1. On the analytic structure of the KN - pS scattering amplitudes
Hiroyuki Kamano
(Excited Baryon Analysis Center, Jefferson Lab)
in collaboration with
Yoichi Ikeda, Toru Sato
(Osaka Univ.)

2. Motivation To explore few-body systems like K-pp,
need reliable information on two-body amplitudes:
NN  NN, YN  YN
KN  KN, KN  pS, … K- p p
Connection with
meson-baryon dynamics and L(1405)
Are there 3-body resonance
states in ?
e.g.) FINUDA collaboration
PRL (2005)
( Few-body systems could access L(1405) )

3. Extracting scattering amplitudes
Data
( Input )
Amplitudes
( Output )
Model
We DO NOT have enough data to
construct a reliable model giving
quantitative evaluations/predictions
of amplitudes and resonance pole
positions !
Data points
Precision
Total cross section
Angular distribution
Polarization … a
Large error bars
Total cross sections (only?)
Examine using Lippmann-Schwinger approach
with Weinberg-Tomozawa term (potential)
Quasi-bound state of KN system
CDD pole coupling with mesons
Models of KN-pS reactions and L(1405)
Symmetries
Dynamics
Approximations

4. Weinberg-Tomozawa Potential
Original:
Weinberg, PRL (1966)
Tomozawa Nuov. Cim. 46A 707(1966)
Chiral Lagrangian:
e.g., Bernard, Kaiser, Meissner
IJMP E4 193 (1995)
meson
baryon
Fixed with SU(3) symmetry
(S-wave) Lippmann-Schwinger equation:
S-wave projection

5. Approximations in WT potential
Weinberg-Tomozawa potential (WT)
Energy-dependent potential
(E-dep.)
Energy-independent potential
(E-indep.)
e.g., Oset, Ramos NPA (1998)
Ikeda, Sato PRC (2007)

6. Cutoff factors
Introduced to regularize loop integral

7. Data-fitting WT E-indep. E-dep. 810 1100 550 Large error bars
Obtained from a simple model
analysis of
 Not “observable” !!
Magnitude is arbitrary.
Few data points

8. Pole positions
Analytic structure on KN-physical (1st-Riemann), pS-unphysical (2nd-Riemann) sheet WT
E-dep.
E-indep.

9. Pole Trajectory × Varying pS-pS coupling constant × × × × WT E-dep.
E-indep. ×
-50
-100
-150 ×
-50
-100
-150 × ×
Im[E] (MeV)
Im[E] (MeV)
Re[E] (MeV)
Re[E] (MeV)

10. Summary
Examined the analytic structure of the KN-pS amplitudes obtained from
solving Lippmann-Schwinger equations using
WT potential and its two different approximations
Within the available data, approximations can make a drastic change
in the analytic structure of the amplitudes.
Also, within the current situation, ONLY the pole around 1420 –i15 MeV
looks “model independent”.
Need much more data to constrain models and
make them reliable for quantitative evaluations/predictions.
J-PARC will be a capable facility to provide such data!!