Charm-strange baryon strong decays in a chiral quark model

Lei-Hua Liu, Li-Ye Xiao, and Xian-Hui Zhong*

Department of Physics, Key Laboratory of Low-Dimensional Quantum Structuresand Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081, China

(Received 16 May 2012; revised manuscript received 18 July 2012; published 24 August 2012)

The strong decays of charm-strange baryons up to N ¼ 2 shell are studied in a chiral quark model. The

theoretical predictions for the well-determined charm-strange baryons, ��cð2645Þ, �cð2790Þ, and

�cð2815Þ, are in good agreement with the experimental data. This model is also extended to analyze

the strong decays of the other newly observed charm-strange baryons �cð2930Þ, �cð2980Þ, �cð3055Þ,�cð3080Þ, and�cð3123Þ. Our predictions are given as follows: (i)�cð2930Þ might be the first orbital (1P)

excitation of�0c with J

P ¼ 1=2� and favors the j�0c2P�1=2

�i or j�0c4P�1=2

�i state. (ii)�cð2980Þ might

correspond to two overlapping 1P excitations of �0c. The broader resonance with a mass m ’ 2:98 GeV

observed in the�þc�K� final state is most likely to be the j�0

c2P�1=2

�i state, while the narrower resonancewith a mass m ’ 2:97 GeV observed in the ��

cð2645Þ� channel is most likely to be the j�0c2P�3=2

�istate. (iii) �cð3080Þ could be classified as the j�cS��1=2

þi, i.e., the first radial (2S) excitation of �c.

(iv)�cð3055Þ is most likely to be the second orbital (1D) excitation of�c with JP ¼ 3=2þ and favors the

j�c2D��3=2

þi state. (v) �cð3123Þ might be assigned to the j�0c4D��3=2

þi, j�0c4D��5=2

þi, or

j�c2D��5=2

þi state. As a byproduct, we calculate the strong decays of the bottom baryons ��b , �

��b ,

and ��b, which are in good agreement with the recent observations as well.

DOI: 10.1103/PhysRevD.86.034024 PACS numbers: 12.39.Jh, 13.30.�a, 14.20.Lq, 14.20.Mr

I. INTRODUCTION

In recent years, several new charm-strange baryons,�cð2930Þ, �cð2980Þ, �cð3055Þ, �cð3080Þ, and�cð3123Þ, have been observed. Their experimental infor-mation has been collected in Table I. In these newlyobserved states, �cð2980Þ and �cð3080Þ are relativelywell established in experiments. Both of their isospin stateswere observed by the Belle Collaboration in the �þ

c�K�

channel [3] and confirmed by BABAR with high statisticalsignificances [4]. Belle also observed a resonance structurearound 2.97 GeV with a narrower width of �18 MeV inthe ��

cð2645Þ� decay channel in a separate study [5],which is often considered as the same resonance,�cð2980Þ, observed in the �þ

c�K� channel. �cð2930Þ

was found by BABAR in the�þc K

� final state by analyzing

the B� ! �þc���c K

� process [2]. However, this structure isnot yet confirmed by Belle. �cð3055Þþ and �cð3123Þþwere only observed by BABAR in the �þ

c K��þ final state

with statistical significances of 6:4� and 3:0�, respectively[4]. No further evidences of them were found when BABARsearched the inclusive �þ

c�K and �þ

c�K�þ�� invariant

mass spectra for new narrow states. It should be mentionedthat BABAR’s observations show that �cð3055Þþ and�cð3123Þþ mostly decay through the intermediate reso-nant modes �cð2455ÞþþK� and �cð2520ÞþþK�, respec-tively. A good review of the recent experimental results oncharmed baryons can be found in Ref. [6].

Charmed baryon mass spectroscopy has beeninvestigated in various models [7–17]. The masses of

charm-strange baryons in the N � 2 shells predictedwithin several quark models have been collected inTables II and III. Comparing the experimental data withthe model predictions, one finds that �cð2930Þ could be acandidate of the first radial (2S) excitation of�c with J

P ¼1=2þ or the first orbital (1P) excitation of �0

c with JP ¼1=2�, 3=2� or 5=2�.�cð2980Þmight be assigned to the 2Sexcitation of �c or �0

c with JP ¼ 1=2þ. �cð3055Þ and�cð3080Þ are most likely to be the second orbital (1D)excitations of �c with JP ¼ 3=2þ or 5=2þ, or the 2Sexcitation of �0

c with JP ¼ 1=2þ. �cð3123Þ might beclassified as the 1D excitation of �0

c with JP ¼ 3=2þ,5=2þ or 7=2þ. Obviously, only depending on the massanalysis it is difficult to determine the quantum numbersof these newly observed charm-strange baryons. On theother hand, the strong decays of these newly observedcharm-strange baryons have been studied in several theo-retical models, such as the heavy hadron chiral perturba-tion theory approach [18] and the 3P0 model [19,20]. In

Ref. [18], Cheng and Chua advocated that the JP numbersof �cð2980Þ and �cð3080Þ could be 1=2þ and 5=2þ,respectively. They claimed that under this JP assignment,it is easy to understand why �cð2980Þ is broader than�cð3080Þ. In Refs. [19,20], Chen et al. analyzed the strongdecays of the N ¼ 2 shell excited charm-strange baryonsin the 3P0 model; they could only exclude some assign-

ments according to the present experimental information.As a whole, although the new charm-strange baryons havebeen studied in several aspects, such as mass spectroscopyand strong decays, their quantum numbers are not clear sofar. Thus, more investigations of these new heavy baryonsare needed.*zhongxh@hunnu.edu.cn

PHYSICAL REVIEW D 86, 034024 (2012)

1550-7998=2012=86(3)=034024(14) 034024-1 � 2012 American Physical Society

To further understand the nature of these newly observedcharm-strange baryons, in this work, we make a systematicstudy of their strong decays in a chiral quark model, whichhas been developed and successfully used to deal with thestrong decays of charmed baryons and heavy-light mesons[21–24]. It should be pointed out that very recently, someimportant progresses in the observation of the bottombaryons have been achieved in experiments as well:

(i) The CDF Collaboration presented improved measure-ments of the masses and first measurements of naturalwidths of the four bottom baryons ��

b and ���b [25].

(ii) The CMS Collaboration observed a new neutral excitedbottom baryon with a mass m ¼ 5945:0� 0:7� 0:3�2:7 MeV, which is most likely to be the ��0

b [26]. As

a byproduct, in this work we also calculate the strongdecays of these bottom baryons according to the newmeasurements.This work is organized as follows. In the Sec. II, the

charm-strange baryon in the quark model is outlined. Thena brief review of the chiral quark model approach is givenin Sec. III. The numerical results are presented and dis-cussed in Sec. IV. Finally, a summary is given in Sec. V.

II. CHARM-STRANGE BARYONIN THE QUARK MODEL

The charmed baryon contains a heavy charm quark,which violates SU(4) symmetry. However, the SU(3) sym-metry between the other two light quarks (u, d, or s) isapproximately kept. According to the symmetry, thecharmed baryons belong to two different SU(3) flavorrepresentations: the symmetric sextet 6F and antisymmet-ric antitriplet �3F. For a charm-strange baryon belonging to�3F, the antisymmetric flavor wave function (�c-type) canbe written as

��c¼

8<:

1ffiffi2

p ðus� suÞc for�þc

1ffiffi2

p ðds� sdÞc for�0c;

(1)

while for a charm-strange baryon belonging to 6F, thesymmetric flavor wave function (�0

c-type) is given by

��0c¼

8<:

1ffiffi2

p ðusþ suÞc for�0þc

1ffiffi2

p ðdsþ sdÞc for�00c :

(2)

In the quark model, the typical SU(2) spin wave func-tions for the charm-strange baryons can be adopted[27,28]:

TABLE I. Summary of the experimental results of the newly observed charm-strange baryons.

Resonance Mass (MeV) Width (MeV) Observed decay channel Collaboration Status [1]

�cð2930Þ0 2931� 3� 5 36� 7� 11 �þc K

� BABAR [2] *

�cð2980Þþ 2978:5� 2:1� 2:0 43:5� 7:5� 7:0 �þc K

��þ Belle [3] ***

2969:3� 2:2� 1:7 27� 8� 2 �þc K

��þ, �cð2455ÞþþK� BABAR [4]

2967:7� 2:3þ1:1�1:2 18� 6� 3 �cð2645Þ0�þ Belle [5]

�cð2980Þ0 2977:1� 8:8� 3:5 43.5 fixed �þc�K0�� Belle [3] ***

2972:9� 4:4� 1:6 31� 7� 8 �þc�K0�� BABAR [4]

2965:7� 2:4þ1:1�1:2 15� 6� 3 �cð2645Þþ�� Belle [5]

�cð3055Þþ 3054:2� 1:2� 0:5 17� 6� 11 �cð2455ÞþþK� BABAR [4] **

�cð3080Þþ 3076:7� 0:9� 0:5 6:2� 1:2� 0:8 �þc K

��þ Belle [3] ***

3077:0� 0:4� 0:2 5:5� 1:3� 0:6 �þc K

��þ, �cð2455; 2520ÞþþK� BABAR [4]

�cð3080Þ0 3082:8� 1:8� 1:5 5:2� 3:1� 1:8 �þc�K0�� Belle [3] ***

3079:3� 1:1� 0:2 5:9� 2:3� 1:5 �þc�K0��, �cð2455; 2520Þ0 �K0 BABAR [4]

�cð3123Þþ 3122:9� 1:3� 0:3 4:4� 3:4� 1:7 �cð2520ÞþþK� BABAR [4] *

TABLE II. Masses (MeV) of the �c-type charm-strange bary-ons in various quark models.

N JP State [13] [16] [15] [12] [17]

0 12þ 1S 2471 2476 2467 2466 2481

1 12� 1P 2799 2792 2792 2773 2801

1 32� 1P . . . 2819 2792 2783 2820

2 12þ 2S 3137 2959 2992 . . . 2923

2 32þ 1D 3071 3059 3057 3012 3030

2 52þ 1D 3049 3076 3057 3004 3042

TABLE III. Masses (MeV) of the�0c-type charm-strange bary-

ons in various quark models.

N JP State [13] [16] [15] [12] [17]

0 12þ 1S 2574 2579 2567 2594 2578

0 32þ 1S 2642 2649 2647 2649 2654

1 12� 1P 2902 2936 2897 2855 2934

1 32� 1P . . . 2935 2910 2866 2931

1 52� 1P . . . 2929 3050 2895 2921

2 12þ 2S 3212 2983 3087 . . . 2984

2 12þ 1D . . . 3163 . . . . . . 3132

2 32þ 1D . . . 3160 3127 . . . 3127

2 52þ 1D 3132 3166 3167 3080 3123

2 72þ 1D . . . 3147 . . . 3094 3136

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-2

�s3=2 ¼"""; �s

�3=2 ¼###;

�s1=2 ¼

1ffiffiffi3

p ð""# þ "#" þ #""Þ;

�s�1=2 ¼

1ffiffiffi3

p ð"## þ ##" þ #"#Þ;

(3)

for the spin-3/2 states with symmetric spin wave functions,

��1=2¼

1ffiffiffi2

p ð"#"� #""Þ; ���1=2¼

1ffiffiffi2

p ð"##� #"#Þ; (4)

for the spin-1/2 states with mixed antisymmetric spin wavefunctions, and

��1=2 ¼ � 1ffiffiffi

6p ð"#" þ #"" �2 ""#Þ;

���1=2 ¼ þ 1ffiffiffi

6p ð"## þ #"# �2 ##"Þ;

(5)

for the spin-1/2 states with mixed symmetric spin wavefunctions.In this work, we adopt the harmonic oscillator states as

the spatial wave functions for the charm-strange baryons.The details of the spatial wave functions can be found inour previous work [21].The product of spin, flavor, and spatial wave functions of

baryons must be symmetric since the color wave functionis antisymmetric. The flavor wave functions of the�c-type

TABLE IV. �c-type charm-strange baryons classified in the quark model and their possible two body strong decay channels. Thenotation of the�c-type charmed baryon is denoted by j�c

2Sþ1L�JPi as used in Ref. [27]. The Clebsch-Gordan series for the spin and

angular-momentum addition j�c2Sþ1L�J

Pi ¼ PLzþSz¼Jz

hLLz; SSzjJJziN��LLz

�Sz��chas been omitted.

Notation N l� l� L S JP Wave function Strong decay channel

j�c2S12

þi 0 0 0 0 12

12þ 0�S

00��Sz��c

. . .

j�c2P�

12�i 1 1 0 1 1

212� 1��

1Lz��Sz��c

�0c�, �

�c�

j�c2P�

32�i 1 1 0 1 1

232�

j�c2P�

12�i 1 0 1 1 1

212� 1��

1Lz��Sz��c

�c�, �0c�, �

�c�

j�c2P�

32�i 1 0 1 1 1

232�

j�c4P�

12�i 1 0 1 1 3

212�

j�c4P�

32�i 1 0 1 1 3

232� 1�

�1Lz

�SSz��c

�c�, �0c�, �

�c�

j�c4P�

52�i 1 0 1 1 3

252�

j�c2SA

12þi 2 1 1 0 1

212þ 2�A

00��Sz��c

�c�,�c�,�cK, �0c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c4SA

32þi 2 1 1 0 3

232þ 2�A

00�sSz��c

�c�, �c�,�cK, �0c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c2PA

12þi 2 1 1 1 1

212þ 2�A

1Lz��Sz��c

�c�,�c�, �cK, �0c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c2PA

32þi 2 1 1 1 1

232þ

j�c4PA

12þi 2 1 1 1 3

212þ �c�,�c�, �cK, �

0c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c4PA

32þi 2 1 1 1 3

232þ 2�A

1Lz�SSz��c

�c�,�c�,�cK, �0c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c4PA

52þi 2 1 1 1 3

252þ �c�, �c�,�cK, �

�c�,�

�cK,�cð2790; 2815Þ�

j�c2DA

32þi 2 1 1 2 1

232þ �c�,�c�, �cK, �

0c�,�cK,�

�c�,�

�cK,�cð2790; 2815Þ�

j�c2DA

52þi 2 1 1 2 1

252þ 2�A

2Lz��Sz��c

j�c4DA

12þi 2 1 1 2 3

212þ �c�,�c�, �cK, �

0c�,�cK,�

�c�,�

�cK,�cð2790; 2815Þ�

j�c4DA

32þi 2 1 1 2 3

232þ

j�c4DA

52þi 2 1 1 2 3

252þ 2�A

2Lz�SSz��c

j�c4DA

72þi 2 1 1 2 3

272þ

j�c2D��

32þi 2 0 2 2 1

232þ �0

c�,�cK,��c�,�

�cK

j�c2D��

52þi 2 0 2 2 1

252þ 2�

��2Lz

��Sz��c

j�c2D��

32þi 2 2 0 2 1

232þ �0

c�,�cK,��c�,�

�cK,D�

j�c2D��

52þi 2 2 0 2 1

252þ 2���

2Lz��Sz��c

j�c2S��

12þi 2 0 0 0 1

212þ 2���

00 ��Sz��c

�0c�,�cK,�

�c�,�

�cK

j�c2S��

12þi 2 0 0 0 1

212þ 2���

00 ��Sz��c

�0c�,�cK,�

�c�,�

�cK,D�

CHARM-STRANGE BARYON STRONG DECAYS IN A . . . PHYSICAL REVIEW D 86, 034024 (2012)

034024-3

charm-strange baryons are antisymmetric under theinterchange of the u (d) and s quarks; thus, the productof spin and spatial wave functions must be symmetric. Incontrast, the product of spin and spatial wave functionsof �0

c-type charm-strange baryons are required to beantisymmetric due to their symmetric flavor wave func-tions under the interchange of the two light quarks. Thenotations, wave functions, and quantum numbers of the�c-type and �0

c-type charm-strange baryons up to N ¼ 2shell in the quark model are given in Tables IV and V,respectively.

III. CHIRAL QUARK MODEL

In the chiral quark model, the effective low energyquark-meson pseudoscalar coupling at tree level is givenby [29–33]

Hm ¼ Xj

1

fm�c j�

j�

j5c j ~ � @ ~�m; (6)

where c j represents the jth quark field in a baryon, and fmis the meson’s decay constant. The pseudoscalar mesonoctet �m is expressed as

TABLE V. �0c-type charm-strange baryons classified in the quark model and their possible two body strong decay channels. The

notation of the�0c-type charmed baryon is denoted by j�0

c2Sþ1L�J

Pi as used in Ref. [27]. The Clebsch-Gordan series for the spin andangular-momentum addition j�0

c2Sþ1L�J

Pi ¼ PLzþSz¼Jz

hLLz; SSzjJJziN��LLz

�Sz��0chas been omitted.

Notation N l� l� L S JP Wave function Strong decay channel

j�0c2S12

þi 0 0 0 0 12

12þ 0�S

00��Sz��0

c. . .

j�0c4S32

þi 0 0 0 0 32

32þ 0�S

00�sSz��0

c�c�

j�0c2P�

12�i 1 1 0 1 1

212� 1��

1Lz��Sz��0

c�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c2P�

32�i 1 1 0 1 1

232�

j�0c4P�

12�i 1 1 0 1 3

212� �c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c4P�

32�i 1 1 0 1 3

232� 1��

1Lz�sSz��0

c

j�0c4P�

52�i 1 1 0 1 3

252�

j�0c2P�

12�i 1 0 1 1 1

212� 1�

�1Lz

��Sz��0

c�0

c�, �cK,��c�, �

�cK

j�0c2P�

32�i 1 0 1 1 1

232�

j�0c2SA

12þi 2 1 1 0 1

212þ 2�A

00��Sz��0

c�0

c�, �cK,��c�, �

�cK

j�0c2PA

12þi 2 1 1 1 1

212þ 2�A

1Lz��Sz��0

c�0

c�, �cK,��c�, �

�cK

j�0c2PA

32þi 2 1 1 1 1

232þ

j�0c2DA

32þi 2 1 1 2 1

232þ �0

c�, �cK,��c�, �

�cK

j�0c2DA

52þi 2 1 1 2 1

252þ 2�A

2Lz��Sz��0

c

j�0c2D��

32þi 2 0 2 2 1

232þ �c�, �c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c2D��

52þi 2 0 2 2 1

252þ 2�

��2Lz

��Sz��0

c

j�0c4D��

12þi 2 0 2 2 3

212þ �c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c4D��

32þi 2 0 2 2 3

232þ 2�

��2Lz

�sSz��0

c

j�0c4D��

52þi 2 0 2 2 3

252þ

j�0c4D��

72þi 2 0 2 2 3

272þ

j�0c2D��

32þi 2 2 0 2 1

232þ �c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�,D�

j�0c2D��

52þi 2 2 0 2 1

252þ 2���

2Lz��Sz��0

c

j�0c4D��

12þi 2 2 0 2 3

212þ �c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�,D�

j�0c4D��

32þi 2 2 0 2 3

232þ 2���

2Lz�sSz��0

c

j�0c4D��

52þi 2 2 0 2 3

252þ

j�0c4D��

72þi 2 2 0 2 3

272þ

j�0c2S��

12þi 2 0 0 0 1

212þ 2�

��00 �

�Sz��0

c�c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c4S��

32þi 2 0 0 0 3

232þ 2�

��00 �

sSz��0

c�c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c2S��

12þi 2 0 0 0 1

212þ 2���

00 ��Sz��0

c�c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

j�0c4S��

32þi 2 0 0 0 3

232þ 2���

00 �sSz��0

c�c�,�c�, �cK, �

0c�, �cK,�

�c�, �

�cK,�cð2790; 2815Þ�

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-4

�m ¼

1ffiffi2

p �0 þ 1ffiffi6

p � �þ Kþ

�� � 1ffiffi2

p �0 þ 1ffiffi6

p � K0

K� �K0 �ffiffi23

q�

0BBBB@

1CCCCA: (7)

To match the nonrelativistic harmonic oscillator spatialwave function N�LLz

in the quark model, we adopt the

nonrelativistic form of Eq. (6) in the calculations, which isgiven by [29–33]

Hnrm ¼ X

j

�!m

Ef þMf

�j � Pf þ !m

Ei þMi

�j � Pi � �j � q

þ !m

2q

�j � p0j

�Ij’m; (8)

where �j is the Pauli spin operator on the jth quark of the

baryon, and q is a reduced mass given by 1=q ¼1=mj þ 1=m0

j with mj and m0j for the masses of the jth

quark in the initial and final baryons, respectively. Foremitting a meson, we have ’m ¼ e�iq�rj , and for absorbinga meson we have ’m ¼ eiq�rj . In the above nonrelativisticexpansions, p0

j ¼ pj �mj=MPc:m: is the internal coordi-

nate for the jth quark in the baryon rest frame. !m and qare the energy and three-vector momentum of the meson,respectively. Pi and Pf stand for the momenta of the initial

final baryons, respectively. The isospin operator Ij in

Eq. (8) is expressed as

Ij¼

8>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>:

ayj ðuÞajðsÞ forKþ;

ayj ðsÞajðuÞ forK�;

ayj ðdÞajðsÞ forK0;

ayj ðsÞajðdÞ for �K0;

ayj ðuÞajðdÞ for��;

ayj ðdÞajðuÞ for�þ;1ffiffi2

p ½ayj ðuÞajðuÞ�ayj ðdÞajðdÞ� for�0;

1ffiffi2

p ½ayj ðuÞajðuÞþayj ðdÞajðdÞ�cos�P

�ayj ðsÞajðsÞsin�P for�;

(9)

where ayj ðu; d; sÞ and ajðu; d; sÞ are the creation and anni-

hilation operators for the u, d, and s quarks, and �P is themixing angle of � meson in the flavor basis [1,34].

For a light pseudoscalar meson emission in the strongdecay process of a baryon, the partial decay amplitudescan be worked out according to the nonrelativisticoperator of quark-meson coupling. The details of howto work out the decay amplitudes can be seen in ourprevious work [21]. The quark model permitted twobody strong decay channels of each charm-strangebaryon have been listed in Tables IV and V as well.With the partial decay amplitudes derived from the

chiral quark model, we can calculate the strong decaywidth by

� ¼��

fm

�2 ðEf þMfÞjqj4�Mið2Ji þ 1Þ

XJiz;Jfz

jMJiz;Jfz j2; (10)

where MJiz;Jfz is the transition amplitude, Jiz and Jfzstand for the third components of the total angularmomenta of the initial and final baryons, respectively.And � as a global parameter accounts for the strengthof the quark-meson couplings. This has been deter-mined in our previous study of the strong decays ofthe charmed baryons and heavy-light mesons [21,22].Here, we fix its value the same as that in Refs. [21,22],i.e., � ¼ 0:557.In the calculation, the standard quark model parameters

are adopted. Namely, we set mu ¼ md ¼ 330 MeV, ms ¼450 MeV, mc ¼ 1700 MeV, and mb ¼ 5000 MeV for theconstituent quark masses. The harmonic oscillator parame-ter � in the wave function N�LLz

is taken as � ¼0:40 GeV. The decay constants for �, K, and � mesonsare taken as f� ¼ 132 MeV, fK ¼ f� ¼ 160 MeV, re-

spectively. The masses of the mesons and baryons usedin the calculations are adopted from the Particle DataGroup [1]. With these parameters, the strong decay prop-erties of the well-known heavy-light mesons and charmedbaryons have been described reasonably [21–24].

IV. RESULTS AND DISCUSSIONS

A. ��cð2645Þ

�0c and ��

cð2645Þ are the two lowest states in the�0

c-type charm-strange baryons. They are assigned to thetwo S-wave states, j�0

c2S12

þi and j�0c4S32

þi, respectively.The decay widths of��

cð2645Þ ! �c� are calculated. Theresults are listed in Table VI, from which we find that ourpredictions are in good agreement with the experimentaldata [1] and compatible with other theoretical results[18,19,35–38].�b and ��

b (�0b and ��

b) are counterparts of �0c and

��cð2645Þ, respectively. Recently, the first measurements

of natural widths of the bottom baryon states ��b and

���b together with the improved measurements of the

masses were reported by the CDF Collaboration [25].Furthermore, a new neutral excited bottom-strange baryonwith a mass m ¼ 5945:0� 0:7� 0:3� 2:7 MeV was ob-served by the CMS Collaboration, which most likely cor-responds to ��0

b with JP ¼ 3=2þ [26]. As a byproduct, we

have calculated the strong decays of the bottom baryons��

b , ���b and ��0

b . Our results together with other model

predictions and experimental data have been listed inTable VII. From the table, it is seen that our predictionsare in good agreement with the measurements [25,26] andthe other model predictions [19,39–42]. It should bepointed out that the strong decay properties of ��

b were

CHARM-STRANGE BARYON STRONG DECAYS IN A . . . PHYSICAL REVIEW D 86, 034024 (2012)

034024-5

studied in Ref. [19,42], where a little larger mass m ’5960 MeV was adopted. With the recent measured massof ��0

b , the predicted decay widths in Ref. [19,42] should

be a little smaller than their previous predictions.

B. �cð2790Þ and �cð2815Þ�cð2790Þ and �cð2815Þ are two relatively well-

determined P-wave charm-strange baryons with quantumnumbers JP ¼ 1=2� and 3=2�, respectively. They wereobserved in the �0

c� and �c�� channels, respectively.The Particle Dada Group suggests they belong to the sameSU(4) multiplet as �cð2593Þ and �cð2625Þ, respectively[1]. According to our previous study, �cð2593Þ and�cð2625Þ can be well explained with the j�2

cP�12�i and

j�2cP�

32�i assignments [21]. Thus,�cð2790Þ and�cð2815Þ

should correspond to the �c-type excited states j�2cP�

12�i

and j�2cP�

32�i, respectively. With these assignments we

have calculated the strong decay properties of �cð2790Þand �cð2815Þ, which are given in Table VI. Our pre-dicted widths are in the range of observations [1] and

compatible with other theoretical predictions [18,19]. Onthe other hand, �cð2790Þ as a dynamically generatedresonance having JP ¼ 1=2� was also discussed inRef. [43].Finally it should be pointed out that �cð2790Þ and

�cð2815Þ cannot be P�-mode excited states j�c2P�

12�i

and j�c2P�

32�i, because these excitations have large par-

tial decay widths into�c� and�þc�K channels (see Fig. 1),

which disagrees with the observations. The strong decayproperties of the P�-mode excitations of �c have been

shown in Fig. 1. We advise experimentalists to search thesemissing P-wave states in �c�, �þ

c�K and ��

cð2645Þ�invariant mass distributions around the energy regionð2:8–2:9Þ GeV.

C. �cð2930Þ�cð2930Þ is not yet confirmed. It was only observed by

BABAR in the �þc�K invariant mass distribution in an

analysis of B� ! �þc���c K

�. The mass analysis of thecharm-strange baryon spectrum indicates that �cð2930Þ

TABLE VII. Decay widths (MeV) of the ground S-wave bottom baryons ��b , �

��b and newly observed ��

bð5945Þ0.Notation Channel � (ours) � [19] � [39] � [40] � [41] � [42] �exp

�bð5811Þþ j�b2S12

þi �0b�

þ 5.9 3.5 6.0 4.35 6.73–13.45 4.82, 4.94 9:7þ5:0�3:9 [25]

�bð5816Þ� j�b2S12

þi �0b�

� 6.7 4.7 7.7 5.77 6.73–13.45 6.31, 6.49 4:9þ4:2�3:2 [25]

��bð5832Þþ j�b

4S32þi �0

b�þ 10.2 7.5 11.0 8.50 10.00–17.74 9.68, 10.06 11:5þ3:7

�3:7 [25]

��bð5835Þ� j�b

4S32þi �0

b�� 11.0 9.2 13.2 10.44 10.00–17.74 11.81, 12.34 7:5þ3:1

�3:2 [25]

��bð5945Þ0 j�0

b4S32

þi �b� 0.6 0.85 . . . . . . . . . 1.83, 1.85 2:1� 1:7 [26]

TABLE VI. Decay widths (MeV) of the well-established charm-strange baryons ��cð2645Þ, �cð2790Þ and �cð2815Þ.

Notation Channel � (ours) �total (ours) �total [19] �total [35] �total [36] �total [37] �total [38] �total [18] �exptotal

��cð2645Þ0 j�0

c4S32

þi �þc �

� 1.55 2.34 1.08 3:12� 0:44 4:2� 1:3 3:03� 0:1 1.88 2:8� 0:2 <5:5�0

c�0 0.79

��cð2645Þþ j�0

c4S32

þi �þc �

0 0.89 2.44 1.13 3:04� 0:50 4:2� 1:3 3:18� 0:1 1.81 2:7� 0:2 <3:1�0

c�þ 1.55

�cð2790Þþ j�c2P�

12�i �0

cþ�0 0.92 2.72 9.9 8:0þ4:7�3:3 <15

�0c0�þ 1.80

��cð2645Þ0�þ 4� 10�5

��cð2645Þþ�0 2� 10�5

�cð2790Þ0 j�c2P�

12�i �0

cþ�� 1.84 2.77 10.3 8:5þ5:0

�3:5 <12�0

c0�0 0.93

��cð2645Þþ�� 4� 10�5

��cð2645Þ0�0 2� 10�5

�cð2815Þþ j�c2P�

32�i �0

c0�þ 0.15 1.50 5.3 1:26� 0:13 7.67 3:4þ2:0

�1:4 <3:5�0þ

c �0 0.08

��cð2645Þ0�þ 0.83

��cð2645Þþ�0 0.44

�cð2815Þ0 j�c2P�

32�i �0

cþ�� 0.17 1.64 5.5 3:6þ2:1

�1:5 <6:5�0

c0�0 0.09

��cð2645Þþ�� 0.87

��cð2645Þ0�0 0.51

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-6

can be assigned to the 1P excitation of �0c or the 2S

excitation of �c (see Tables II and III) [16,17].We have analyzed the strong decay properties of all the

2S excitations of �c and the 1P excitations of �0c, which

have been shown in Figs. 2 and 3, respectively. First, wecan exclude the 2S excitations of �c as assignments to�cð2930Þ for the decay channel �þ

c�K of these states is

forbidden (see Fig. 2). In the 1P excitations of �0c (see

Fig. 3), we have noted that the decay modes�þc�K and�c�

for the P�-mode excited states, j�0c2P�ð1=2�Þi and

j�0c2P�ð3=2�Þi, are forbidden; thus, these states as assign-

ments to �cð2930Þ should be excluded. Furthermore, it isfound that the strong decays of j�0

c2P�ð3=2�Þi and

j�0c4P�ð5=2�Þi are governed by the �c� channel, and

the ��cð2645Þ� decay mode dominates the decay of

j�0c4P�ð3=2�Þi. They might be hard observed by BABAR

for their rather small �þc�K branching ratios.

Given the decay modes and decay widths, two JP ¼1=2� states j�0

c4P�ð1=2�Þi and j�0

c2P�ð1=2�Þi seem to be

the possible assignments to �cð2930Þ. Considering�cð2930Þ as the j�0

c2P�ð1=2�Þi, from Fig. 3 we find that

its decays are dominated by �þc�K and �0

c�, and the otherpartial decay widths are negligibly small. Its total widthand the partial decay width ratio between �þ

c�K and

�0c� are

� ¼ 10:6 MeV;�ð�þ

c�KÞ

�ð�0c�Þ 1:1: (11)

On the other hand, if considering �cð2930Þ as thej�0

c4P�ð1=2�Þi, we see that the �þ

c�K governs the decays,

and the other two decay channels �c� and �0c� have

sizeable widths as well. The calculated total width andpartial decay width ratios are

� ¼ 16:7 MeV;�ð�þ

c�KÞ

�ð�c�Þ 2:8;�ð�þ

c�KÞ

�ð�0c�Þ 4:6:

(12)

As a whole, �cð2930Þ is most likely to be the 1Pexcitation of �0

c with JP ¼ 1=2�, and favorsj�0

c4P�1=2

�i or j�0c2P�1=2

�i. To confirm �cð2930Þ, fur-ther observations in the �0

c�, �c�, �þc�K invariant mass

distributions and measurements of these partial decay ra-tios are very crucial in experiments.

D. �cð2980Þ�cð2980Þ with a width of �40 MeV was first found by

the Belle Collaboration in the �þc�K� channel, and then

confirmed by BABAR with large significances in both theintermediate resonant �cð2455Þ �K and nonresonant �þ

c�K�

decay channels. Belle also observed a resonance structurearound 2.97 GeV with a narrower width of �18 MeV inthe ��

cð2645Þ� decay channel in a separate study [5],which is often considered as the same state of �cð2980Þ.It should be pointed out that BABAR and Belle had ana-lyzed the �þ

c�K and �c� invariant mass distributions,

respectively, but they did not find any structures around2.98 GeV, which indicates that these partial decay widthsare too small to be observed or these decay modes areforbidden. Although �cð2980Þ is well established in ex-periments, its quantum numbers are still unknown.Recently, Ebert et al. calculated the mass spectra of heavybaryons in the heavy-quark-light-diquark picture in theframework of the QCD-motivated relativistic quark model;they suggested �cð2980Þ could be assigned to the 2S

0

10

20

30

40

2820 2880 2940

0

20

40

60

802820 2880 2940

0

10

20

30

2Pρ(1/2)- 2P

ρ(3/2)-

4Pρ(1/2)-

4Pρ(3/2)-

Mass(MeV)

Γ(M

eV)

Γ(M

eV)

Γ(M

eV)

4Pρ(5/2)-

total Λ

cK

Ξcπ

Ξc(2645)π

ΣcK

FIG. 1 (color online). Strong decay properties of the P�-modeexcitations of �c.

FIG. 2 (color online). Strong decay properties of the first radial(2S) excitations of �c and �0

c.

CHARM-STRANGE BARYON STRONG DECAYS IN A . . . PHYSICAL REVIEW D 86, 034024 (2012)

034024-7

excitation of �0c with JP ¼ 1=2þ [16], which also agrees

with their early mass analysis [17]. Cheng et al. alsodiscussed the possible classification of �cð2980Þ. Theyconsidered that �cð2980Þ might be the 2S excitation of�c with JP ¼ 1=2þ [18].

We have analyzed the strong decay properties of the 2Sexcitations of both �c and �0

c, which have been shown inFig. 2. From the figure, it is seen that the 2S excitations ofboth �c and �0

c have narrow decay widths (< 2 MeV),which are at least an order smaller than those of�cð2980Þ.Furthermore, the decay modes of these first radial excita-tions are in disagreement with the observations of�cð2980Þ. Thus, the 2S excitations of both �c and �0

c

are excluded as assignments to �cð2980Þ in the presentwork. Our conclusion is in agreement with that of 3P0

calculations [19].�cð2980Þmight be one of the orbital excitations of�c in

theN ¼ 2 shell since the masses of these states are close to2980 MeV. Their calculated partial decay widths and totalwidths are shown in Fig. 4. It is seen that the 2SAð1=2þÞ,4SAð3=2þÞ, PAð1=2þ; 3=2þ; 5=2þÞ, DAð5=2þ; 7=2þÞ,D��ð3=2þ; 5=2þÞ, and D��ð3=2þ; 5=2þÞ states have too

narrow decay widths to compare with the observations of�cð2980Þ. Furthermore, although the decay widths ofDAð1=2þ; 3=2þÞ are compatible with the measurement,their decay modes are dominated by�þ

c�K and�c�, which

disagrees with the observations as well. As a whole, all thestates shown in Fig. 4 are not good assignments to�cð2980Þ; either their decay widths are too narrow tocompare with the observations or their decay modes dis-agree with the observations.

The P�-mode excitations j�0c2P�ð1=2�Þi and

j�0c2P�ð3=2�Þi could be candidates of �cð2980Þ (see

Fig. 3). We have noted that excitation of the � variable is

different from excitation of the � variable for a baryoncontaining a heavy quark. The P�-mode excitation of

charm-strange baryon is �70 MeV heavier than the P�

mode [44,45]. According to our analysis in Sec. IVC,�cð2930Þ might be assigned to a P�-mode excitation of�0

c. Thus, the expected mass of the P�-mode excitation is

�3:0 GeV, which is comparable with that of�cð2980Þ. Asthe j�0

c2P�ð1=2�Þi and j�0

c2P�ð3=2�Þi candidates, respec-

tively, the partial decay widths and total width of�cð2980Þhave been given in Table VIII. If the resonance structurearound 2.97 GeV observed in the ��

cð2645Þ� decay chan-nel is the same state observed in the�þ

c�K� decay channel,

�cð2980Þ is most likely to be the JP ¼ 1=2� excited statej�0

c2P�ð1=2�Þi. The reasons are as follows: (i) The decay

modes of j�0c2P�ð1=2�Þi are in agreement with the obser-

vations. From Table VIII, we see that the strong decays ofj�0

c2P�ð1=2�Þi are dominated by �c

�K, and the partial

decay width of ��cð2645Þ� is sizeable as well. The

�þc�K� final state mainly comes from a intermediate

process in �cð2980Þ ! �c�K ! �þ

c�K�. (ii) The total de-

cay width

� ’ 44 MeV (13)

is in good agreement with the data. (iii) The decay chan-nels �c�, �

þc�K and ��

cð2520Þ �K of j�0c2P�ð1=2�Þi are

forbidden, which can naturally explain why these decaychannels were not observed by Belle and BABAR. It shouldbe mentioned that the same JP quantum number (i.e., JP ¼1=2�) for �cð2980Þ is also suggested in Ref. [43], wherethe �cð2980Þ is considered as a dynamically generatedresonance.We have noted that the total width of �cð2980Þ mea-

sured by Belle and BABAR in the �þc�K� channel is about

0

20

40

60

80

2880 2960 3040

2880 2960 3040

0

10

20

30

40

2880 2960 30402880 2960 3040

2Pρ(1/2-)

Γ (M

eV)

2Pρ(3/2-)

2Pλ(3/2-)

4Pλ(5/2-)

Mass (MeV)

2Pλ(1/2-)

Γ(M

eV)

Ξc(2815)π

Ξc(2790)π

4Pλ(1/2-) 4P

λ(3/2-)

Total Ξ

cπ

Ξc’ π

Ξc(2645)π

ΣcΚ

ΛcΚ

FIG. 3 (color online). Strong decay properties of the first orbital (1P) excitations of �0c.

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-8

two times larger than that measured by Belle in the��

cð2645Þ� decay channel in a separate study. Thus, theresonance with a mass m ’ 2970 MeV [denoted by�cð2970Þ in this work] observed in the ��

cð2645Þ� decaychannel might be a different resonance from the �cð2980Þobserved in the �þ

c�K� channel, although they have com-

parable masses. According to our analysis, the �cð2970Þobserved in the ��

cð2645Þ� channel and �cð2980Þ ob-served in the �þ

c�K� channel might be assigned to the

j�0c2P�ð1=2�Þi and j�0

c2P�ð3=2�Þi excitations, respec-

tively. If the j�0c2P�ð3=2�Þi is considered as the

�cð2970Þ observed in the ��cð2645Þ� channel, its total

decay width

� ’ 16 MeV (14)

and dominant decay channel��cð2645Þ� are in good agree-

ment with the observations (see Table VIII). Furthermore,it is interestingly found that when the j�0

c2P�ð1=2�Þi and

j�0c2P�ð3=2�Þi excitations are considered as the reso-

nances observed in the �þc�K� and ��

cð2645Þ�, respec-tively, we can naturally explain why the width measured in

FIG. 4 (color online). Strong decay properties of the N ¼ 2 shell orbital excitations of �c. Some decay channels, such as �c�,�cð2790; 2815Þ�, are not shown in the figure for their small partial decay widths.

TABLE VIII. Partial decay widths and total width (MeV) for�cð2980Þ as the 2P�ð1=2�Þ and 2P�ð3=2�Þ excitations of �0

c,

respectively.

�c�K ��

cð2645Þ� �0c� total

j�0c2P�ð1=2�Þi 37 3 4 44

j�0c2P�ð3=2�Þi 0.1 12 4 16

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the �cð2645Þ�� channel is about a factor 2 smaller thanthat measured in the �þ

c�K� channel.

In brief, the �cð2970Þ observed in the ��cð2645Þ� final

state is most likely a different state from the �cð2980Þobserved in the �þ

c�K� final state. The �cð2980Þ and

�cð2970Þ, as two largely overlapping resonances, com-monly classified as the j�0

c2P�1=2

�i and j�0c2P�3=2

�i,respectively. Of course, for the uncertainties of the data wecannot exclude the �cð2970Þ and �cð2980Þ as the sameresonance, which is commonly assigned to thej�0

c2P�1=2

�i. To finally clarify whether the �cð2970Þobserved in ��

cð2645Þ� is the same resonance observedin the�þ

c�K� channel or not, we expect experimentalists to

measure the partial width ratio �½��cð2645Þ��:�ð�c

�KÞfurther. If there is only one resonance assigned toj�0

c2P�1=2

�i, the ratio �½��cð2645Þ��:�ð�c

�KÞ might

be �0:08. Otherwise, if the �cð2980Þ and �cð2970Þcorresponds to overlapping resonances j�0

c2P�1=2

�iand j�0

c2P�3=2

�i, respectively, the ratio might be

�½��cð2645Þ��:�ð�c

�KÞ’0:41.

E. �cð3080Þ�cð3080Þþ and its isospin partner state �cð3080Þ0 were

first observed by Belle in the�þc K

��þ and�þc�K0�� final

state, respectively. The existence of �cð3080Þþ;0 has beenconfirmed by the BABAR Collaboration. Furthermore,BABAR’s analysis shows that most of the decay of�cð3080Þþ proceeds through the intermediate resonantmodes �cð2455ÞþþK� and �cð2520ÞþþK� with roughlyequal branching fractions.

Although�cð3080Þ has been established in experiments,its quantum is still unclear. Recently, Ebert et al. suggested�cð3080Þ might be classified as the 1D excitation of �c

with JP ¼ 5=2þ according to their mass calculations in theQCD-motivated relativistic quark model [16]. Cheng et al.discussed the possible classification of �cð3080Þ as well.They suggested that �cð3080Þ might be the 1D excitationof �c with JP ¼ 3=2þ or JP ¼ 5=2þ [18]. More possibleassignments to the�cð3080Þwere suggested by Chen et al.in their 3P0 strong decay analysis [19].

BABAR’s observations provide us two very importantconstraints on the assignments to �cð3080Þ: (i) the strongdecay is governed by both�cð2455Þ �K and�cð2520Þ �K, and(ii) the partial width ratio �ð�cð2455Þ �KÞ=�ð�cð2520Þ �KÞ ’1. We analyzed the strong decay properties of all theN ¼ 2shell excitations of both �c and �0

c, which were shown inFigs. 2–5. From the figures we find that only the 2Sexcitation j�c

2S��1=2þi satisfies the two constraints of

BABAR’s observations at the same time: (i) At m ’3:08 GeV the strong decays of j�c

2S��1=2þi are domi-

nated by �cð2455Þ �K and �cð2520Þ �K; the partial other twodecay modes ��

cð2645Þ� and �0c� only contribute a very

small partial width to the decay. (ii) The predicted partialwidth ratio between �cð2455Þ �K and �cð2520Þ �K is

�½�cð2455Þ �K��½�cð2520Þ �K�

’ 0:8: (15)

Furthermore, if the j�c2S��1=2

þi is considered as an

assignment to �cð3080Þ, the predicted total width

� ’ 4 MeV (16)

is also in good agreement with the measurements.Finally, it should be pointed out that as a candidate of

�cð3080Þ, the mass of j�c2S��1=2

þi consists with the

quark model expectations as well. According to our analy-sis in Sec. IVD, the�cð2980Þ (observed in the�þ

c�K� final

state) and�cð2930Þ could be assigned to P�- and P�-mode

excitations of �0c, respectively. The estimated mass split-

ting between P�- and P�-mode excitation in the N ¼ 1

shell is

�M’ℏ!��ℏ!�’ð2980�2930ÞMeV¼50MeV: (17)

With the above relation, we can estimate the mass splittingbetween S�� and S�� excitations in theN ¼ 2 shell, which is

MðS��Þ �MðS��Þ ’ 2ℏ!� � 2ℏ!� ’ 100 MeV: (18)

In most of the quark models, the predicted masses for theS�� excitation of �c are in the range of ð2:92–2:99Þ GeV(see Table II); thus, the mass of S�� excitation of�c should

be in the range of ð3:02–3:09Þ GeV, which is comparablewith the mass of �cð3080Þ.As a whole, the mass, decay modes, partial width ratio

�ð�cð2455Þ �KÞ:�ð�cð2520Þ �KÞ, and total decay width ofj�c

2S��1=2þi strongly support j�c

2S��1=2þi is assigned

to �cð3080Þ.

F. �cð3055Þþ�cð3055Þþ as a new structure was observed by BABAR

in the �þc�K� mass distribution with a statistical signifi-

cance of 6:4�. It decays through the intermediate resonantmode �cð2455ÞþþK�. BABAR also searched the inclusive�þ

c�K and �þ

c�K�� invariant mass spectra for evidence of

�cð3055Þþ, but no significant structure was found. Thisstate has not yet been confirmed by Belle. According to thecalculations of the charm-strange baryon spectrum in vari-ous quark models, �cð3055Þ might be assigned to the 1Dexcitation of �c (see Table II).We have analyzed the strong decay properties of the

second orbital excitations of �c, which have been shownin Fig. 4. From the figure, we find that the PAð1=2þ;3=2; 5=2þÞ excitations can be easily excluded as the candi-dates of�cð3055Þþ because neither their decay modes northeir decay widths concur with the observations.Furthermore, from Fig. 4 it is seen that the �þ

c�K is one of

the main decay modes of 4DAð1=2þ; 3=2; 7=2þÞ and2DAð3=2þ; 5=2þÞ; if the �cð2455ÞþþK� decay mode forthese states is observed in experiments, the �þ

c�K decay

mode should be observed as well, which disagrees with the

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-10

observations of BABAR. Thus, these states as assignmentsto �cð3055Þþ should be excluded. The strong decays of4DAð5=2þÞ, 2D��ð5=2þÞ, and 2D��ð5=2þÞ are dominated

by ��cð2645Þ� and �cð2520Þ �K; the partial width of

�cð2455Þ �K is negligibly small; thus, these states couldnot be considered as candidates of �cð3055Þþ as well.

Finally, we find that only two JP ¼ 3=2þ states,j�c

2D��3=2þi and j�c

2D��3=2þi, might be candidates

of �cð3055Þ. The partial decay widths and total width of�cð3055Þ as the j�c

2D��3=2þi and j�c

2D��3=2þi candi-

dates have been listed in Table IX, respectively. From thetable it is seen that the total widths of both states arecompatible with the measurement of �cð3055Þ within itsuncertainties. The strong decays of both states are domi-nated by �cð2455Þ �K and the partial width of �cð2520Þ �Kis negligibly small, which can explain why BABARonly observed the intermediate resonant decay mode

�cð2455ÞþþK� for �cð3055Þ. The �þc�K decay mode is

forbidden for both j�c2D��3=2

þi and j�c2D��3=2

þi,which agrees with the observation that no structureswere found around Mð�þ

c�KÞ ’ 3:05 GeV. As a whole,

�cð3055Þ could be assigned to the 1D excitations of �c

with JP ¼ 3=2þ; our conclusion is in agreement with thatof Ebert et al. according to their mass analysis. However, itis difficult to determine which one can be assigned to�cð3055Þþ in the j�c

2D��3=2þi and j�c

2D��3=2þi

FIG. 5 (color online). Strong decay properties of the N ¼ 2 shell orbital excitations of �0c. Some decay channels, such as �c�,

�cð2790; 2815Þ�, are not shown in the figure for their too narrow partial decay widths to compare with the others’.

TABLE IX. Partial decay widths and total width (MeV) for�cð3055Þ as the 2D��ð3=2þÞ and 2D��ð3=2þÞ excitations of �c,

respectively.

�c�K ��

cð2645Þ� �0c� ��

c�K D� total

j�c2D��ð3=2þÞi 2.3 0.5 1.0 0.1 0.1 4.0

j�c2D��ð3=2þÞi 5.6 0.8 3.3 0.3 - 10.0

CHARM-STRANGE BARYON STRONG DECAYS IN A . . . PHYSICAL REVIEW D 86, 034024 (2012)

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candidates only depending on the strong decay properties.We have noted that �cð3080Þ is most likely to be the�cS�� assignment. According to various quark model

predictions, the mass of the second orbital excitation�cD�� should be larger than that of the first radial excita-

tion�cS��, which indicates that the mass of�cD�� might

be larger than 3.08 GeV. From this point of view, thej�c

2D��3=2þi as an assignment to �cð3055Þþ should be

excluded. Thus, the�cð3055Þ is most likely to be classifiedas the j�c

2D��3=2þi excitation.

G. �cð3123Þþ�cð3123Þþ is another new narrow structure observed

by BABAR in the �þc�K� final state only with a weak

statistical significance 3:0�. It decays through a intermedi-ate resonant process in �cð3123Þþ ! �cð2520ÞþþK� !�þ

c K��þ. BABAR also searched �cð3123Þþ in the �þ

c�K

and�þc�K�� final states further; however, they did not find

any evidence in these channels. �cð3123Þþ has not yetbeen confirmed by Belle.

From Table II, it is seen that the predicted masses ofthe 1D excitations of �0

c in various quark models areð3:12–3:17Þ GeV. Thus, the 1D excitations of �0

c mightbe candidates of �cð3123Þþ. We have analyzed the strongdecay properties of these excitations, which have beenshown in Fig. 5.

In these 1D excitations of �0c, we can first excluded the

2D��ð3=2þÞ, 4D��ð1=2þÞ, 2D��ð3=2þÞ, 2D��ð5=2þÞ,4D��ð1=2þÞ, and 4D��ð7=2þÞ as assignments to�cð3123Þþ for their partial width of �cð2520Þ �K is negli-gibly small compared with that of �cð2455Þ �K or �þ

c�K.

Furthermore, we do not consider the 2D��ð5=2þÞ,4D��ð3=2þÞ, and 4D��ð7=2þÞ as good candidates of

�cð3123Þþ although the �cð2520Þ �K is their dominantdecay channel. The reason is that the �þ

c�K has a large

partial width which should be observed by BABAR; how-ever, this decay mode was not observed yet.

Finally, only three excitations j�0c4D��ð3=2þÞi,j�0

c4D��ð5=2þÞi, and j�0

c4D��ð5=2þÞimight be candidates

of�cð3123Þþ. They decay mainly through�cð2520Þ �K witha narrow decay width, which is consistent with the obser-vations of�cð3123Þþ. To clearly see the decay properties ofj�0

c4D��ð3=2þÞi, j�0

c4D��ð5=2þÞi, and j�0

c4D��ð5=2þÞi,

as candidates of �cð3123Þþ their partial decay widths andtotal width have been listed in Table X.

According to our analysis in Sec. IV F,�cð3055Þ is mostlikely to be the j�c

2D��3=2þi excitation. We have noted

that the quark model predicted mass of �0cD�� is typically

�100 MeV heavier than that of �cD��. Thus, when thej�0

c4D��3=2

þi or j�0c4D��5=2

þi excitation is assigned to�cð3123Þ, the quark model predicted mass �3:15 GeV iscompatible with the observation. With the relation ofðℏ!� � ℏ!�Þ ’ 50 MeV in Eq. (17), we can further esti-

mate the mass splitting between D�� and D�� excitations

in the N ¼ 2 shell, which is

MðD��Þ�MðD��Þ’2ℏ!��2ℏ!�’100MeV: (19)

Thus, the estimated mass of j�0c4D��5=2

þi is�3:25 GeV.

Obviously, the j�0c4D��5=2

þi could not be considered as agood assignment to �cð3123Þ.It should be pointed out that in the 1D excitations of�c,

the D�� excitation j�c2D��5=2

þi might be an assignment

to�cð3123Þ as well. According to Eq. (19) the mass of the� variable excitation D�� is about 100 MeV heavier than

the D�� excitation. In Sec. IX, we have predicted that�cð3055Þ is most likely to be the j�c

2D��3=2þi excita-

tion; thus, the estimated masses for j�c2D��5=2

þi might

be �3:15 GeV, which are close to the mass of �cð3123Þ.Its partial decay widths and total width have been listed inTable X. From the table it is seen that both the decay modesand total width of j�c

2D��5=2þi are compatible with the

observations of �cð3123Þ.As a conclusion, for the scarce experimental information,

we cannot determine the JP numbers of�cð3123Þ. Given themass, decay mode, and total width observed in experiment,�cð3123Þ could be assigned to the 1D excitationj�0

c4D��3=2

þi, j�0c4D��5=2

þi, or j�c2D��5=2

þi. Sincethe j�0

c4D��3=2

þi, j�0c4D��5=2

þi, and j�c2D��5=2

þihave a comparable mass, the �cð3123Þ structure might cor-respond to several highly overlapping states around 3.1 GeV.From Table X, it is seen that the partial decay width ratios�ð�c

�KÞ:�ð��c�KÞ, �ð��

c2645�Þ:�ð��c�KÞ, and �ð�c�Þ:

�ð��c�KÞ for these possible assignments to �cð3123Þ are

very different; thus, the measurements of these ratios areimportant to understanding the nature of �cð3123Þ.

V. SUMMARY

In the chiral quark model framework, the strong decaysof charm-strange baryons are studied. As a byproduct we

TABLE X. Partial decay widths and total width (MeV) for �cð3123Þ as the �0c4D��ð3=2þÞ, �0

c4D��ð5=2þÞ, �0

c4D��ð5=2þÞ, and

�c2D��ð5=2þÞ excitations, respectively.

�c�K ��

cð2645Þ� �c� ��c�K �c

�K �0c� �cð2815Þ� �cð2790Þ� D� total �ð�c

�KÞ�ð��

c�KÞ

�ð��cð2645Þ�Þ�ð��

c�KÞ

�ð�c�Þ�ð��

c�KÞ

j�0c4D��ð3=2þÞi 1.2 1.0 0.9 2.6 0.9 0.4 0.9 0.4 1.2 10.5 0.46 0.38 0.35

j�0c4D��ð5=2þÞi 0.07 2.6 1.1 2.9 0.6 0.1 0.1 0.05 0.09 7.8 0.02 0.90 0.38

j�0c4D��ð5=2þÞi 0.1 4.3 1.5 6.3 0.7 0.2 0 0 0 13.0 0.01 0.68 0.24

j�c2D��ð5=2þÞi 0.8 4.5 0 4.8 0 1.5 0 0 0 11.6 0.17 0.94 0

LEI-HUA LIU, LI-YE XIAO, AND XIAN-HUI ZHONG PHYSICAL REVIEW D 86, 034024 (2012)

034024-12

also calculate the strong decays of the S-wave bottombaryons ��

b , ���b , �0

b, and ��b. We obtain good descrip-

tions of the strong decay properties of the well-determinedcharm-strange baryons ��ð2645Þ, �ð2790Þ, and �ð2815Þ.Furthermore, the calculated strong decay widths of ��

b ,

���b , and ��

b are in good agreement with the recent

measurements.�cð2930Þ, if it could be confirmed in experiments, might

be a 1P excitation of �0c with JP ¼ 1=2�. j�0

c2P�1=2

�iand j�0

c4P�1=2

�i could be candidates of�cð2930Þ accord-ing to the present data. Further observations in the �0

c�,�c�, �

þc�K invariant mass distributions and measurements

of these partial decay ratios are very crucial to uncoveringthe nature of �cð2930Þ.

�cð2980Þ might correspond to two different 1P excita-tions of �0

c: one resonance is the broader (� ’ 44 MeV)excitation j�0

c2P�1=2

�i, which was observed in the

�þc�K� final state by BABAR and Belle, and the other

resonance is the narrower (� ’ 16 MeV) excitationj�0

c2P�3=2

�i, which was observed in the ��cð2645Þ�

channel by Belle in a separate study. If the structuresobserved in the �þ

c�K� and ��

cð2645Þ� final states corre-spond to the same resonance �cð2980Þ, which could onlybe assigned to the j�0

c2P�1=2

�i excitation. To finally

clarify whether the �cð2970Þ observed in ��cð2645Þ� is

the same resonance observed in the �þc�K� channel or not,

we expect experimentalists to measure the partial widthratio �½��

cð2645Þ��:�ð�c�KÞ further.

�cð3080Þ could be identified as the 2S excitationj�c

2S��1=2þi. The width, decay modes, and ratio

�ð�cð2455Þ �KÞ=�ð�cð2520Þ �KÞ ’ 0:8 are in good agree-ment with the observations. As a assignment to�cð3080Þ, the mass of j�c

2S��1=2þi is also consistent

with the quark model expectations.

Given the mass, decay modes, and decay width,�cð3055Þ is most likely to be classified as the 1D excita-tion j�c

2D��3=2þi. To confirm it in experiments, more

observations in the �c�K, �0

c�, and ��cð2645Þ� channels

are needed.�cð3123Þ is most likely to be the 1D excitations of

the charm-strange baryon with JP ¼ 3=2þ or 5=2þ. It couldbe assigned to the �0

c excitation j�0c4D��3=2

þi orj�0

c4D��5=2

þi. For the scarce experiment informationabout �cð3123Þ, we cannot exclude it as the assignment tothe�c excitation j�c

2D��5=2þi. Since the j�0

c4D��3=2

þi,j�0

c4D��5=2

þi, and j�c2D��5=2

þi have a comparable

mass, the �cð3123Þ structure might correspond to severallargely overlapping resonances. For a good understanding of�cð3123Þ structure, further observations in the ��

cð2645Þ�,��

c�K and �c� channels are expected.Finally, according to our predictions we can establish a

spectroscopy for the observed charm-strange baryons,which is summarized in Fig. 6. We also estimate the massesof the charm-strange baryons with different variable (� or�) excitation from these newly observed states in experi-ments, which are given in Fig. 6. These missing statesmight be found in future experiments. To provide helpfulinformation for the search for the missing charm-strangebaryons, in Figs. 1–5 our predictions of their strong decayproperties have been shown as well.

ACKNOWLEDGMENTS

This work is supported, in part, by the National NaturalScience Foundation of China (11075051), Program forChangjiang Scholars and Innovative Research Team inUniversity (IRT0964), the Program Excellent TalentHunan Normal University, and the Hunan ProvincialNatural Science Foundation (11JJ7001).

2.4

2.6

2.8

3.0

3.2

3.4

Ξc*(2645)

Ξc’

Ξc’(3123)?

Ξc’(3123)?

Ξc(3123)?

Ξc(3055)

Ξc(3080)

Ξc’(2970)?Ξ

c’(2980)

Ξc’(2930)

Ξc(2815)

JP value

1/2+

1/2+1/2-3/2+

1/2+ 5/2+3/2+5/2+3/2+3/2-

1/2-1/2+

mas

s (G

eV)

3/2-

1S 2S 1D1P

Ξc(2790)

Ξc

FIG. 6 (color online). Charm-strange baryon spectrum up to N ¼ 2 shell according to our predictions. In 1P, 2S, and 1D excitations,there are two lines for each JP value, which correspond to the masses of the excitations of the � variable (upper line) and � variable(lower line), respectively. The mass gap between the � variable excitation and the � variable excitation is assumed to be 50 MeV forthe 1P states, and 100 MeV for the 2S and 1D states. The thin lines stand for the states unobserved in experiments. In the 1P (1D)excitations, the fist two JP values are for the excitations of �c, while the last two JP values are for the excitations of �0

c. In 2Sexcitations, the fist JP value is for the excitations of �c, while the second JP value is for the excitations of �0

c.

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