1. The Baryon octet-vector meson interaction and dynamically generated resonances in the S=0 sector 孙宝玺 北京工业大学 合作者 : 吕晓夫 四川大学 FHNP’15, 怀柔, 北京

2. Content 1. Vector meson-baryon decuplet interaction S. Sarkar, B. -X. Sun, E. Oset, M. J. Vicente Vacas, EPJA 44: 431 (2010). 2. Vector meson-baryon octet interaction E. Oset, A. Ramos, EPJA 44: 445 (2010). 3. Vector meson-baryon octet interaction K. P. Khemchandani, H. Kaneko, H. Nagahiro, A. Hosaka, PRD 83:114041 (2011) 4. My present work on this topic B. -X. Sun and X. -F. Lu, Arxiv:1406.1841

3. Lippman-Schwinger Eqution With a kernel of effective interaction, we can solve the LS equation. The amplitude satisfies the unitary relation exactly, and the properties of hadronic resonances generated dynamically can be obtained. These resonances do not appear in the effective Lagrangian density.

4. Hidden-gauge symmetry In order to construct the vector meson-baryon octet interaction Largrangian density, we consider the SU(3) flavor local gauge symmetry neglecting the mass term, and then we obtain

5. S. Sarkar, B. -X. Sun, E. Oset, M. J. Vicente Vacas, EPJA 44: 431 (2010). When the momentum transfer is far less than the mass of the vector meson in the propagator, we can neglect the square of the momentum in the propagator. Therefore the t-channel interaction between vector meson and baryon is obtained:

6. u-channel and s-channel We neglected the contribution from s- channel and u-channel interaction since we thought their effects are trivial at that time.

7. Vector meson – baryon loop function in the dimensional regularization scheme

8. S. Sarkar, B. X. Sun, E.Oset et al., EPJA 44, 431 (2010)

9. Ten resonances in the different strangeness and isospin channels. Degenerate in JP=1/2-, 3/2-, 5/2-.

10. Vector-baryon octet interaction E. Oset and A. Ramos, EPJA 44, 445 (2010).

11. Tensor coupling between vector meson and baryon octet K. P. Khemchandani, H. Kaneko, H. Nagahiro and A. Hosaka, PRD 83, 114041 (2011). In this article, a tensor coupling term between vector meson and baryon octet is added, which is relevant to the magnetic moments of the baryons, and is also gauge invariant.

12. K. P. Khemchandani et al.,PRD 83, 114041 (2011)

13. In addition to t-channel, the s-channel,u-channel and contact interaction are taken into account, and a non-relativistic interaction potential between vector meson and baryon octet with strangeness S=0 is obtained. When u-channel and s-channel are taken into account, the hadronic resonances generated dynamically with different spins are not degenerate again.

14. Results for Strangeness S=0 S=0 K. P. Khemchandani et al.,PRD 83, 114041 (2011) I=1/2, S=0, E. Oset and A. Ramos, EPJA 44, 445 (2010).

15. K. P. Khemchandani, H. Kaneko, H. Nagahiro and A. Hosaka, PRD 83, 114041 (2011) The effect of tensor term is not taken into account in the t-channel interaction. Moreover, The parameters D=2.4 and F=0.82 are not correct. Since the magnetic momentum of the proton is 2.79, F=1.82 is reasonable to give an anomalous magnatic momentum. (Jido et al. PRC66,025203)

16. SU(3) vector –baryon interaction The SU(3) generalized form of the vector meson baryon interaction Lagrangian can be written as

17. Mixing of the vector octet and singlet In order to obtain the right couplings for the physical omega meson and phi meson, we need to consider the mixing of their octet and singlet components.

18. Vector meson-baryon-baryon vertices The Lagrangian related to the s-, u-, t- channel interactions is explicitly written as Moreover, the contact term between the vector meson and the baryon can be obtained from

19. t- channel interaction If the momentum of the initial meson is similar to that of the final vector meson, i.e., q_2~q_1, the momentum transfer k=q_2-q_1 is trivial null approximately, and then the t- channel interaction can be written as

20. BBV Vertex The vertex of two baryons and a vector meson can be written as g_1 and g_2 are different for different baryons and vector mesons, and their values can be obtained with the SU(3) symmetry.

21. t-channel supplement However, if the difference between q_2 and q_1 is taken into account, an additional term should be supplemented in the t- channel of the baryon and meson interaction.

22. u-, s- channel interactions The u- channel and s- channel interactions between the baryon and the vector meson can be written as In the u-channel interaction, we make an approximation in the denominator

23. Contact term The contact interaction between baryons and mesons is written as Of course, the coupling constant can be obtained from SU(3) symmetry.

24. Total potentials the total kernel of the vector meson- baryon octet interaction is a summation of the t-, s-, u- channels and contact term, which is functions of the total energy in the center of mass system and the scattering angle θ.

25. Lippman-Schwinger Equation The relativistic coupling-channel Lippman- Schwinger equation is written as with a loop function in the on-shell factorization approach

26. Experimental data The experimental values on coupling constants of vector mesons to baryons are taken from the article [L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rept. 127, 1 (1985)].

27. Parameters we can fit the parameters related to vector coupling terms F_V, D_V and C_V in the Lagrangian with these data. Moreover, we set the parameters of tensor terms F_T, D_T and C_T to be equal to F_V, D_V and C_V, respectively.

28. Partial wave analysis In the S-wave approximation of the partial wave analysis of, L^\prime=0, L=0,2. I calculate the amplitudes with different spins:,,.

29. Partial wave analysis in S-wave approximation

30. I=1/2, J=1/2

31. I=1/2, J=3/2

32. Isospin 1/2

33. Isospin 3/2

34. Summary N(1650)1/2-, N(1700)3/2- N(1895)1/2-, N(1875)3/2- ? N(2120)3/2- Δ(1620)1/2-, Δ(1700)3/2 -

35. Pseudoscalar meson and baryon octet interaction N(1535 ）, M=1537MeV, Γ=110MeV.

36. 最近感兴趣的问题 On-shell approximation of the loop function in the Lippmann-Schwinger equation. P-wave ?

37. Thanks