1. Exotic states in S=1 N  K system and low lying ½+ S=-1 resonances Kanchan Khemchandani, Departamento de Fisica, Universidad de Coimbra, Portugal. 19th International IUPAP Conference on Few-Body Problems in Physics 31.08 - 05.09.2009 - University of Bonn / Germany Fri, Sept.4 2009

2. Collaborators: Alberto Martinez Torres and Eulogio Oset IFIC-Univ. de Valencia, Spain

3. Why study the  KN system? A peak  K + n invariant mass in the γ n → K + K − n reaction at the Spring8/Osaka  pentaquark The picture is not clear yet. KN interaction  chiral dynamics  repulsive suggestions   KN bound state Some investigations have already been done  results not promising Our study of the  KN (S=-1) system  several resonances  revisit  KN and make a conclusive study ( T. Nakano [LEPS Collaboration], Talk at the PANIC 2002 (Oct. 3, 2002, Osaka); T. Nakano et al., Phys. Rev. Lett. 91, 012002 (2003) ) ( P. Bicudo, G. M. Marques, Phys. Rev. D69, 011503, 2004; F. J. Llanes-Estrada, E. Oset and V. Mateu, Phys. Rev. C 69, 055203 (2004). )

4. We started studying the system: All the interactions are in S-wave. There are some S=-1, 1/2 + baryonic states in the energy region 1500- 1800 MeV whose properties, as spin-parity, are not well understood. 1 D. Jido, J. A. Oller, E. Oset, A. Ramos, U. G. Meissner, Nucl. Phys. A 725 (2003) 181-200. 2 T. Inoue, E. Oset, M. J. Vicente Vacas, Phys. Rev. C 65 035204. 3 J. A. Oller, E. Oset, J. R. Peláez, Phys. Rev. D 59 074001 (199). 2 3 1 The  KN system.

5.   137+1405 =1542 MeV Seems to show up in  production

6. 4 L. Roca, S. Sarkar, V. K. Magas and E. Oset, Phys. Rev. C 73, 045208 (2006). 5 S. Prakhov et al., Phys. Rev. C 69, 042202 (2004). (1600) Some of them seem to remain unexplained in terms of two- body dynamics e.g., a detailed study of the K - p   reaction by Roca et al. 4 explains the bulk of the data 5, but fails to explain a bump in the (1600) region.

7. We solve the Faddeev equations The matrices contain all the possible diagrams where the last two successive interactions are t i and t j And they satisfy the equations: The Formalism

8. In th e Coupled channel approach ( pseudo-scalar mesons of the SU(3) octet + baryons of the 1/2 + octet) → couple to S=-1 ↓ add 

9. We solve the Faddeev equations The matrices contain all the possible diagrams where the last two successive interactions are t i and t j And they satisfy the equations: The Formalism

10. ´

12. Chiral amplitudes

13. = 0

14. where

15. We extend the procedure for the rest of diagrams involving more than three t-matrices Variables of the eqn:  s,  s 23

16. Σ(1660) P 11 [ I(J P )=1(1/2 + ) ] *** Results (S= -1 system, I=1)

17. Σ(1620) S 11 [ I(J P )=??] ** Σ(1660) P 11 [ I(J P )=1(1/2 + ) ] *** R. Armenteros et al. Nucl. Phys. B 8, 183 (1968). B. R. Martin et al, Nucl. Phys. B 127, 349 (1977). Σ(1560)159070 Σ(1770)179024

18. Λ(1810) P 01 [ I(J P )=0(1/2 + ) ] *** 1750 to 1850 (~ 1810) OUR ESTIMATE Results ( S= -1 sytem,I =0 )

19. Λ(1600) P 01 [ I(J P )=0(1/2 + ) ] *** 1560 to 1700 (~ 1600) OUR ESTIMATE There are quite possibly two P01 states in this region. 1568 - i 60/2 MeV

20. We study  KN system using the same formalism. We take p  0 K 0, n  0 K +, p  − K +, n  + K 0 as coupled channels. For which, we take K +  0, K 0  +, K + ,  0 p,  + n, ηp  charge +1. K +  −, K 0  0, K 0 ,  − p,  0 n, ηn  charge 0.  + K 0,  0 K + for  K  charge +1.  − K +,  0 K 0 for  K  charge 0. K 0 p, K + n  charge +1 K 0 n  charge 0 and K + p  charge +2.  N interaction  K interaction KN interaction The  KN system.

21. We find no peak around 1540 MeV. We find a bump at ~ 1720 MeV with 200 MeV of FWHM in isospin 0 amplitude  with  K in isospin 0 configuration and with  K mass ~ 800 MeV No peak in other isospin cases. A bump also in the time delay analysis of KN data N. G. Kelkar et. al. JPG 29, 1001 (2003) K.P. Khemchandani, A. Martinez Torres, E. Oset Phys. Lett. B (2009)

22. Γ (PDG) (MeV) Peak position (this work) (MeV) Γ (this work) (MeV) Isospin = 1 Σ(1560)10-100159070 Σ(1620)10-100163039 Σ(1660)40-200165630 Σ(1770)60-100179024 Isospin = 0 Λ(1600)50-2501568,170060, 136 Λ(1810)50-250174020 Summary Ref: A Martínez Torres, K. P. Khemchandani, E. Oset, Phys. Rev. C77:042203,2008; Eur. Phys. J. A35: 295-297,2008 J p = ??

23.  S= -1 sector → four Σ’s and two Λ’s resonances (all the 1/2 + Σ and Λ states in the energy region 1500- 1870. )  S=+1 → a bump around 1720 MeV with ~ 200 MeV of width, No resonance around 1540 MeV.