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 University of Bonn / Germany Fri, Sept
Collaborators: Alberto Martinez Torres and Eulogio Oset IFIC-Univ. de Valencia, Spain
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, (2003) ) ( P. Bicudo, G. M. Marques, Phys. Rev. D69, , 2004; F. J. Llanes-Estrada, E. Oset and V. Mateu, Phys. Rev. C 69, (2004). )
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 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) T. Inoue, E. Oset, M. J. Vicente Vacas, Phys. Rev. C J. A. Oller, E. Oset, J. R. Peláez, Phys. Rev. D (199) The KN system.
=1542 MeV Seems to show up in production
4 L. Roca, S. Sarkar, V. K. Magas and E. Oset, Phys. Rev. C 73, (2006). 5 S. Prakhov et al., Phys. Rev. C 69, (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.
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
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
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
´
Chiral amplitudes
= 0
where
We extend the procedure for the rest of diagrams involving more than three t-matrices Variables of the eqn: s, s 23
Σ(1660) P 11 [ I(J P )=1(1/2 + ) ] *** Results (S= -1 system, I=1)
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) Σ(1770)179024
Λ(1810) P 01 [ I(J P )=0(1/2 + ) ] *** 1750 to 1850 (~ 1810) OUR ESTIMATE Results ( S= -1 sytem,I =0 )
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 i 60/2 MeV
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.
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)
Γ (PDG) (MeV) Peak position (this work) (MeV) Γ (this work) (MeV) Isospin = 1 Σ(1560) Σ(1620) Σ(1660) Σ(1770) Isospin = 0 Λ(1600) ,170060, 136 Λ(1810) Summary Ref: A Martínez Torres, K. P. Khemchandani, E. Oset, Phys. Rev. C77:042203,2008; Eur. Phys. J. A35: ,2008 J p = ??
S= -1 sector → four Σ’s and two Λ’s resonances (all the 1/2 + Σ and Λ states in the energy region ) S=+1 → a bump around 1720 MeV with ~ 200 MeV of width, No resonance around 1540 MeV.