Possible assignments of highly excited Λc(2860)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2860)^+$$\end{document}, Λc(2880)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2880)^+$$\end{document} and Λc(2940)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2940)^+$$\end{document}

Possible assignments of highly excited Λc(2860)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2860)^+$$\end{document}, Λc(2880)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2880)^+$$\end{document} and Λc(2940)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2940)^+$$\end{document} are explored in a 3P0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3P_0$$\end{document} strong decay model. Decay widths, branching fraction ratios R=Γ(Σc(2520)π)Γ(Σc(2455)π)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}$$\end{document} and the branching fractions of DN channels of theses assignments are computed. D0p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D^0p$$\end{document} channel is a very important channel to provide information on the inner excitation and structure of these highly excited Λc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c$$\end{document}. In our analysis, Λc(2860)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2860)^+$$\end{document} may be a 1D-wave excited Λc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c$$\end{document} with JP=32+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J^P={3\over 2}^+$$\end{document}, which has dominant DN decay channels with a branching fraction B(Λc(2860)+→DN)=75%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {B}}(\varLambda _c(2860)^+\rightarrow DN)=75\%$$\end{document} and a branching ratio R=Γ(Σc(2520)π)Γ(Σc(2455)π)=0.12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.12$$\end{document}. Λc(2880)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2880)^+$$\end{document} is very possibly a 1F-wave excited Λc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c$$\end{document} with JP=52-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J^P=\frac{5}{2}^-$$\end{document}; In this assignment, the predicted total decay width (Γ≈4.49\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma \approx 4.49$$\end{document} MeV) is comparable to the measured Γ=5.6-0.6+0.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma =5.6^{+0.8}_{-0.6}$$\end{document} MeV, and the predicted R=Γ(Σc(2520)π)Γ(Σc(2455)π)=0.12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.12$$\end{document} is consistent with the measured R=0.225±0.062±0.025\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=0.225\pm 0.062\pm 0.025$$\end{document}; The DN channels are its dominant strong decay channels with a branching fraction B(Λc(2880)+→DN)=94%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {B}}(\varLambda _c(2880)^+\rightarrow DN)=94\%$$\end{document}. Λc(2880)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2880)^+$$\end{document} seems impossibly a 1D-wave excited Λc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c$$\end{document} with JP=52+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J^P=\frac{5}{2}^+$$\end{document} once the presently measured R=Γ(Σc(2520)π)Γ(Σc(2455)π)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}$$\end{document} is confirmed. Λc(2940)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2940)^+$$\end{document} may be a 2P-wave excited Λc1,11,0(32-,2P)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda ^{1,0}_{c1,1}(\frac{3}{2}^-,2P)$$\end{document}. In this case, Λc(2940)+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c(2940)^+$$\end{document} has a total decay width Γ=17.56\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma =17.56$$\end{document} MeV, a branching ratio R=Γ(Σc(2520)π)Γ(Σc(2455)π)=0.89\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.89$$\end{document} and the DN decay channels with a branching fraction B(Λc(2940)+→DN)=43%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {B}}(\varLambda _c(2940)^+\rightarrow DN)=43\%$$\end{document}. In order to understand the inner excitation and structure of these highly excited Λc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _c$$\end{document}, measurements of those predicted quantities are required in the future.


Introduction
Charmed baryons with single charmed quark provide ideal windows to study the baryon structure and quark dynamics. The heavy-quark symmetry works approximately in singlya e-mail: zhangal@shu.edu.cn (corresponding author) charmed baryons, and the quarks inside may correlate and exhibit their structure through their strong decays. There are now 36 established singly-charmed baryons [1], but their J P numbers have seldom been measured in experiments.
The quarks in baryons may make complex structures and have complex excitations. In order to study the internal structures and excitations, the three-quark baryons are usually described by Jacobi coordinates: a relative coordinate ρ between any two quarks, and a relative coordinate λ between the center of mass of the two quarks and the other quark. As known, a diquark may be an important correlation and cluster in hadrons with more than two quarks, and the diquark has been introduced to interpret the light scalar mesons, the missing nucleons, the charmonium-like X, Y, Z , and so on. The diquark has also been employed to describe singly-charmed baryons in many models [10,12,13,[17][18][19][20][21]. However, there is no evidence for the existence of diquark in baryons. In this paper, the strong decay properties of Λ c baryons with different ρ or λ mode excitations will be studied, and the relation between the excitations and the diquark correlation is explored.
In Ref. [15], all the observed Λ c states except for the ground Λ c (2286) + were systematically examined as the 1Pwave, 1D-wave, or 2S-wave Λ c baryons from their strong decay properties in the 3 P 0 model, and their possible assignments were suggested. In this paper, we continue the examination of Λ c (2860) + , Λ c (2880) + and Λ c (2940) + with the highly excited 1D, 1F and 2P orbital or radial excitations assignments in detail.
The paper is organized as follows. A simple introduction of 3 P 0 strong decay model and analyses of the strong decay properties of Λ c (2860) + , Λ c (2880) + and Λ c (2940) + are given in Sect. 2. Conclusions and discussions are reserved in Sect. 3. In order to fix the quantum numbers and to understand the internal structure of Λ c (2860) + , Λ c (2880) + and Λ c (2940) + , the 3 P 0 strong decay model is employed. As well known, the 3 P 0 model is usually known as the quark pair creation model. It was proposed by Micu [22] and developed by Le Yaouanc et al. [23][24][25][26][27][28]. This model has been employed to compute the Okubo-Zweig-Iizuka-allowed (OZI) strong decays widths with two final states and obtained good agreements with experiments.
Following Refs. [15,[29][30][31][32][33], the strong decay width for an initial baryon A decaying into two final hadrons B and C in the 3 P 0 model is where M M J A M J B M J C is the helicity amplitude. The explicit expression of the helicity amplitude, the flavor matrix, the space integral and some relevant notations could be found in detail in Ref. [15]. As indicated in Ref. [15], ρ is the relative coordinate between the two light quarks (quarks 1 and 2), and λ is the relative coordinate between the center of mass of the two light quarks and the charmed quark. In a constituent quark model, the internal structure of a baryon is also described by a set of quantum numbers n ρ , n λ , L ρ , L λ and S ρ . n ρ and n λ denote the nodal quantum numbers of the ρ and λ coordinates, respectively. L ρ and L λ denote the orbital angular momentum between the two light quarks and the orbital angular momentum between the charm quark and the twolight-quark system. S ρ denotes the total spin of the two light quarks. The total orbital angular momentum L = L ρ + L λ and the total angular momentum of the baryons J = J l + 1 Therefore, in the constituent quark model with the heavyquark symmetry [15,34], there are one 1S-wave, seven 1P-wave, seventeen 1D-wave, and thirty-one 1F-wave Λ c baryons. For the first radial excitations, the corresponding states doubled. That is to say, there are two 2S-wave, fourteen 2P-wave, thirty-four 2D-wave, and sixty-two 2F-wave Λ c baryons. Internal quantum numbers of the 1D-wave excited Λ c were given in Ref. [15], quantum numbers of the 1F-wave and 2P-wave excited Λ c are given in the appendix.
Some parameters are chosen as those in Refs. [15,32,35]. The dimensionless pair-creation γ = 13.4. The β λ,ρ = 600 MeV in 1S-wave baryon wave function, β = 400 MeV in the wave function of π and K mesons, β = 600 MeV for the D meson [15,35]. β ρ,λ = 400 MeV is for the excited Λ c (2860) + , Λ c (2880) + and Λ c (2940) + . The masses of relevant hadrons are chosen from Particle Data Group [1]. D 0 p mode is an important channel for Λ c baryons in the 3 P 0 model. In this channel, the heavy charmed quark in initial baryon enters the final D meson and other two light quarks enter the final p baryon. Therefore, this channel may provide some information on the inner excitation and structure of Λ c .
In theory, the helicity amplitudes of many high-lying Λ c decaying into D 0 p channel vanish. Therefore, many possible assignments of Λ c (2860) + , Λ c (2880) + and Λ c (2940) + can be excluded through the observed D 0 p final states. So does the D + n channel. Possible high-lying Λ c which can decay into D 0 p channel are given in Table 1. In these Λ c excita- excitation, while others have only λ mode excitation.

2P-wave excitations
There are fourteen 2P-wave excited Λ c , among which there are four excitations with D 0 p decay channels. As indicated in Table 1 Table 6 Possible decay widths (MeV), branching fraction of DN channels and R = Γ (Σc(2520)π ) Γ (Σc(2455)π ) of Λ c (2940) + as four 2P-wave excitations ). The numerical results are given in Table 6. In comparison with the D-wave and F-wave excited Λ c with λ mode excitation only, the 2P-wave excited Λ c with ρ mode excitation has a much lower branching fraction of DN channels.
Based on experimental results, some possible or favored assignments of these excited Λ c are suggested to them, and some impossible assignments are pointed out. In experiment, only the D 0 p channel has been observed, the observation of other decay channels such as Σ c π or Σ c (2520)π and measurement of their branching fractions are required to the understand its inner excitation and structure.
As reported in Ref. [4], an analysis of angular distribution in Λ c (2880) + → Σ c (2455) 0,++ π +,− strongly favors the Λ c (2880) + with spin 5 2 . In their analysis, the measured R = Γ (Σ c (2520)π ) Γ (Σ c (2455)π ) = 0.225 ± 0.062 ± 0.025 is found around the prediction of heavy quark symmetry R = 0. Accordingly, the J , P quantum numbers of Λ c (2880) + can not be J P = 3 surement of all the branching fractions of these channels is very important for the understanding of this state. In [5], the most likely spin-parity assignment for Λ c (2940) + was suggested with J P = 3 2 − . However, other solutions with spins 1 2 to 7 2 have not been excluded. In our analysis, Λ c (2940) + could be the 2P-wave excited So far, D 0 p channel has been observed in all highly excited Λ c above their threshold, which may imply that the two light quarks in initial baryons enters the final baryon in the strong decay process. In the same time, the DN channels are dominant and the two internal light quarks in initial baryons coupling with a total spin S ρ = 0 in all possible assignments of Λ c (2860) + , Λ c (2880) + and Λ c (2940) + , which may imply that the two light quarks in initial Λ c make a good diquark. Furthermore, the 2P-wave excited Λ c with ρ mode excitation has a much lower branching fraction of DN channel in comparison with the 1D-wave and 1F-wave excited Λ c with λ mode excitation only. The existence and properties of diquark require more exploration.
In addition to the normal uncertainties, three-body decay cannot be computed in the 3 P 0 model. In our analyses, the parameters β are chosen the same for ρ mode and λ mode for simplicity though the parameters β (represent the inverse root mean square radius) of ρ and λ mode excitation may be different. More highly excited possibilities to these Λ c have not yet analyzed. In order to identify these highly-excited Λ c baryons and to understand their inner structure and dynamics, measurements of the J , P quantum numbers and branching fractions of the main decay channels of these highly excited Λ c are required, more theoretical analyses in different models are also required.
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Appendix
In the constituent quark model with the heavy-quark symmetry, internal quantum numbers of 1F-wave and 2P-wave