1. 手征夸克模型的一些应用
钟显辉
湖南师范大学物理与信息科学学院

2. Meson-Baryon scattering in the quark model
e.g. πNηN, KNΣ π,…
Photo-production process in the quark model
e.g. γNηN, γNNπ,…
Strong decay of the heavy hadrons in the quark model
e.g. Λc,Σc , Ξc , Ξ ; D, Ds, B, Bs

3. The chiral quark model :
Glozman and Riska: Phys. Rept. 268,263(1996); Nucl. Phys. A663,103c(2000)
Z Y Zhang, A. Faessler, U. Straub, L. Ya. Glozman,
Nucl. Phys.A578,573(1994)
Z Y Zhang Y W. Yu,P. N. Shen, et al.,
Nucl. Phys.A625,59(1997)
L.R.Dai, Z.Y.Zhang,Y.W.Yu,P.Wang,
Nucl.Phys.A727,321(2003) ……

4. Part I: Meson-Baryon scattering in the quark model
Meson-Baryon scatterings at low energies inform us much information of meson-baryon interactions, coupling constants, the properties of baryon resonances,…
M.Doring, E. Oset, B. S. Zou, arXiv: ;
J J Xie, B. S.Zou, Phys.Lett.B649:405,2007;
B.C Liu, B.S. Zou, Phys.Rev.Lett.96:042002,2006.
Fei Huang et al., Chin.Phys. C33 (2009)
Puze Gao, Jun Shi, B.S. Zou, Phys.Rev. C86 (2012) …

5. 1) quark-meson interactions
A. The model
1) quark-meson interactions
The effective Lagrangian of quark-meson interactions:
The quark-meson pseudovector coupling at tree level:

6. quark-meson interactions
The non-relativistic form:
Vector pj is the internal momentum for the j-th quark in the baryon rest frame, q is the meson momentum, Ij is the isospin operator,…
See series papers of Zhenping Li and Qiang Zhao

7. 2) Scattering amplitudes
Two kinds of amplitudes for s- and u-channels, one is the mesons couple with the same quark, the other is the mesons couple with different quarks.

8. Amplitudes for the s-channel

9. Amplitudes for the u-channel

10. Breit-Wigner

11. Partial wave amplitudes

12. 1) Resonance contribution
B. πpηn
1) Resonance contribution
a) the n=0 shell
In the case of n=0, only the nucleon pole term contributes to the transition amplitude (P-wave).
XH Zhong Q Zhao, J He , B Saghai, PRC76,065205(07)

13. b) In the n=1 shell
In n=1 shell, both S-wave and D-wave resonances contribute to the amplitude.
The S-wave resonances:
S11(1535), S11(1650)
The D-wave resonances:
D13(1520), D13(1700), D15(1675)

14. c) In the n=2 shell
In n=2 shell, both P-wave and F-wave resonances contribute to the amplitude.
The P-wave resonances:
P11(1440), P11(1710), P13(1720),
P13(1900),…
The F-wave resonances:
F15(1680), F15(2000)

15. 2) results

16. results
Near threshold, the S11(1535) dominates the reactions, while the interferences from the S11(1650) turn out to be destructive around W<1.6 GeV.
The D13(1520) is crucial to give correct shapes of the differential cross sections.
The nucleon pole term contributions are significant.

17. 1) Resonance contribution n=0 shell: Λ pole
C. Kp Σπ
1) Resonance contribution
n=0 shell: Λ pole
n=1 shell: Λ(1670)S01 , Λ(1405) S Λ(1520)D03, Λ(1690) D03
XH Zhong and Q Zhao, PRC79,045202(09); PRC88,015208(13)

18. 2) Results:differential cross section

19. 2) Results: polarizations

20. 2) Results: cross section

21. conclusion dominant resonance: Λ(1405) S01 ,Λ(1520)D03
obvious evidences: Λ(1670) S01 ,Λ(1690)D03
configuration mixings:Λ(1405) S01 , Λ(1670) S01

22. D. Kp Λπ
1) Resonance contribution
P wave: Σ(1193),Σ(1385)
S wave: [70,210]S11? , [70,28]S11? , [70,48]S11 ? D wave: [70,210]D13 ?, [70,28]D13 ?, [70,48]D13?, [70,48]D15

23. 2) Results:differential cross section

24. 2) Results: polarizations

25. 2) Results: cross section

26. conclusion dominant contributors: u and t backgrounds and Σ(1385) P13
obvious evidences: Σ(1750) [70,48]S11 ,
Σ(1775) [70,48]D15

27. Part II: strong decays of hadrons
The strong decays of hadrons is sensitive to their structures, thus, study their decay properties is useful to classify the hadrons, especially to the new found hadrons at Belle, Babar,...

28. I. Charmed baryon strong decays
New charmed baryons:
Λc(2880,2940,2765), Σc(2800) ,
Ξc(2980,3055,3080,3123)…
How to classify these states?
XH Zhong and Q Zhao, PRD77,074008(08)
LH Liu, LY Xiao, XH Zhong,PRD77,034024(12)

29. 1) spectroscopy in the quark model
The SU(3)f symmetry is broken by the heavy quark.
How to classify the heavy baryons, we can see series papers of
Isgur et al.

30. Λc spectroscopy

31. Σc spectroscopy

32. Ξc spectroscopy

33. 2) Strong decay amplitudes

34. 3) Λc,Σc baryons

35. Λc(2880)
observed in Λcππ[PRL86,4479 (01) ,CLEO], Σcπ,Σ*cπ[PRL98,262001(07)Belle],Dp[PRL98,012001(07)BaBar]

36. Λc(2880) as the possible states
Seems to favor a JP=3/2+ state

37. Λc(2940)
observed in Dp [PRL98, (07) BaBar] ;Σcπ,Σ*cπ [PRL98, (07) Belle]

38. Λc(2940) as the possible states
Seems to favor a JP=5/2+ state

39. Λc(2765)
Observed inΛcππ,resonated through Σcπ&Σc(2520) π(PRL86,4479 (01) CLEO)
Γ≈ 50 MeV

40. Λc(2765) is possible a Pρ mode Λc excite state, according to the mass in the quark model prediction
If Σcπdominates the decay, it seems to favor a JP=1/2- state.

41. Σc(2800)
Observed in the Λc πchannel. PRL94,122002(05)[Belle]

42. Σc(2800)
Seems to favor a JP=1/2- state, JP=5/2- can not be excluded

43. 4) Charm-strange baryon
Newly observed charmed strange baryons

44. Results for well-established states

45. Ξc(2980/2970)
observed in ΛcKπ[PRL97, (06) ,Belle; PRD77,012002(08)].
M=2980 MeV, Γ=45 MeV
M=2970 MeV, Γ=27 MeV
observed in Ξc(2645)π [PLB665,9(08) Belle]
M=2970 MeV, Γ=18 MeV
The same state or two different state?

46. Two cases are possible!
One state: Ξc(2980) might be the JP=1/2- state!
Two states: Ξc(2980/2970) might be the JP=1/2- and 3/2- states, respectively!

47. Ξc(3080) observed in ΛcKπ[PRL97,162001 (06) ,Belle].
M=3077 MeV, Γ=6.2 MeV
observed in ΛcKπ, Σc(2455,2520)K
[PRD77,012002(08),BaBar]
M=3077 MeV, Γ=5.5 MeV

48. Ξc(3080) might be the 2S state with JP=1/2+

49. Other prediction

50. 5) conclusions
Λc(2880) andΛc(2940) maybe favor JP=3/2+ and Jp=5/2+, respectively.
Λc(2765) maybe favor a P-wave ρ-mode excited states with JP=1/2-, the other possibilities can not be excluded.
Σc(2800) maybe favor a JP=1/2- state, JP=5/2- can not be excluded.
Ξc(2980/2970) maybe favor a JP=1/2- state, two sate case can not be excluded.
Ξc(3080) favors the 2S ρ-mode excited states with JP=1/2+

51. II. Heavy-light meson strong decays
New heavy-light mesons:
Ds(2860), Ds (2700), B1(5725) ,B*2(5740), Bs1(5829), B(5970)
Bs2(5840), D(2550), D(2600), D(2750,2760)
Undetermined mesons (old):
D(2640), Ds(2632)…
Can find other new heavy mesons?
S L Zhu (group); Z. Y. Zhang(group); P N Shen, F K Guo, et al.

52. 1) The heavy-light meson spectroscopy
flavor symmetry is broken,
no longer the charge conjugation eigenstates
XH Zhong and Q Zhao, PRD78,014029(08); 81,014031(10).
XH Zhong, PRD82,114014(10)
LY Xiao and XH Zhong, PRD90,074029(14)

53. D and Ds mesons

54. B and Bs mesons

55. 2) Strong decay amplitudes

56. 3) Decay widths

57. Results for well established shates
Mixed states:

58. Mixed states for P waves
The broad state should have larger mass, which is
in agreement with the PDG

59. 23S1-13D1 mixing
D(2600) favors the low-mass mixed state |SD>L! Its high-mass partner is a broad state.

60. 23S1-13D1 mixing
Ds(2710) favors the low-mass mixed state |SD>L! Its higher mass partner might be Ds1(2850)!

61. 13D2 -11D2 mixing
D(2750) favors the high-mass mixed state |D2>H! Its low-mass partner might be broad!

62. 13D2 -11D2 mixing
The high-mass mixed state Ds(|D2>H) with JP=2- might have been observed around 2.86 GeV.

63. 3D3-wave state
D(2760)
D(2760) favors 3D3-wave state!

64. 3D3-wave state 3D3-wave state DS3(2860)
DS3(2860) favors 3D3-wave state!

65. DS(3040)
DS(3040) favors the Low-mass mixed state |P1>L!

66. D (3000) is the partner of Ds(3040)
observed in D*π[JHEP09,145 (13) ,LHCb].
M=2972 MeV, Γ=188 MeV

67. B (5970) as the 3D3 state observed in Bπ[PRD90,012013 (14) ,CDF].
M=5970 MeV , Γ=70 MeV

68. 4) conclusion D(2600), Ds(2710): a SD mixing state
D(2760), Ds3(2860), B(5970): 13D3 state
D(2750): 1D2-3D2 mixing state,
Ds2(2860): observed a partner of D(2750)?
Ds1(2850): a SD mixing state, the partner of Ds(2710)
Ds(3040): 1P1-3P1 mixing state
D(3000): 1P1-3P1 mixing state, the partner of Ds(3040)
We can find more heavy-light mesons in future.

69. Thanks!