Understanding the newly observed Ξ 0 c states through their decays
aa r X i v : . [ h e p - ph ] A p r Understanding the newly observed Ξ c states through their decays Kai-Lei Wang ∗ , Li-Ye Xiao , † , and Xian-Hui Zhong , ‡
1) Department of Electronic Information and Physics, Changzhi University, Changzhi, Shanxi,046011,China2)School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China3) Department of Physics, Hunan Normal University, and Key Laboratory of Low-DimensionalQuantum Structures and Quantum Control of Ministry of Education, Changsha 410081, China and4) Synergetic Innovation Center for Quantum E ff ects and Applications (SICQEA), Hunan Normal University, Changsha 410081, China Inspired by the newly observed Ξ c states by the LHCb Collaboration, we investigate the OZI-allowed two-body strong decays of the λ -mode 1 P wave Ξ ′ c states within the chiral quark model. Our results indicate that:(i) the newly observed states Ξ c (2923) and Ξ c (2939) are good candidates of the λ -mode 1 P wave Ξ ′ c stateswith the spin-parity J P = / − , namely | P λ / − i and | P λ / − i , respectively. (ii) The another newly observedstate Ξ c (2965) mostly corresponds to the λ -mode 1 P -wave Ξ ′ c state with the spin-parity J P = / − , namely | P λ / − i . (iii) For the two λ -mode J P = / − mixed states, the | P λ / − i is a narrow state with a width of Γ ∼
15 MeV and mainly decays into Ξ ′ c π ; while the | P λ / − i state has a width of Γ ∼
52 MeV and dominantlydecays into Ξ c π and Λ c K channels. If the broad structure around 2880 MeV observed at LHCb arises from thenew Ξ c state, this state is very likely to be the | P λ / − i state. PACS numbers:
I. INTRODUCTION
As an important kind of singly heavy baryons, the charmed-strange baryon Ξ ′ c spectrum belonging to the flavor sextet F plays a crucial role in perfecting baryon spectra. Althoughthere are some discussions for the Ξ ′ c states in theory dur-ing the past several decades [1–4], no obvious progress ofthe observations for the Ξ ′ c state has been achieved in exper-iments [5]. In the Ξ ′ c spectrum, only the two ground states Ξ ′ c with J P = / + and Ξ ∗ c (2645) with J P = / + (1 S wave)have been established. So far, the low-lying P -wave Ξ ′ c statespredicted in the quark model are still missing. It should bementioned that in 2007 a structure Ξ c (2930) was observedby BaBar in the Λ + c K − mass spectrum in B − → K − Λ + c ¯ Λ − c process [6]. Later, the Ξ c (2930) was confirmed by the BelleCollaboration in the same decay process [7], while its chargedpartner Ξ c (2930) + was also observed in ¯ K Λ + c final state inthe reaction ¯ B → ¯ K Λ + c ¯ Λ − c [8]. In addition, another structure Ξ c (2970) was first observed by BaBar in the Σ c (2455) K S decay mode [9]. This structure was also observed in both Ξ ′ + c π − [10] and Ξ c (2645) + π − [11] final states at Belle. Thestructures Ξ c (2930) and Ξ c (2970) may be some signals ofthe missing P -wave Ξ ′ c states first observed in experiments.Very recently, the LHCb Collaboration observed three newstates Ξ c (2923) , Ξ c (2939) , and Ξ c (2965) in the Λ + c K − massspectrum with a large significance [12], and their masses andnatural widths are determined to be m [ Ξ c (2923) ] = . ± .
59 MeV , Γ [ Ξ c (2923) ] = . ± . , ∗ Corresponding author, E-mail: [email protected] † Corresponding author, E-mail: [email protected] ‡ Corresponding author, E-mail: [email protected] m [ Ξ c (2939) ] = . ± .
52 MeV , Γ [ Ξ c (2939) ] = . ± . , m [ Ξ c (2965) ] = . ± .
54 MeV , Γ [ Ξ c (2965) ] = . ± . . As pointed out in Ref. [12], the Ξ c (2930) observed in B − → K − Λ + c ¯ Λ − c process [6, 7] might be due to the overlap of the twonew narrower states, Ξ c (2923) and Ξ c (2939) . Stimulatedby these three newly observed states, recently some groupshave discussed their nature. In Ref. [13], these three newlyobserved states Ξ c (2923) , Ξ c (2939) , and Ξ c (2965) are sug-gested to be assigned as the P -wave Ξ ′ c states. In Ref. [14], Ξ c (2923) and Ξ c (2939) may be good candidates of the P-wave states with J P = / − and 5 / − states and Ξ c (2965) can be assigned as Ξ ′ c (2 S ) state. To understand the nature ofthese newly observed states and clarify whether they can beidentified as the Ξ ′ c (1 P ) and Ξ ′ c (2 S ) state or not, more theoret-ical analysis is urgently needed.For the mass spectrum of the Ξ ′ c baryon, there exist manycalculations with various models and e ff ective theories in theliterature [15–25]. We collect the predicted masses in Table I.From this table, it is found that the masses of the three Ξ c states observed by the LHCb Collaboration [12] are in the pre-dicted region of the λ -mode 1 P wave Ξ ′ c excitations. Here, “ λ -mode” denotes one orbital excitation in a Jacobi coordinatebetween the light quarks and the heavy c quark. Moreover,the possibility as 2 S excitations cannot be excluded absolutelybased simply on the predicted masses. In addition, it should beemphasized that in the light of the equal spacing rule [26, 27],the Ξ c (2923) , Ξ c (2939) and Ξ c (2965) states probably cor-respond to their flavour multiplets Ω c (3050) , Ω c (3065) and Ω c (3090) , respectively. Meanwhile, based on our previouswork [28], Ω c (3050) and Ω c (3065) could be assigned to betwo J P = / − states, | P λ / − i and | P λ / − i , respec-tively; Ω c (3090) very likely corresponds to the J P = / − state | P λ / − i . To this extent, Ξ c (2923) and Ξ c (2939) arelikely to have J P = / − , and Ξ c (2965) has J P = / − . Be-sides mass spectra, the radiative and strong decay propertiesare crucial in pining down the inner structures of a state. Be-fore the LHCb’s measurement [12], there are also some dis-cussions of the radiative and strong decay properties of the 1 P wave Ξ c states [21, 25, 28–36].In our previous works [28, 35], the decay properties of the1 P wave Ξ c states were estimated with a chiral quark model,the mostly predicted decay widths of the λ -mode 1 P wave Ξ ′ c states were about a few dozen MeV, which were roughlyconsistent with the LHCb’s measurement [12]. In the presentwork, by combining the newest data we further analyze thestrong decay properties of the λ -mode 1 P wave Ξ ′ c states withthe chiral quark model, and attempt to put forward views onthe inner structures of the three Ξ c states observed by theLHCb Collaboration [12].This paper is organized as follows. In Sec. II we give abrief introduction of the strong decay model. We discuss thestrong decays of the low-lying λ -mode 1 P wave Ξ ′ c states inSec. III and summarize our results in Sec. IV. II. THE MODEL
In this work we apply the chiral quark model [37] to studythe strong decay properties. Within the chiral quark model,the e ff ective low energy quark-pseudoscalar-meson couplingin the SU(3) flavor basis at tree level is adopted as [37] H m = X j f m ¯ ψ j γ j µ γ j ψ j ~τ · ∂ µ ~φ m , (1)where f m is the pseudoscalar meson decay constant; ψ j rep-resents the j th quark field in a baryon, and φ m denotes thepseudoscalar meson octet.To match the nonrelativistic harmonic oscillator spatialwave function in our calculations, one should adopt a non-relativistic form of the quark-pseudoscalar coupling [38–40] H nrm = X j n ω m E f + M f σ j · P f + ω m E i + M i σ j · P i − σ j · q + ω m µ q σ j · p ′ j o I j e − i q · r j , (2)where ( ω m , q ) denote the energy and three-vector momen-tum of the final light pseudoscalar meson; ( E i , M i , P i ) and( E f , M f , P f ) are the energy, mass and three-vector mo-mentum of the initial and final baryons, respectively. The p ′ j ( = p j − ( m j / M ) P c.m. ) stands for the internal momentum ofthe j th quark in the baryon rest frame; σ j sands for the Paulispin vector on the j th quark; µ q represents the reduced massexpressed as 1 /µ q = / m j + / m ′ j . The isospin operator I j associated with π and K mesons is given by I j = √ [ a † j ( u ) a j ( u ) − a † j ( d ) a j ( d )] for π , a † j ( u ) a j ( d ) for π − , a † j ( u ) a j ( s ) for K − . (3) Here, a † j ( u , d ) and a j ( u , d , s ) are the creation and annihilationoperator for the u , d and u , d , s quarks on j th quark, respec-tively.Then the partial decay width for the emission of a lightpseudoscalar meson in a hadron strong decay can be calcu-lated with [41, 42] Γ = δ f m ! ( E f + M f ) | q | π M i J i + X J iz J fz |M J iz , J fz | , (4)where δ is a global parameter accounting for the strength ofthe quark-meson couplings; J iz and J fz are the third com-ponents of the total angular momenta of the initial and finalbaryons, respectively; M J iz , J fz denotes the transition ampli-tude.With momentum q of the final light pseudoscalar mesonincreasing, the relativistic e ff ect should be significant [43].To partly remedy the inadequacy of the nonrelativistic wavefunction as the momentum q increases, a commonly usedLorentz boost factor γ f is introduced into the decay ampli-tudes [42, 44–46] M ( q ) → γ f M ( γ f q ) , (5)where γ f ≡ M f / E f . In most decays, the corrections from theLorentz boost are not drastic and the nonrelativistic prescrip-tion is reasonable.The model parameters have been well determined in pre-vious works [28, 35], and we collect them in Table II. In thecalculations the masses of the final baryons and mesons aretaken from the PDG [5] and collected in Table II as well. Theharmonic oscillator space-wave functions Ψ nlm = R nl Y lm areadopted to describe the spatial wave function of the initial andfinal baryons, and the harmonic oscillator parameter α ρ in thewave functions for ds / us system is taken as α ρ =
420 MeV.Another harmonic oscillator parameter α λ can be related to α ρ with the relation α λ = [3 m c / (2 m q + m c )] / α ρ , where m q denotes the light quark mass. III. RESULTS AND ANALYSIS
The masses of the three Ξ c states newly observed by theLHCb Collaboration [12] are in the predicted mass region ofthe λ -mode 1 P wave Ξ ′ c states(see Table I). To clarify the pos-sibility and further investigate their inner structures, we con-duct a systematic study of the strong decay properties for the λ -mode 1 P wave Ξ ′ c states within the framework of a chiralquark model. Our results and theoretical predictions are pre-sented as follows. A. P states with J P = / − In the Ξ ′ c family, there are two λ -mode J P = / − states | P λ / − i and | P λ / − i . Their masses are predicted tobe about M = (2830 − Ξ c π , Ξ ′ c π , TABLE I: The mass spectrum of Ξ ′ c belonging to F up to the 1 P -wave states in various models and e ff ective theories. The Ξ ′ c states aredenoted by | N S + L σ J P i in the LS coupling scheme. The unit of mass is MeV in the table. | N S + L σ J P i Ref. [15] Ref. [23] Ref. [22] Ref. [24] Ref. [16] Ref. [17] Observed state | S + i Ξ ′ + (0) c | S + i Ξ ∗ c | P λ − i · · ·| P λ − i · · · · · · Ξ c (2939) ? | P λ − i · · · · · ·| P λ − i · · · · · · Ξ c (2923) ? | P λ − i Ξ c (2965) ?TABLE II: The parameters and final hadron’ masses [5] used in thiswork. The unit is MeV except the parameter δ , which is a dimen-sionless quantity. Ξ ∗ c denotes Ξ c (2645) in the table.State Mass State Mass Ξ + c π − Ξ c π Ξ ′ + c K − Ξ ′ c Λ + c Ξ ∗ + c Ξ ∗ c δ f π f K α ρ m q m s m c Ξ ∗ c π and Λ + c K − . Considering the uncertainties of the pre-dicted masses, we plot the partial decay widths as functionsof the masses of the states Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i inFig. 1. Their decay properties remain relatively stable withinthe mass range of (2830 − Ξ ′ c | P λ / − i , the total decay width varies inthe region of Γ ∼ (23 −
27) MeV, and the dominant decaymodes are Ξ c π , Ξ ′ c π and Λ c K . The branching fraction foreach of the dominant decay mode is about 30%. For the other J P = / − state Ξ ′ c | P λ / − i , the total decay width is about Γ ∼ (29 −
40) MeV with mass varied in the region what weconsidered. It mainly decays into Ξ c π and Λ c K . Meanwhile,the partial decay width of the Ξ ′ c π mode is significant with abranching ratio of ∼ J P = / − are very likely to be mixed states between | P λ / − i and | P λ / − i by the following mixing scheme, | P λ / − i | P λ / − i = cos φ sin φ − sin φ cos φ | P λ / − i| P λ / − i . (6)The mixing angle φ may rang from φ = ◦ to that of P 1/2 - ( M e V ) M(MeV) c ’ c *c c K Total P 3/2 - ( M e V ) M(MeV) P 1/2 - ( M e V ) M(MeV) P 3/2 - ( M e V ) M(MeV) P 5/2 - ( M e V ) M(MeV)
FIG. 1: The strong decay partial width for the 1 P wave Ξ ′ c states as afunction of mass. heavy quark symmetry limit ( φ = ◦ ). In our previouswork [28, 48], we obtained that the state Ω c (3000) could beexplained as the mixed state | P λ / − i with a mixing angle φ ≃ ◦ . As the same flavour multiplet, the mixing angle inthe Ξ ′ c family should be comparable with that in the Ω c fam-ily. Meanwhile, according to the equal spacing rule [26, 27],the mass of the mixed state | P λ / − i in the Ξ ′ c family islighter about ∼
120 MeV than that of state in the Ω c family,namely M Ξ ′ c | P λ / − i ≃ | P λ / − i state as a function of the mix-ing angle φ in the range of (0 ◦ , 35 ◦ ) by fixing the mass at M = Λ c K and Ξ c π modes for Ξ ′ c | P λ / − i arerapidly suppressed and the Ξ ′ c π decay channel almost saturates *c c K c ’ c |1P 1/2 - > ( M e V ) (degree) |1P 1/2 - > ( M e V ) (degree) Total FIG. 2: The strong decay partial width for the J P = / − mixed Ξ ′ c states as a function of the mixing angle φ . The masses of the mixedstates | P λ / − i and | P λ / − i are fixed at M = its total decay width. Taking a possible mixing angle φ ≃ ◦ constrained by the Ω c (3000) state, we find the Ξ ′ c | P λ / − i state has a narrow width of Γ ∼ . Ξ ′ c π is B [ Ξ ′ c | P λ / − i → Ξ ′ c π ] ≃ . (7)The decay rate of Ξ ′ c | P λ − i into Λ c K strongly depends onthe mixing angle. If taking a slightly larger mixing φ ≃ ◦ than that ( φ ≃ ◦ ) determined by Ω c (3000), one finds thedecay rate into the Λ c K channel is nearly zero. Thus, the Ξ ′ c | P λ − i may be hardly observed in the Λ c K final state.Furthermore, the predicted decay width of the mixed state Ξ ′ c | P λ / − i seems to be comparable with the decay widthof the three Ξ c states observed by the LHCb Collabora-tion [12]. However, it should be kept in mind that the mass of Ξ ′ c | P λ / − i should be around ∼ Ω c (3000). Thus,most likely the three Ξ c states as the state Ξ ′ c | P λ / − i isexcluded. Considering the predicted width of Ξ ′ c | P λ / − i being narrow, this state might be observed in the Ξ ′ c π channelwhen enough data are accumulated in experiments.The other mixed state | P λ / − i should be a relativelybroad state with a width much larger than the three newlyobserved Ξ c states. At this moment we investigate its widthrange with M = Γ ∼ (38 −
50) MeV with themixing angle varying in range of (0 ◦ , 35 ◦ ). Taking a possiblemixing angle φ = ◦ constrained by the Ω c (3000) state, wefind that the mixed state Ξ ′ c | P λ / − i has a width of Γ ∼ Ξ c π and Λ c K final states with comparable branching fractions B [ Ξ ′ c | P λ / − i → Ξ c π ] ≃ , (8) B [ Ξ ′ c | P λ / − i → Λ c K ] ≃ . (9)Both the mass and decay width of this mixed state are in-consistent with the observations of the three newly observed Ξ c states, thus, the three Ξ c states as the state Ξ ′ c | P λ / − i should be excluded. Since Ξ ′ c | P λ / − i is not a very broadstate, it might be observed in the Ξ c π and Λ c K channels.It should be remarked that according to the LHCb’ mea-surement [12], the Λ c K mass spectrum shows a broad struc-ture around 2880 MeV, which might be due to the presenceof additional new Ξ c states. Combining the predicted decayproperties of Ξ ′ c | P λ / − i in this work, if the broad struc-ture in the region around M ∼ Ξ c state, this state is very likely to be the Ξ ′ c | P λ / − i state.Moreover, the possibility of the broad structure arising fromthe overlapping of Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i cannotbe ruled out as well. B. P states with J P = / − There are two λ -mode J P = / − states Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i . The predicted masses of these two states arelisted in Table I. From the table, it is seen that predictedmasses are about ∼ Ξ c (2923) and Ξ c (2939) measured by the LHCbCollaboration [12]. As the good candidates of Ξ c (2923) and Ξ c (2939), it is essential to study the decay properties of the Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i .We plot the decay properties of the Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i as functions of their masses in the range of M = (2860 − Ξ ′ c | P λ / − i is about Γ ∼ (7 − Ξ ′ c | P λ / − i is Γ ∼ (7 −
18) MeV withmasses increasing in the range what we considered. The dom-inant decay mode of Ξ ′ c | P λ / − i is Ξ c π , while Ξ ′ c | P λ / − i mainly decays into Ξ ′∗ c π channel.The predicted decay widths of Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i are also comparable with the observedvalues of Ξ c (2939) and Ξ c (2923) within the uncertainties.Meanwhile, with the similar masses, | P λ / − i is slightlybroader than | P λ / − i . By combining the width order Γ [ Ξ c (2939) ] > Γ [ Ξ c (2923) ] from experiments and ourtheoretical predictions, we may conclude that Ξ c (2939) and Ξ c (2923) prefer to the Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i states, respectively. In addition, according to the equalspacing rule [26, 27], the Ξ c (2923) and Ξ c (2939) statesprobably correspond to their flavour multiplets Ω c (3050) and Ω c (3065) , respectively. In our previous work [28, 48], Ω c (3050) could be assigned to be | P λ / − i and Ω c (3065) was assigned to be | P λ / − i . To this extend, the Ξ c (2923) and Ξ c (2939) states assigned to be | P λ / − i and | P λ / − i , respectively, is reasonable as well.Fixing the mass of Ξ ′ c | P λ / − i with M = TABLE III: The decay properties of the P -wave Ξ ′ c states compared with the observations. Γ thtotal presents the total decay width calculated in thepresent work, while Γ exptotal presents the total width obtained from the LHCb experiment [12]. The units of mass and width are MeV in the table.State Mass Γ [ Ξ c π ] Γ [ Ξ ′ c π ] Γ [ Ξ ∗ c π ] Γ [ Λ c K ] Γ thtotal Γ exptotal Possible assignment | P λ − i · · · · · ·| P λ − i · · · · · ·| P λ − i . ± . ± . Ξ c (2923) | P λ − i . ± . ± . Ξ c (2939) | P λ − i . ± . ± . Ξ c (2965) obtain Γ total [ Ξ ′ c | P λ / − i ] ≃
13 MeV . (10)The predicted branching fraction of the dominant decay mode Ξ ∗ c π is B [ Ξ ′ c | P λ / − i → Ξ ∗ c π ] ≃ . (11)Meanwhile, the decay rates of Ξ ′ c | P λ / − i into Ξ c π and Λ c K are considerable, and the predicted branching fractions are B [ Ξ ′ c | P λ / − i → Ξ c π ] ≃ , (12) B [ Ξ ′ c | P λ / − i → Λ c K ] ≃ . (13)The sizeable branching fraction for Ξ ′ c | P λ / − i into Λ c K is consistent with the nature of Ξ c (2923) , which is observedin the Λ c K channel. If Ξ c (2923) corresponds to the state Ξ ′ c | P λ / − i indeed, the Ξ c π and Ξ ∗ c π also may be measuredin future experiments due to their large branching fractions.In the same way, we fix the mass of Ξ ′ c | P λ / − i with M = Γ total [ Ξ ′ c | P λ / − i ] ≃
20 MeV . (14)This state mainly decays into Ξ c π channel with the branchingfraction B [ Ξ ′ c | P λ / − i → Ξ c π ] ≃ . (15)The partial decay widths of the other three decay channels Ξ ′ c π , Ξ ∗ c π , and Λ c K are comparable. The partial decay ratiosare Γ [ Ξ ′ c | P λ / − i → Λ c K ] Γ [ Ξ ′ c | P λ / − i → Ξ ′ c π ] ≃ . , (16) Γ [ Ξ ′ c | P λ / − i → Ξ ∗ c π ] Γ [ Ξ ′ c | P λ / − i → Ξ ′ c π ] ≃ . . (17)If Ξ c (2939) observed in the Λ c K channel corresponds tothe state Ξ ′ c | P λ / − i indeed, the comparable partial decaywidths indicate this state may be established in the Ξ c π , Ξ ′ c π and Ξ ∗ c π decay channels as well in future experiments.Moreover, assigning the Ξ c (2923) and Ξ c (2939) to Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i , respectively, we notice thatthe predicted total decay width ratio R = Γ total [ Ξ ′ c | P λ / − i ] Γ total [ Ξ ′ c | P λ / − i ] ≃ . , (18)highly agrees with the observed central value R exp1 = Γ total [ Ξ c (2923) ] Γ total [ Ξ c (2939) ] ≃ . C. P states with J P = / − There is only one λ -mode J P = / − state | P λ / − i . Thepredicted mass of this state is listed in Table I. In terms of thepredicted mass, the possibility of the three newly observed Ξ c states taken as the state Ξ ′ c | P λ / − i cannot be excluded. Toinvestigate the e ff ects of the uncertainties of the mass on thedecay properties of the Ξ ′ c | P λ / − i state, we show the vari-ation of the partial decay width with the change of mass inFig. 1. From the figure, the variation curves between the par-tial decay width and the mass for this state is similar to that for Ξ ′ c | P λ / − i . The dominant decay mode for Ξ ′ c | P λ / − i is Ξ c π . Meanwhile, the partial decay width of the Λ c K modeis sizeable, and becomes more and more significant with themass increasing in the region of (2860 − Ξ ′ c | P λ / − i are consis-tent with the observations of Ξ c (2965) . Meanwhile, consid-ering the equal spacing rule [26, 27], Ξ c (2965) most likelycorresponds to its flavour mulitiplet Ω c (3090), which wasassigned to the | P λ / − i state according to our previousstudy [28]. Thus, it is reasonable to assign Ξ c (2965) as the Ξ ′ c | P λ / − i state.According to our calculations, we get Γ total [ Ξ ′ c | P λ / − i ] ≃ . M = Ξ c π with the branching fraction B [ Ξ ′ c | P λ / − i → Ξ c π ] ≃ . (20)The decay rate of Ξ ′ c | P λ / − i into the Λ c K channel is sig-nificant as well, and the predicted branching ratio is B [ Ξ ′ c | P λ / − i → Λ c K ] ≃ . (21)The sizeable branching fraction of Ξ ′ c | P λ / − i into Λ c K isconsistent with the observation of the Ξ c (2965) signal in the Λ c K decay channel.In addition, the total decay width ratios among the Ξ ′ c | P λ / − i , Ξ ′ c | P λ / − i , and Ξ ′ c | P λ / − i states are pre-dicted to be R = Γ total [ Ξ ′ c | P λ / − i ] Γ total [ Ξ ′ c | P λ / − i ] ≃ . , (22) R = Γ total [ Ξ ′ c | P λ / − i ] Γ total [ Ξ ′ c | P λ / − i ] ≃ . . (23)The predicted ratios are good consistent with the experi-mental central values ( R exp2 = Γ total [ Ξ c (2923) ] Γ total [ Ξ c (2965) ] ≃ .
50 and R exp3 = Γ total [ Ξ c (2939) ] Γ total [ Ξ c (2965) ] ≃ .
77) of those among the three states Ξ c (2923) , Ξ c (2939) , and Ξ c (2965) , respectively.Finally, it should be mentioned that the known Ξ c (2970) was observed in the Σ c (2455) K S [9], Ξ ′ + c π − [10], and Ξ c (2645) + π − [10, 11] decay modes may correspond two dif-ferent resonances with a very similar mass. The Ξ c (2970) was observed in the Σ c (2455) K S [9] final state cannot beconsidered as the same state of Ξ c (2965) although theyhave a very similar mass, because the Σ c (2455) K S mode of Ξ c (2965) is forbidden as the Ξ ′ c | P λ / − i state. However,one cannot exclude the Ξ c (2965) resonance as the same res-onance observed in the Ξ ′ + c π − [10], and Ξ c (2645) + π − [10, 11]final states. The Ξ c (2970) observed in the Σ c (2455) K S fi-nal state may be explained with the ρ -mode 1 P wave Ξ ′ c states [35], or the first positive parity excitations of the Ξ c [29, 31]. IV. SUMMARY
In this paper, we carry out a systematic study of the OZIallowed two-body strong decays of the λ -mode 1 P wave Ξ ′ c states in the framework of a chiral quark model. Combin-ing our theoretical predictions and the experimental observa-tions, we give possible interpretations for the three new states Ξ c (2923) , Ξ c (2939) , and Ξ c (2965) observed by the LHCbCollaboration.Our theoretical results show that the newly observed states Ξ c (2923) and Ξ c (2939) are most likely to be explained as the λ -mode 1 P wave Ξ ′ c states with spin-parity J P = / − , namely Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i , respectively. The Ξ c (2923) and Ξ c (2939) may be flavour partners of Ω c (3050) and Ω c (3065) , respectively. Meanwhile, if the arrangementsin this work are correct, then the dominant decay mode of Ξ c (2923) is Ξ ′∗ c π and that of Ξ c (2939) is Ξ c π . This can betested in future experiments.The another newly observed state Ξ c (2965) may corre- sponds to the λ -mode 1 P -wave Ξ ′ c state with spin-parity J P = / − , namely Ξ ′ c | P λ / − i . The Ξ c (2965) may be a flavourpartner of Ω c (3090) . Besides the Λ c K decay channel, the de-cay rate of Ξ ′ c | P λ / − i into Ξ c π is significant as well, andthe predicted branching ratio is about 59%. The large branch-ing fraction indicates that this state may be reconstructed inthe Ξ c π decay channel as well.There are strong configuration mixings in the J P = / − λ -mode states. The mixed state Ξ ′ c | P λ / − i might be a flavourpartner of Ω c (3000) . This J P = / − mixed state may havea mass of M ∼ Γ ∼ | P λ / − i is Ξ ′ c π witha branching fraction of > Λ c K isstrongly suppressed due to the heavy quark symmetry. The Ξ ′ c | P λ / − i may be observed in the Ξ ′ c π final state.The other J P = / − mixed state Ξ ′ c | P λ / − i has arelatively broad width of Γ ∼
48 MeV, which is about 3times larger than that of Ξ ′ c | P λ / − i . The Ξ ′ c | P λ / − i mainly decays into Ξ c π and Λ c K channels with branching ra-tios 45% and 54%, respectively. Considering the mass anddecay properties, if the broad structure in the Λ c K mass spec-trum around M ∼ Ξ c state, this state is very likely tobe the Ξ ′ c | P λ / − i state. Moreover, the possibility of thebroad structure arising from the overlapping of Ξ ′ c | P λ / − i and Ξ ′ c | P λ / − i cannot be ruled out as well.Finally it should be mentioned that combining our previ-ous study [49] of the newly observed Ω ∗ b states at LHCb [50],we find that the Ξ c (2923) , Ξ c (2939) , and Ξ c (2965) maybe flavour partners of Ω b (6330), Ω b (6340), and Ω b (6350), re-spectively. The missing mixed state Ξ ′ c | P λ / − i may be aflavour partner of Ω b (6316). Acknowledgements
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