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Low-Lying Charmed and Charmed-Strange Baryon States

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Low-Lying Charmed and Charmed-Strange Baryon States Eur. Phys. J. C (2017) 77:154 DOI 10.1140/epjc/s10052-017-4708-x Regular Article - Theoretical Physics Low-lying charmed and charmed-strange baryon states Bing Chen1,3,a, Ke-Wei Wei1,b, Xiang Liu2,3,c, Takayuki Matsuki4,5,d 1 Department of Physics, Anyang Normal University, Anyang 455000, China 2 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China 3 Research Center for Hadron and CSR Physics, Institute of Modern Physics of CAS & Lanzhou University, Lanzhou 730000, China 4 Tokyo Kasei University, 1-18-1 Kaga, Itabashi, Tokyo 173-8602, Japan 5 Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198, Japan Received: 15 December 2016 / Accepted: 19 February 2017 © The Author(s) 2017. This article is published with open access at Springerlink.com ( )0,+,++ ( )0,+ ( )0,+ ( )0,+ Abstract In this work, we systematically study the mass c 2520 , c 2470 , c 2580 , c 2645 , 0,+ 0,+ () 0 0,+ spectra and strong decays of 1P and 2S charmed and c(2790) , c(2815) , c (2930) , c(2980) , 0,+ 0,+ () + charmed-strange baryons in the framework of non-relativistic c(3055) , c(3080) , and c (3123) . For brevity, constituent quark models. With the light quark cluster–heavy we call these charmed and charmed-strange baryons just quark picture, the masses are simply calculated by a poten- charmed baryons in the following. Among these observed tial model. The strong decays are studied by the Eichten– states, some new measurements have been performed by Hill–Quigg decay formula. Masses and decay properties experiments in the past several years. The masses and 0,+,++ 0,+,++ + of the well-established 1S and 1P states can be repro- widths of c(2455) , c(2520) , c(2595) , ( )0,+,++ + duced by our method. c 2800 can be assigned as and c(2625) have been measured with significantly small − − a c2(3/2 ) or c2(5/2 ) state. We prefer to interpret the uncertainties with the efforts of CDF [2] and Belle [3]. Very 0 + signal c(2850) as a 2S(1/2 ) state although at present recently, the Belle Collaboration updated the measurements ( )0,+ ( )0,+ ( )0,+ ( )0,+ we cannot thoroughly exclude the possibility that this is of c 2580 , c 2645 , c 2790 , c 2815 , ( )0 ( )+ ( )+ 0,+ the same state as c 2800 . c 2765 or c 2765 and c(2980) [4]. On the other hand, new decay modes +( ) + ( / −) could be explained as the c 2S state or c1 1 2 state, for the higher excited charmed baryon states have been found respectively. We propose to measure the branching ratio by experiment. For instance, the decay channel of D+ was B( ( )π)/B( ( )π) + + of c 2455 c 2520 in the future, which may first found for c(3055) and c(3080) , and the follow- disentangle the puzzle of this state. Our results support ing ratios of branching fractions were first reported by Belle 0,+ 0,+ c(2980) as the first radial excited state of c(2470) several months ago [5]: P = / + ( )0 with J 1 2 . The assignment of c 2930 is analogous + + 0,+,++ − − B(c(3055) → D ) to c(2800) , i.e., a (3/2 ) or (5/2 ) state. In = . ± . ± . , c2 c2 B( ( )+ → ( )++ −) 5 09 1 01 0 76 addition, we predict some typical ratios among partial decay c 3055 c 2455 K widths, which are valuable for experimental search for these B( ( )+ → +) missing charmed and charmed-strange baryons. c 3080 D = . ± . ± . , + ++ − 1 29 0 30 0 15 B(c(3080) → c(2455) K ) and 1 Introduction B( ( )+ → ( )++ −) c 3080 c 2520 K = . ± . ± . , B( ( )+ → ( )++ −) 1 07 0 27 0 01 At present, the particle data group (PDG) lists nine charmed c 3055 c 2455 K + and ten charmed-strange baryons [1]. They are c(2286) , where the uncertainties are statistical and systematic. Obvi- + + + + c(2595) , c(2625) , c(2765) (or c(2765) ), ously, these new measurements are very useful to understand + + 0,+,++ 0,+,++ c(2880) , c(2940) , c(2800) , c(2455) , the nature of these excited charmed baryon states. Theoretically, the charmed baryons which contain one a e-mail: [email protected] heavy quark and two light quarks occupy a particular posi- b e-mail: [email protected] tion in the baryon physics. Since the chiral symmetry and c e-mail: [email protected] heavy quark symmetry (HQS) can provide some qualitative d e-mail: [email protected] insight into the dynamics of charmed baryons, the investiga- 123 154 Page 2 of 17 Eur. Phys. J. C (2017) 77:154 tion of charmed baryons should be more helpful for improv- of low-lying 1P and 2S charmed baryons. We pay attention ing our understanding of the confinement mechanism. The to only the charmed baryons inside of which degrees of free- spectroscopy of charmed baryons has been investigated in dom of two light quarks are frozen. It means that two light various models. So far, the several kinds of quark potential quarks are not considered to be excited, neither radially nor models [6–10], the relativistic flux tube (RFT) model [11,12], orbitally. As illustrated in Ref. [44], these kinds of charmed the coupled channel model [13],theQCDsumrule[14–16], excitations carry lower-excited energies, which means these and the Regge phenomenology [17] have been applied to excited charmed baryons may more likely be detected by study the mass spectra of excited charmed baryons, and so did experiments. Fortunately, our results indicate that most of the lattice QCD [18,19]. The strong decay behaviors of charmed observed charmed baryons can be accommodated in this way. baryons have been studied by several methods, such as the The paper is arranged as follows. In Sect. 2, the masses heavy hadron chiral perturbation theory (HHChPT) [20,21], of low-excited charmed baryons are calculated by the non- 3 the chiral quark model [22,23], the P0 model [24], and a relativistic quark potential model. In Sect. 3, the Eichten– non-relativistic quark model [25]. The decays of 1P c and Hill–Quigg (EHQ) decay formula, which is employed to c baryons have also been investigated by a light front quark study the strong decays of excited charmed baryons, is intro- model [26,27], a relativistic three-quark model [28], and the duced. The properties of low-lying charmed baryon states QCD sum rule [29]. are fully discussed in Sect. 4. Finally, the paper ends with a Although many experimental and theoretical efforts have conclusion and an outlook. Some detailed calculations and been made for the research of charmed baryons, most of definitions are collected in the appendices. the 1P and 2S charmed baryons are not yet established. + 0,+,++ Several candidates, including c(2765) , c(2800) , 0 0,+ c(2930) , and c(2980) are still in controversy. 2 The deduction of mass spectra + c(2765) was first observed by the CLEO Collaboration ( )+ → +π +π − in the decay channel of c 2765 c [30], and 2.1 Treating charmed baryon system as a two-body confirmed by Belle in the c(2455)π mode [31,32]. Because problem + + +π +π − both c and c excitations can decay through c and c(2455)π, we even do not know whether the observed To study the baryon dynamics, one crucial question which + + charmed baryon signal around 2765 MeV is the c or c should be answered is “What are the relevant degrees of free- + − state, or their overlapping structure [33]. In the e e anni- dom in a baryon?” [45]. In constituent quark models, a baryon 0,+,++ hilation process, an isotriplet state, c(2800) ,was system consists of three confined quarks. Thus the dynamics +π observed by Belle in the channel of c , and it was ten- of a baryon resonance is surely more complex than a meson. P − tatively identified as the c2 state with J = 3/2 [34]. Due to the HQS, however, the dynamics of charmed baryons Interestingly, another neutral resonance was later found by could be greatly simplified. The HQS suggests that the cou- − → ∗0 ¯ → +π − ¯ BaBar in the process of B c p c p with the plings between a c quark and two light quarks are weak [46]. ± ± +33 mass 2846 8 10 MeV and decay width 86−22 MeV [35]. Therefore, two light quarks in a charmed baryon could first The higher mass and the weak evidence of J = 1/2 indi- couple with each other to form a light quark cluster.1 Then cate that the signal observed by BaBar might be different the light quark cluster couples with a charm quark, and a from the Belle observation. In this paper, we denote the sig- charmed baryon resonance forms. With this assumption, two 0 0 nal discovered by BaBar by c(2850) . c(2930) , which light quarks have the same status to a c quark, including the + − was only seen by BaBar in the decay mode c K [36], still average distances to a c quark. In the light cluster–heavy 0,+ needs more confirmation. c(2980) was first reported by quark picture, the dynamics of heavy baryon can be sim- + −π + + 0π − Belle in the channels c K and c KS [37], and plified. In the non-relativistic constituent quark model, the was later confirmed by Belle [4,38] and BaBar [39]inthe spin-independent part of the Hamiltonian is ( )π ( )π ( ) channels c 2580 , c 2645 and c 2455 K , respec- 3 2 α tively. However, the decay widths reported by Refs. [4,37– pi 2 b H = + mi + − + rij , (1) 39] were quite different from each other. More experimental 2mi 3rij 2 i=1 i< j information as regards the charmed baryons can be found in Refs.
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