1. Quantum Numbers of Charmed Baryons
Hai-Yang Cheng (鄭海揚)
Academia Sinica, Taipei
c states
c states
c(’) states
c states
UCAS, June 21, 2017

2. Spectroscopy In SU(3) representation, diquark = 33 = 3+6
3: c+, c+, c all decay weakly
6: c0, ’+c, ’0c, c++,+,0 only c0 decays weakly
c*0, *+c, *0c, c*++,+,0 (JP = 3/2+)
Sl= Sl=1
Many excited states observed:
Orbitally excited p-wave states: Ll=1
e.g. c(2595), c(2625), c(2790), c(2815),… etc. (CLEO)
Positive parity excitations: Ll=2,1,0
e.g. c(2880) with JP =5/2+ (Belle ’06) 2

3. Charmed baryon states c c c c ’c(3123) c(3080) c(3055)
3/2-
’c(2930)
c(2880)
5/2+
c(2860)
3/2+
c(2815)
3/2- (1P)
c(2800)
c(2790)
1/2- (1P)
c(2765)
c(2770)
3/2+
c(2765)
c(2695)
1/2+
’c(2645)
3/2+
c(2625)
3/2- (1P)
c(2595)
1/2- (1P)
’c(2575)
1/2+
c(2520)
3/2+
c(2470)
1/2+
c(2455)
1/2+
c(2287)
1/2+
c c c c

4. 03/14/2017 c(2695) & c* don’t have strong decays
3050
3066
3000
3090
3119
03/14/2017
c(2695) & c* don’t have strong decays
5 narrow excited c states decaying into c(’)K

5. Agaev, Azizi, Sundu [ ]
H. Chen, Mao, W. Chen, Hosaka, Liu, Zhu [ ]
Karliner, Rosner [ ]
Yang, Ping [ ] pentaquark
K. Wang, Xiao, Zhong, Zhao [ ]
W. Wang, R. Zhu [ ]
Padmanath, Mathur [ ]
Cheng, Chiang [ ]
Huang, Ping, F. Wang [ ] pentaquark
Z.G. Wang [ ]
B. Chen, Liu [ ]
Z. Zhao, Ye, Zhang [ ]
Aliev, Bilmis, Savci [ ]
Kim, Polyakov, Praszalowicz [ ]
Agaev, Azizi, Sundu [ ]
An, H. Chen [ ] pentaquark

6. Orbitally excited charmed baryon states
L½+L¸ = Ll (not L½+L¸= Ll !)
Two possible p-wave states (L+L=1):
 state L½=1, L¸=0; antisymmetric under q1q2
 state L½=0, L¸=1; symmetric under q1q2
Jl = Sl+Ll, J = Sc+Jl
In HQ limit, Jl & Sc are separately conserved
Seven lowest-lying p-wave c states denoted by
symmetric
antisymmetric
(denoted by a tilde)

7. Assume Sl=1 (axial-vector diquark) for sextet, we have 5 P-wave
c states.
Many have assumed that the observed 5 narrow c baryons can be assigned to 5 P-wave states. We argue that it cannot be the case.
In the presence of spin-orbital interaction Sc L & tensor interaction, states with same J but different Jl will mix together
Chen, Liu

8. Masses in MeV
nL, JP
Ebert
Shah
B. Chen
T.W. Chiu
Agaev
Expt
1S,1/2+
2698
2695
2696
269528
2685123
2695.22.0
2S,1/2+
3088
3100
3185
3075142
(3090)
1S,3/2+
2768
2767
2764
278125
276989
2765.92.0
2S,3/2+
3123
3126
3226
3119108
(3119)
(1P,1/2-)l
2966
3011
2975
301545
2990129
(3000)
(1P,1/2-)h
3055
3028
3063
(1P,3/2-)l
3029
2976
3066
(1P,3/2-)h
3054
2993
3120
3056103
(3050)
1P, 5/2-
3051
2947
3057
(3066) JP
State
Lattice
PDG 0+
Ds0*(2317)
2317155
2317.70.6
1’+
D’s1(2460)
2463139
2459.60.6 1+
Ds1(2536)
2536124
0.06
We take relativistic quark model results of Ebert, Faustov, Galkin (’11) as a benchmark.
Yu-Chih Chen, Ting-Wai Chiu (’17) based on Nf =2+1+1 optimal domain wall fermion with m =280 MeV

9. Agaev H. Chen Karliner (i) (ii) Padmanath K. Wang W. Wang c(3000)
1/2-
1/ /2-
c(3050)
3/2-
c(3066)
1/2+
1/2+ or 1/2-
3/ /2-
c(3090)
3/ /2+
5/2-
c(3119)
3/2+
5/ /2+
1/2+ or 3/2+
Cheng
Huang
Z. Wang
Zhang
B. Chen
Aliev
c(3000)
1/2-
1/2+ or 3/2+
c(3050)
3/2-
5/2+ or 7/2+
5/2-
c(3066)
3/2- or 5/2-
c(3090)
1/2+
c(3119)
3/2+

10. An ideal place for testing heavy quark symmetry and chiral symmetry: heavy hadron chiral perturbation theory (HHChPT)
Yan, Cheng, Cheung, Lin, Lin, Yu; Wise; Burdman, Donoghue (’92)
Strong decays of S-wave charmed baryons are governed by two couplings g1 & g2. While info on g1 is absent due to the lack of c*→ c , g2 can be fixed by the measured rate of c++ c++

11. Isospin relation c00 = ½ c+- adapted by PDG is strongly violated
s-wave (d-wave) transitions between P-wave and S-wave baryons are described by six couplings h2,…,h7 (eight couplings h8,…,h15)
Pirjol, Yan (’97)
In principle, h2 can be determined from c(2593)c. However, m(c++) + m(-) = MeV, m(c0)+m(+) = MeV, thus strong decays of c(2593) are very close to threshold and very sensitive to the pion mass difference, m() – m(0) = 4.6 MeV  important threshold effects on c(2593) mass and coupling
Isospin relation c00 = ½ c+- adapted by PDG is strongly violated
Blechman, Falk, Pirjol, Yelton (’03)
Previous fit  h2 =
Chua, HYC (’06)
CDF (’11) has measured decays of c(2593) to c+-
and obtained m[c(2593)] =  0.28 MeV, h2 = 0.600.07

12. Strong decays of p-wave charmed baryons
h8=h10
h10
8.91.0
10.01.1
h2 = 0.600.07, h10  ( )10-3 MeV-1
(c00)  4.5 (c+- )
Predicted too large rates for c(2790)0 & c(2815)+ 12

13. P-wave c states decay into ¥cK or ¥’cK in s- or d-wave transition
Using quark model relation h3=2 h2 & assuming mass 3000 MeV
¡ (c0)= MeV for h2 = 0.437
811 MeV for h2 = 0.60
1400 MeV by Zhao, Ye, Zhang
420 MeV by H.X. Chen et al. using QCD sum rules
35 MeV by B. Chen, Liu using Eichten, Hill, Quigg decay formula
32 MeV by Wang et al. based on chiral quark model

14. The other state (1P,1/2-)h must be too broad to be seen!
With width of 410 MeV for c0 and the data of 4.5 0.7 MeV for c(3000), the mixing angle is constrained to be 96o or 84o (111o by B. Chen & Liu, 24o or 47o by K. Wang et al.)
c1(1/2-) is prohibited to decay into cK in HQ limit
The other state (1P,1/2-)h must be too broad to be seen!
Using h10=( )10-3 extracted from measured width of Sc(2800), we obtain
Expt
¡(c(3050))= sin2µ2( ) MeV, (0.80.20.1) MeV
¡(c(3066))= ( ) MeV, (3.50.40.2) MeV
 sin2 ¼ 160o, predicted width for c(3066) is too large by a factor of 4

15. The state (1P,1/2-)h is too broad to be seen!
Agaev
H. Chen
Karliner
(i) (ii)
Padmanath
K. Wang
W. Wang
c(3000)
1/2-
1/ /2-
c(3050)
3/2-
c(3066)
1/2+
1/2+ or 1/2-
3/ /2-
c(3090)
3/ /2+
5/2-
c(3119)
3/2+
5/ /2+
1/2+ or 3/2+
Cheng
Huang
Z. Wang
Zhang
B. Chen
Aliev
c(3000)
1/2-
1/2+ or 3/2+
c(3050)
3/2-
5/2+ or 7/2+
5/2-
c(3066)
3/2- or 5/2-
c(3090)
1/2+
c(3119)
3/2+

16. Decay widths in MeV LHCb Agaev K. Wang B. Chen Zhang Cheng c(3000)
4.5 0.7
4.71.2
constraint on 1
5.0
constraint
on 1
c(3050)
0.80.2
0.60.2
0.94
2.7
0.2
on 2
c(3066)
3.50.4
6.41.7
4.96
3.3
8.5
c(3090)
8.71.3
9.53
11.5
15.1
c(3119)
1.10.9
1.90.6
1.15
0.73
1.0

17. Regge trajectories in (JP, M2) plane: J = M2 + 0,
in (nr, M2) plane: nr= M2+0
natural parity (P=(-1)J-1/2): /2+, 3/2-,…
unnatural parity (P=(-1)J+1/2): 1/2-, 3/2+, 5/2-,…
It is important to consider both spectroscopy & decay widths.

18. Charmed baryon states c c c c ’c(3123) c(3119) 3/2+(2S) c(3090)
5/2- (1P)
c(3055)
c(3050)
3/2- (1P)
c(3000)
1/2- (1P)
’c(2970)
c(2940)
3/2-
’c(2930)
c(2880)
5/2+
c(2860)
3/2+
c(2815)
3/2- (1P)
c(2800)
c(2790)
1/2- (1P)
c(2765)
c(2770)
3/2+
c(2765)
c(2695)
1/2+
’c(2645)
3/2+
c(2625)
3/2- (1P)
c(2595)
1/2- (1P)
’c(2575)
1/2+
c(2520)
3/2+
c(2470)
1/2+
c(2455)
1/2+
c(2287)
1/2+
c c c c

19. Excited c states
c(2595), c(2625) → c1(1/2-,3/2-) doublet: J = Jl 1/2
c1(1/2-) [c]S, c1(3/2-) [c]P, [c]D
⇒ c(2625) with < 0.97 MeV is narrower than c(2595) with
 = 2.60.6 MeV
c(2765): radial excitation (2S) JP = ½- (Ebert, Faustov, Galkin ’07)
even-parity orbital excitation ½+ (QM, Capstick, Isgur ‘86)
c(2940): its spin-parity assignment is quite diverse
radial excitation (2P) of c(2595) with JP= ½- (Ebert et al.)
predicted mass too large by ~ 50 MeV
a D*0p molecular ½- state with binding energy  5 MeV as
m(D*0)+m(p)=2945 MeV (X.G. He, X.Q. Li, X. Liu, X.Q. Zeng, ’07)
or 1/2+,3/2+, 5/2- suggested by others
or c(2765)

20. c(2880): first positive parity excited charmed baryon
Angular analysis of c(2880)→ c by Belle (’06) ⇒ J=5/2 is preferred
Candidates for spin-5/2 states:
HQS
⇒ parity assignment for c(2880)
JP=5/2- is
disfavored
However, c2(5/2+) can decay into c* in a P-wave; prediction of R is not robust
robust prediction
c(2880) could be an admixture of
Chua, HYC (’06)

21. Remarks:
Based on the diquark idea, JP[c(2880)] = 5/2+ is predicted
Wilczek and Selem (’06); Ebert, Faustov, Galkin (’07)
Peking group (Zhu et al., hep-ph/ ) has studied the strong
decays of charmed baryons using 3P0 model
⇒ Since c(2880) decays into D0p, it cannot be a radial excitation
⇒ c2(5/2+), ’c2(5/2+), ’’c2(5/2+) & c2(5/2+) all ruled out as they don’t
decay into D0p in 3P0 model. Moreover, too large ratio of c*/c
for the first three & too large width ( 137 MeV) for the last one
⇒ c(2880) is a pure state    
Some issues with ’’c3(5/2+) :
1. QM  m[c2(5/2+)]  2910MeV, and ’’c3(5/2+) is even heavier
2. The predicted width 28.3 MeV is larger than the measured one
[c(2880)] = 5.81.1 MeV  22

22. c(2860): another D-wave excited state
Existence of a new 3/2+ state was noticed even before LHCb experiment
B. Chen, Wei, Liu, Matsuki (’16)
Lu, Dong, Liu, Matsuki (’16)
B. Chen, Liu, Zhang (’17)
c(2860) observed by LHCb in D0p amplitude in b D0p- decay. It has JP = 3/2+.
M= MeV
 = MeV

23. c(2940): JP = 3/2- or 1/2- ?
LHCb (’17) studied spin & parity of ¤c(2940) and found JP= 3/2-. However, its Regge line is not parallel to other two Regge trajectories; ¤c(3005) predicted by quark-diquark model fits better.
We suggest that ¤c(2940) is most likely an 1/2-(2P) state
LHCb: “The most likely spin-parity assignment for ¤c(2940) is JP=3/2- but the other solutions with spin 1/2 to 7/2 cannot be excluded.”

24. Charmed baryon states c c c c ’c(3123) c(3119) 3/2+(2S) c(3090)
5/2- (1P)
c(3055)
c(3050)
3/2- (1P)
c(3000)
1/2- (1P)
’c(2970)
c(2940)
1/2- (2P)
’c(2930)
c(2880)
5/2+ (1D)
c(2860)
3/2+ (1D)
c(2815)
3/2- (1P)
c(2800)
c(2790)
1/2- (1P)
c(2765)
1/2+ (2S)
c(2770)
3/2+
c(2765)
c(2695)
1/2+
’c(2645)
3/2+
c(2625)
3/2- (1P)
c(2595)
1/2- (1P)
’c(2575)
1/2+
c(2520)
3/2+
c(2470)
1/2+
c(2455)
1/2+
c(2287)
1/2+
c c c c 24

25. Antitriplet states

26. ’c baryons
A missing ’c state with JP= 5/2- & mass ~ 2890 MeV. We assign it to ’c(2921) predicted by Ebert et al
’c(2930) & ’c(2921) form a P-wave doublet ’c2 (3/2-, 5/2-)
’c(2930) cK, c, ’cK
HHChPT (’c(2930))= ( ) MeV which deviates from measured 3613 MeV by 2.1. The QM relation h112= 2h102 could be broken.

28. c baryons
c(2800) was the only excited state found after the ground states c(2455) & c(2520). It decays into c+ with width ~ 70 MeV
Since c1 c in heavy quark limit as c1→[c]P . c(2800) is assigned to c0(1/2-) or c2 (3/2-, 5/2-).
(c0++c++) 425 MeV for h2=0.437
If c0(1/2-) is identified with c(2800), mixing angle  > 66o; otherwise, c(2800) should have JP =3/2-.

29. 29 ?? 3/2- 5/2+ c(3080) c(2980) c(2940) c(2880) c(2815) c(2800)

30. Sextet states

31. X.G. He et al. (’07), Y.B. Dong et al. (’14) c(2800)  DN
A few more remarks:
Strong decay modes:
heavy baryon + light meson(s): c, c, c,…
heavy meson + light baryon: D0p, D,…
Molecule picture:
c(2940)+  D*0p
X.G. He et al. (’07), Y.B. Dong et al. (’14)
c(2800)  DN
Y.B. Dong et al. (’10)
c(2970)  D
m(D0)+m() = MeV > m[c(2970)0] =  0.8 MeV

32. Charmed baryon states c c c c ’c(3123) 7/2+ (1D) c(3119)
5/2+
(1D)
c(3066)
5/2- (1P)
c(3055)
3/2+
(1D)
c(3050)
3/2- (1P)
c(3000)
1/2- (1P)
’c(2970)
1/2+
(2S)
c(2940)
1/2- (2P)
’c(2930)
3/2-
(1P)
c(2880)
5/2+ (1D)
c(2860)
3/2+ (1D)
c(2815)
3/2- (1P)
c(2800)
3/2-
(1P)
c(2790)
1/2- (1P)
c(2765)
1/2+
(2S)
c(2770)
3/2+
c(2765)
3/2-
(1P)
c(2695)
1/2+
’c(2645)
3/2+
c(2625)
3/2- (1P)
c(2595)
1/2- (1P)
’c(2575)
1/2+
c(2520)
3/2+
c(2470)
1/2+
c(2455)
1/2+
c(2287)
1/2+
c c c c

33. Conclusions
If (1P,1/2-)l is identified with c(3000), the other state (1P,1/2-)h will be too broad to be seen!
c(2940) is most likely an 1/2-(2P) state. Search for c baryon with mass ~ 3005 MeV and JP =3/2-.
Regge trajectories fit nicely to c & c states; their mass differences lies between 180 ~200 MeV.