g2=19±2g2∗=40±10g5=20±2g5∗=42±10.For scenario (b),(34)g2=2.2±0.2g2∗=2.0±0.5g5~=6±1g5~∗=8±1.Figure 5
The dependence of strong coupling constant forΩc(3066)→ΞcK on cos⁡θ at s0=11GeV2 and at three fixed values of M2 for scenario (a).Figure 6
Same as in Figure5, but for Ωc(3090)→ΞcK transition.Figure 7
Same as in Figure5, but for scenario (b).Figure 8
Same as in Figure6, but for scenario (b).The decay widths of these transitions can be calculated straightforwardly and we get(35)Γ=gi216πmi3mi+m0′2-mK2λ1/2mi2,m0′2,mK2Γ=gi∗2192πmi∗5mi∗+m0′2-mK2λ3/2mi∗2,m0′2,mK2,where mi(mi∗) and m0′ are the mass of initial spin 1/2 (spin 3/2) Ωc baryon and Ξc baryons, respectively, and λ(x,y,z)=x2+y2+z2-2xy-2xz-2yz. Having the relevant strong coupling constants, the decay width values for scenario (a) and (b) are shown in Table 1.Table 1
Decay widths for the two-scenarios considered are shown.
Scenario (a) Scenario (b) (GeV) (GeV) ΓΩc3000→ΞcK 8.1 ± 1.8 0.10 ± 0.02 ΓΩc3050→ΞcK 14.1 ± 3 3.8 ± 1.2 × 1 0 - 3 ΓΩc3066→ΞcK 6.6 ± 3 × 1 0 - 3 1.6 ± 0.6 × 1 0 - 5 ΓΩc3090→ΞcK 1.3 ± 0.5 × 1 0 - 2 0.10 ± 0.04Our results on the decay widths are also drastically different than the one presented in [11]. In our opinion, the source of these discrepancies is due to the following facts:(i)
In [11], the contributions coming from Ξc- baryons are all neglected.(ii)
The second reason is due to the procedure presented in [11]; namely, by choosing the relevant threshold s0, isolating the contributions of the corresponding Ωc baryons is incorrect. From analysis of various sum rules, it follows that s0=mground+δ2, where 0.3GeV≤δ≤0.8GeV. Since the mass difference between Ωc(3000) and Ωc(3090) is around 0.1GeV, isolating the contribution of each baryon is impossible while their contributions should be taken into account simultaneously. For these reasons our results on decay widths are different than those one predicted in [11]. From experimental data on the width of Ωc, there are [16](36)ΓΩc3000⟶Ξc+K-=4.5±0.6±0.3MeVΓΩc3050⟶Ξc+K-=0.8±0.2±0.1MeVΓΩc3066⟶Ξc+K-=3.5±0.4±0.2MeVΓΩc3090⟶Ξc+K-=8.7±1.0±0.8MeVΓΩc3119⟶Ξc+K-=1.1±0.8±0.4MeV.We find out that our predictions strongly differ from the experimental results.By comparing our predictions with the experimental data, we conclude that both scenarios are ruled out.


## 4. Conclusion

In conclusion, we calculated the strong coupling constants of negative parityΩc baryon with spins 1/2 and 3/2 with Ξc and K meson in the framework of light cone QCD sum rules. Using the obtained results on coupling constants we estimate the corresponding decay widths. We find that our predictions on the decay widths under considered scenarios are considerably different from experimental data as well as theoretical predictions and considered both scenarios are ruled out. Therefore further theoretical studies for determination of the quantum numbers of Ωc states as well as for correctly reproducing the decay widths of Ωc baryons are needed.



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