Quantum Numbers of Charmed Baryons HaiYang Cheng Academia

Quantum Numbers of Charmed Baryons Hai-Yang Cheng (鄭海揚) Academia Sinica, Taipei l c states l c(’) states l c states UCAS, June 21, 2017

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

Charmed baryon states ’c(3123) c(3080 ) c(3055 ) ’c(2970) c(2940 3/2) c(2880 5/2+ ) c(2860 3/2+ ) c(2765 ) ’c(2930) c(2800 ) c(2815) 3/2 - (1 P) c(2790 1/2 - (1 P) ) ’c(2645) 3/2+ c(2625 3/2 - (1 P) ) c(2595 1/2 - (1 P) ) c(2770) 3/2+ c(2695) 1/2+ ’c(2575) 1/2+ c(2520 3/2+ ) c(2287 1/2+ ) c c(2455 1/2+ ) c c(2470 1/2+ ) c c 3

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

Agaev, Azizi, Sundu [1703. 07091] H. Chen, Mao, W. Chen, Hosaka, Liu, Zhu [1703. 07703] Karliner, Rosner [1703. 07774] Yang, Ping [1703. 08845] pentaquark K. Wang, Xiao, Zhong, Zhao [1703. 09150] W. Wang, R. Zhu [1704. 00179] Padmanath, Mathur [1704. 00259] Cheng, Chiang [1704. 00396] Huang, Ping, F. Wang [1704. 01421] pentaquark Z. G. Wang [1704. 01854] B. Chen, Liu [1704. 02583] Z. Zhao, Ye, Zhang [1704. 02688] Aliev, Bilmis, Savci [1704. 03439] Kim, Polyakov, Praszalowicz [1704. 04082] Agaev, Azizi, Sundu [1704. 04928] An, H. Chen [1705. 08571] pentaquark 5

Orbitally excited charmed baryon states L½+L¸ = Ll (not L½+L¸= Ll !) Two possible p-wave states (L +L =1): 1. state L½=1, L¸=0; antisymmetric under q 1 q 2 2. state L½=0, L¸=1; symmetric under q 1 q 2 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)

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 7

Masses in Me. V n. L, JP Ebert Shah B. Chen T. W. Chiu Agaev 1 S, 1/2+ 2698 2695 2696 2695 28 2685 123 2 S, 1/2+ 3088 3100 3185 1 S, 3/2+ 2768 2767 2764 2 S, 3/2+ 3123 3126 3226 (1 P, 1/2 -)l 2966 3011 2975 (1 P, 1/2 -)h 3055 3028 3063 (1 P, 3/2 -)l 3029 2976 3066 (1 P, 3/2 -)h 3054 2993 3120 1 P, 5/2 - 3051 2947 3057 3075 142 2781 25 3015 45 2769 89 Expt 2695. 2 2. 0 (3090) 2765. 9 2. 0 3119 108 (3119) 2990 129 (3000) 3056 103 (3050) (3066) P J State quark model Latticeresults of. PDG n We take relativistic Ebert, Faustov, Galkin + 0 Ds 0*(2317) 2317 15 5 2317. 7 0. 6 (’ 11) as a benchmark. 1’+ 2463 13 9 2459. 6 0. 6 s 1(2460) n Yu-Chih Chen, D’Ting-Wai Chiu (’ 17) based on Nf =2+1+1 optimal 1+ fermion Ds 1(2536) 2535. 10 0. 06 domain wall with m 2536 12 4 =280 Me. V 8

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

An ideal place for testing heavy quark symmetry and chiral symmetry: heavy hadron chiral perturbation theory (HHCh. PT) Yan, Cheng, Cheung, Lin, Yu; Wise; Burdman, Donoghue (’ 92) Strong decays of S-wave charmed baryons are governed by two couplings g 1 & g 2. While info on g 1 is absent due to the lack of c*→ c , g 2 can be fixed by the measured rate of c++ c+ + 10

n s-wave (d-wave) transitions between P-wave and S-wave baryons are described by six couplings h 2, …, h 7 (eight couplings h 8, …, h 15) Pirjol, Yan (’ 97) n In principle, h 2 can be determined from c(2593) c. However, m( c++) + m( -) = 2593. 55 Me. V, m( c 0)+m( +) = 2593. 31 Me. V, thus strong decays of c(2593) are very close to threshold and very sensitive to the pion mass difference, m( ) – m( 0) = 4. 6 Me. V important threshold effects on c(2593) mass and coupling Blechman, Falk, Pirjol, Yelton (’ 03) n Isospin relation c 0 0 = ½ c + - adapted by PDG is strongly violated n Previous fit h 2 = 0. 437+0. 114 -0. 102 Chua, HYC (’ 06) n CDF (’ 11) has measured decays of c(2593) to c + and obtained m[ c(2593)] = 2592. 25 0. 28 Me. V, h 2 = 0. 60 0. 07 11

Strong decays of p-wave charmed baryons h 2 & h 8=h 10 8. 9 1. 0 10. 0 1. 1 l h 2 = 0. 60 0. 07, h 10 (0. 88+0. 12 -0. 11) 10 -3 Me. V-1 l ( c 0 0) 4. 5 ( c + - ) l Predicted too large rates for c(2790)0 & c(2815)+ 12

n P-wave c states decay into ¥c. K or ¥’c. K in s- or d-wave transition n Using quark model relation h 3= 2 h 2 & assuming mass 3000 Me. V ¡ ( c 0)= 410 Me. V for h 2 = 0. 437 811 Me. V for h 2 = 0. 60 1400 Me. V by Zhao, Ye, Zhang 420 Me. V by H. X. Chen et al. using QCD sum rules 35 Me. V by B. Chen, Liu using Eichten, Hill, Quigg decay formula 32 Me. V by Wang et al. based on chiral quark model 13

With width of 410 Me. V for c 0 and the data of 4. 5 0. 7 Me. V for c(3000), the mixing angle is constrained to be 96 o or 84 o. (111 o by B. Chen & Liu, 24 o or 47 o by K. Wang et al. ) c 1(1/2 -) is prohibited to decay into c. K in HQ limit The other state (1 P, 1/2 -)h must be too broad to be seen! Using h 10=(0. 85+0. 11 -0. 08)10 -3 extracted from measured width of c(2800), we obtain Expt ¡( c(3050))= sin 2µ 2(8. 6+2. 2 -1. 6) Me. V, (0. 8 0. 2 0. 1) Me. V ¡( c(3066))= (13. 3+3. 4 -2. 5) Me. V, (3. 5 0. 4 0. 2) Me. V sin 2 ¼ 160 o, predicted width for c(3066) is too large by a factor of 4 14

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

Decay widths in Me. V LHCb Agaev K. Wang c(3000) 4. 5 0. 7 4. 7 1. 2 constraint on 1 c(3050) 0. 8 0. 2 0. 6 0. 2 0. 94 c(3066) 3. 5 0. 4 6. 4 1. 7 c(3090) 8. 7 1. 3 c(3119) 1. 1 0. 9 1. 9 0. 6 B. Chen Zhang Cheng 5. 0 constraint on 1 2. 7 0. 2 constraint on 2 4. 96 3. 3 8. 5 13. 3+3. 4 -2. 5 9. 53 11. 5 15. 1 1. 15 0. 73 1. 0 0. 2 16

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

Charmed baryon states ’c(3123) c(3080 ) c(3055 ) ’c(2970) c(2940 3/2) c(2880 5/2+ ) c(2860 3/2+ ) c(2765 ) c(3119) c(3090) c(3066) c(3050) c(3000) + 3/2+(2 S) 1/2 - (2 S) 5/2 - (1 P) 3/2 (1 P) 1/2 (1 P) ’c(2930) c(2800 ) c(2815) 3/2 - (1 P) c(2790 1/2 - (1 P) ) ’c(2645) 3/2+ c(2625 3/2 - (1 P) ) c(2595 1/2 - (1 P) ) c(2770) 3/2+ c(2695) 1/2+ ’c(2575) 1/2+ c(2520 3/2+ ) c(2287 1/2+ ) c c(2455 1/2+ ) c c(2470 1/2+ ) c c 18

Excited c states n c(2595), c(2625) → c 1(1/2 -, 3/2 -) doublet: J = Jl 1/2 c 1(1/2 -) [ c ]S, c 1(3/2 -) [ c ]P, [ c ]D ⇒ c(2625) with < 0. 97 Me. V is narrower than c(2595) with = 2. 6 0. 6 Me. V n c(2765): or c(2765) radial excitation (2 S) JP = ½- (Ebert, Faustov, Galkin ’ 07) even-parity orbital excitation ½ + (QM, Capstick, Isgur ‘ 86) n c(2940): its spin-parity assignment is quite diverse radial excitation (2 P) of c(2595) with JP= ½- (Ebert et al. ) predicted mass too large by ~ 50 Me. V a D*0 p molecular ½- state with binding energy 5 Me. V as m(D*0)+m(p)=2945 Me. V (X. G. He, X. Q. Li, X. Liu, X. Q. Zeng, ’ 07) or 1/2+, 3/2+, 5/2 - suggested by others 19

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 n disfavored n However, c 2(5/2+) can decay into c* in a P-wave; prediction of R is not robust n robust prediction c(2880) could be an admixture of Chua, HYC (’ 06) 20

Remarks: u Based on the diquark idea, JP[ c(2880)] = 5/2+ is predicted Wilczek and Selem (’ 06); Ebert, Faustov, Galkin (’ 07) u Peking group (Zhu et al. , hep-ph/0704. 0075) has studied the strong decays of charmed baryons using 3 P 0 model ⇒ Since c(2880) decays into D 0 p, it cannot be a radial excitation ⇒ c 2(5/2+), ’’c 2(5/2+) & c 2(5/2+) all ruled out as they don’t decay into D 0 p in 3 P 0 model. Moreover, too large ratio of c* / c for the first three & too large width ( 137 Me. V) for the last one ⇒ c(2880) is a pure state Some issues with ’’c 3(5/2+) : 1. QM m[ c 2(5/2+)] 2910 Me. V, and ’’c 3(5/2+) is even heavier 2. The predicted width 28. 3 Me. V is larger than the measured one [ c(2880)] = 5. 8 1. 1 Me. V 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 D 0 p amplitude in b D 0 p - decay. It has JP = 3/2+. M= 2856. 1+2. 3 -5. 9 Me. V = 67. 6+11. 8 -21. 6 Me. V 22

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 -(2 P) 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. ” 23

Charmed baryon states ’c(3123) c(3080 ) c(3055 ) ’c(2970) - c(2940 1/2 (2 P) ) c(2880 5/2+ (1 D) ) c(2860 3/2+ (1 D) ) + c(2765 1/2 (2 S) ) c(2765 ) c(3119) c(3090) c(3066) c(3050) c(3000) + 3/2+(2 S) 1/2 - (2 S) 5/2 - (1 P) 3/2 (1 P) 1/2 (1 P) ’c(2930) c(2800 ) c(2815) 3/2 - (1 P) c(2790 1/2 - (1 P) ) ’c(2645) 3/2+ c(2625 3/2 - (1 P) ) c(2595 1/2 - (1 P) ) c(2770) 3/2+ c(2695) 1/2+ ’c(2575) 1/2+ c(2520 3/2+ ) c(2287 1/2+ ) c c(2455 1/2+ ) c c(2470 1/2+ ) c c 24

Antitriplet states 25

’c baryons n A missing ’c state with JP= 5/2 - & mass ~ 2890 Me. V. We assign it to ’c(2921) predicted by Ebert et al n ’c(2930) & ’c(2921) form a P-wave doublet ’c 2 (3/2 -, 5/2 -) ’c(2930) c. K, c , ’c. K HHCh. PT ( ’c(2930))= (77+20 -14) Me. V which deviates from measured 36 13 Me. V by 2. 1. The QM relation h 112= 2 h 102 could be broken. 26

27

c baryons n c(2800) was the only excited state found after the ground states c(2455) & c(2520). It decays into c+ with width ~ 70 Me. V Since c 1 c in heavy quark limit as c 1→[ c ]P. c(2800) is assigned to c 0(1/2 -) or c 2 (3/2 -, 5/2 -). ( c 0++ c+ +) 425 Me. V for h 2=0. 437 If c 0(1/2 -) is identified with c(2800), mixing angle > 66 o; otherwise, c(2800) should have JP =3/2 -. 28

5/2+ c(3080) c(2980) ? ? (2940) c c(2880) 3/2 c(2800) c(2815) c(2790) c(2770) c(2645) c(2625) c(2595) ’c c(2520) 29

Sextet states 30

A few more remarks: n Strong decay modes: heavy baryon + light meson(s): c , … heavy meson + light baryon: D 0 p, D , … n Molecule picture: c(2940)+ D*0 p 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(D 0)+m( ) = 2980. 54 Me. V > m[ c(2970)0] = 2969. 4 0. 8 Me. V 31

Charmed baryon states ’c(3123) 7/2+ (1 D) c(3080 5/2+ (1 D) ) c(3055 3/2+ (1 D) ) ’c(2970) 1/2+ (2 S) c(2940 1/2 - (2 P) ) c(2880 5/2+ (1 D) ) c(2860 3/2+ (1 D) ) c(2765 1/2+ (2 S) ) c(2765 3/2 - (1 P) ) c(3119) c(3090) c(3066) c(3050) c(3000) + 3/2+(2 S) 1/2 - (2 S) 5/2 - (1 P) 3/2 (1 P) 1/2 (1 P) ’c(2930) 3/2 - (1 P) c(2800 3/2 - (1 P) ) c(2815) 3/2 - (1 P) c(2790 1/2 - (1 P) ) ’c(2645) 3/2+ c(2625 3/2 - (1 P) ) c(2595 1/2 - (1 P) ) c(2770) 3/2+ c(2695) 1/2+ ’c(2575) 1/2+ c(2520 3/2+ ) c(2287 1/2+ ) c c(2455 1/2+ ) c c(2470 1/2+ ) c c 32

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