Exotic states in S=1 NK 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

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, 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).)

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.

1D. 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.

137+1405=1542 MeV

Seems to show up in production

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 data5, 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 ti and tj

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 ti and tj

And they satisfy the equations:

The Formalism

´

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

offjkoni VsVV )(

offij

joffki

jon

ijioffjk

ion

jiji

Vg

VsVgVsVVgV

/1

))(())((

= 0

where

We extend the procedure for the rest of diagrams involving more than three t-matrices

Variables of the eqn: s, s23

Σ(1660) P11 [ I(JP)=1(1/2+) ] ***

Results (S= -1 system , I=1)

Σ(1620) S11 [ I(JP)=??] **

Σ(1660) P11 [ I(JP)=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) 1590 70

Σ(1770) 1790 24

Λ(1810) P01 [ I(JP)=0(1/2+) ] ***1750 to 1850 (~ 1810) OUR ESTIMATE

Results (S= -1 sytem ,I =0)

Λ(1600) P01 [ I(JP)=0(1/2+) ] ***1560 to 1700 (~ 1600) OUR ESTIMATE

There are quite possibly two P01 states in this region.

1568 - i 60/2 MeV

We study KN system using the same formalism.

We take p 0K0, n 0K+, p −K+, n +K0 as coupled channels.

For which, we takeK+0, K0+, K+, 0p, +n, ηp charge +1.

K+ −, K0 0, K0 , −p, 0n, ηn charge 0. +K0, 0K+ for K charge +1.

−K+, 0K0 for K charge 0.

K0p, K+n charge +1

K0n 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) 10-100 1590 70

Σ(1620) 10-100 1630 39

Σ(1660) 40-200 1656 30

Σ(1770) 60-100 1790 24

Isospin = 0

Λ(1600) 50-250 1568,1700 60, 136

Λ(1810) 50-250 1740 20

Summary

Ref: A Martínez Torres, K. P. Khemchandani, E. Oset , Phys. Rev. C77:042203,2008; Eur. Phys. J. A35: 295-297,2008

Jp = ??

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.