0 + ++ Ground and Excited state masses of Ωc , Ωcc and Ωccc baryons Juhi Oudichhya, Keval Gandhi,∗ and Ajay Kumar Rai Department of Physics, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India (Dated: May 25, 2021) 0 + ++ The masses of ground and excited states of Ωc , Ωcc and Ωccc baryons are calculated within the framework of Regge phenomenology. Here our attempt is to assign a possible spin-parity to these − obtained masses. Our calculated masses in (J, M 2) plane with both natural (J P = 1/2+, 3/2 , − 5/2+, ....) and unnatural (J P = 3/2+, 5/2 , 7/2+, ....) spin-parities are in agreement with the experimental observations where available and reasonably close to other theoretical predictions. Further we fix the slope and intercept of each Regge line in (n, M 2) plane and estimate the masses of higher excited states of these baryons. The obtained mass relations and the mass value predictions could provide an useful information in future experimental searches and the spin-parity assignment of these states. I. INTRODUCTION Upto the date there are different research aspects to study the hadron spectroscopy, one of the prominent way In 2017, the LHCb collaboration observed five new to determine the properties of hadronic states is mass 0 0 0 spectrum analysis. So far there are various method to narrow excited Ωc states such as Ωc(3000) , Ωc(3050) , 0 0 0 depict the mass spectrum. The authors of Refs. [18–21] Ωc(3066) , Ωc(3090) and Ωc(3119) decaying into − calculate the excited state masses of singly, doubly and Ξ+K [1]. Except for Ω (3119)0 other four states were c triply heavy baryons using non-relativistic approach of further confirmed by Belle [2] in 2018. Frequent ques- hypercentral constituent quark model (hCQM). In Ref. tions have been arises with this discovery, for instance [22] mass analysis is carried out for the newly excited (i) why only five states were observed ? (ii) why they are Ω baryons by proposing a new scheme of state classi- so narrow ?. Many authors have been addressed these c/b fication called Jls mixing coupling which goes beyond jj questions with recent studies given in Refs. [3–15]. Since coupling. The results favor to predict the spin-parity of Ω0 is composed of two strange quarks (ss) and one charm c these states. The ground state and excited state spectra quark (c), if ss diquark remains in its color triplet it has of Ω0 baryon are estimated from lattice QCD with dy- spin-1, as symmetry rules do not allow a spin-0 diquark. c namical quark field in Ref. [5] and results predicted the This spin combined with spin 1/2 of c quark, we have P 0 0 J assignments of the states Ωc(3000) , Ωc(3050) and S = 1/2 or 3/2. Now consider states with relative or- 0 0 0 − − Ωc(3066) , Ωc(3090) and Ωc(3119) with 1/2 , 3/2 bital momentum L = 1 and combining with S = 1/2 − and 3/2 gives the total spin J = 1/2, 3/2 and J = 1/2, and 5/2 , respectively. The authors of Ref. [4] predicts 3/2, 5/2, respectively. All these five states have negative the existence of five states with negative parity by assum- parity. Also these states are extremely narrow which in- ing these baryonic states as bound state of c-quark and dicates that it is difficult to pull apart the two s quarks a P wave ss-diquark. Ebert et al. [23] determine mass in a diquark [4]. spectra of excited heavy baryons consisting of two light The study of heavy-light bound state provides an ideal (u,d,s) and one heavy (c,b) quarks, in the framework platform to understand the dynamics of quantum chro- of QCD-motivated by relativistic quark model. Robert modynamics (QCD) at low energy regime. The strong et al.[24] used non-relativistic hamiltonian quark model interaction coupling is small for the hadrons containing to calculate the masses of heavy baryons. Ref. [25] es- heavy quark (c or b) which makes it easier to under- timate the masses and residues of these newly observed arXiv:2105.10647v1 [hep-ph] 22 May 2021 0 stand the QCD perturbatively than the system contain- Ωc baryon states within QCD sum rules and try to deter- ing only light quark [16]. Different experimental facilities mine the nature of these states. So far none of the dou- have provided new information in the sector of hadron bly/triply Ω baryons have been experimently detected. spectroscopy like masses, decay width, branching ratios, Although many authors have predicted the masses of isospin mass splittings, apin, parity, polarisation ampli- Ωcc and Ωccc baryons using various theoretical and phe- tude, etc. It is very crucial to assign the spin-parity of nomenological models, like Relativistic quark model [26] hadrons which facilitate the determination of experimen- , Salpeter model [27], Lattice QCD [28, 29], the Hamil- 0 tonian model [30], the Hypercentral constituent quark tal properties. Experimentally only the ground state Ωc 0 and Ωc(2770) are observed with their quantum numbers, model [18, 19] etc. P 1 + 3 + Wei et al. [31] derive some useful mass relations such J = 2 and 2 respectively [17], where J is the total spin and P denotes the parity. The J P values of excited as linear mass inequalities, quadratic mass inequali- state Ω0 baryons are still missing as shown in Table I. ties and quadratic mass equalities for hadrons using c quasilinear Regge trejectory ansatz. Based on these relations they determine mass ranges of some mesons P and baryons and predict J assignments of Ξc(2980), ∗ [email protected] Ξc(3055), Ξc(3077) and Ξc(3123) baryons. Ref. [32] 2 P 0 posed by Nambu [33, 34]. He assumed that the uniform TABLE I. Masses, width and J value of Ωc baryons reported interaction of quark and antiquark pair form a strong flux by LHCb [1]. tube and at the end of the tube the light quarks rotating Resonance Mass(MeV) Width(MeV) J P with the speed of light at radius R. The mass originating 0 ± 1 + in this flux tube is estimated as [35], Ωc 2695.2 1.7 - 2 0 3 + c ± Ω (2770) 2765.9 2.0 - 2 R 0 ± ± ± ± ? σ Ωc(3000) 3000.4 0.22 0.1 4.5 0.6 0.3 ? M =2 dr = πσR, (1) 0 ? 2 Ωc(3050) 3050.2±0.1 ± 0.1 0.8 ± 0.2 ± 0.1 ? 0 1 − ν (r) 0 ? Z Ωc(3065) 3065.6±0.1 ± 0.3 3.5 ± 0.4 ± 0.2 ? where σ represent the string tension, i.e the mass density 0 ? Ωc(3090) 3090.2±0.3 ± 0.9 8.7±0.1 ± 0.8 ? per unit length. Likewise,p the angular momentum of this 0 ? Ωc(3120) 3119±0.3 ± 0.9 1.1±0.8 ± 0.4 ? flux tube is evaluated as, R 2 σrν(r) πσR ′ J =2 dr = + c , (2) 1 − ν2(r) 2 the same group extended this methodology to compute Z0 the masses of ground state and excited state of other ∗ ∗ one can also write, p doubly and triply charmed baryons such as Ωcc, Ξcc, Ωcc and Ωccc. In the present work we have used the same 2 M ′′ approach of Regge phenomenology with the assumption J = + c , (3) of linear Regge trejectories. We obtained relations 2πσ between intercept, slope ratios and baryon masses in ′ ′′ where c and c are the constants of integration. Hence both (J, M 2) and (n ,M 2) planes. Using these relations r we can say that, J and M 2 are linearly related to each we determine the mass spectra of Ω baryon and try to c other. The plots of Regge trejectories of hadrons in assign a possible spin-parity to these recently observed the (J, M 2) plane are usually called Chew-frautschi plots five baryonic states. Further we apply the same scheme [36]. Also hadrons lying on the same Regge line pos- for doubly and triply charmed omega baryons. Since sess the same internal quantum numbers. From Eq. (3), these baryons are yet to be observed by experiments the most general form of linear regge trejectories can be and therefore they are not listed in PDG [17] yet. This 0 + expressed as [31], motivate us to study the mass spectra of Ωc, Ωcc and Ω++ baryons. ′ ccc J = α(M)= a(0) + α M 2, (4) The remainder of this paper is organised as follows. ′ where a(0) and α represents the intercept and slope of After introduction, in sec II we briefly explain the linear the trejectory respectively. These parameters for differ- Regge trejectories and extract the quadratic mass rela- ent quark constituents of a baryon multiplet can be re- tion in (J, M 2) plane to calculate the ground state and lated by two relations [31, 37–40], excited state masses of Ωc baryon. Further we extend this work and again derive some mass equations to eval- aiiq (0) + ajjq (0) = 2aijq (0), (5) uate the mass spectra for Ωcc and Ωccc baryons. In addi- tion, we estimate the masses of these baryons in (n,M 2) plane by calculating Regge slopes and intercepts of par- ticular regge lines. The discussions of our results appear 1 1 2 ′ + ′ = ′ , (6) in sec.III. α iiq α jjq α ijq where i, j, q represent quark flavors, mi < mj and q de- II. THEORETICAL FRAMEWORK notes an arbitrary light or heavy quark.