on the analytic structure of the kn - ps scattering amplitudes
DESCRIPTION
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.). K -. p. p. Connection with meson-baryon dynamics and L (1405). Motivation. - PowerPoint PPT PresentationTRANSCRIPT
On the analytic structure of On the analytic structure of the the KNKN - - scattering amplitudes scattering amplitudes
Hiroyuki Kamano Hiroyuki Kamano
(Excited Baryon Analysis Center, Jefferson Lab)(Excited Baryon Analysis Center, Jefferson Lab)
in collaboration within collaboration with
Yoichi Ikeda, Toru SatoYoichi Ikeda, Toru Sato
(Osaka Univ.)(Osaka Univ.)
Are there 3-body resonance
states in ?
Motivation
K-
p
p
NN NN, YN YN
KN KN, KN , …
Connection with meson-baryon dynamics and (1405)
e.g.) FINUDA collaboration PRL94 212303 (2005)
To explore few-body systems like K-pp,need reliable information on two-body amplitudes:
( Few-body systems could access (1405) )
Data points
Precision
Total cross section Angular distribution Polarization …
Data points
Precision
Total cross section Angular distribution Polarization …
We DO NOT have enough data to construct a reliable model givingquantitative evaluations/predictionsof amplitudes and resonance polepositions !
Symmetries
Dynamics
Approximations
Symmetries
Dynamics
Approximations
Extracting scattering amplitudes
Amplitudes( Output )
ModelData
( Input )
Quasi-bound state of KN system
CDD pole coupling with mesons
Quasi-bound state of KN system
CDD pole coupling with mesons
Models of KN- reactions and (1405)a
Large error bars
Total cross sections (only?)
Examine using Lippmann-Schwinger approach
with Weinberg-Tomozawa term (potential)
Examine using Lippmann-Schwinger approach
with Weinberg-Tomozawa term (potential)
Weinberg-Tomozawa Potential
Fixed with SU(3) symmetryFixed with SU(3) symmetry
S-wave projection
Original:Weinberg, PRL17 616 (1966)
Tomozawa Nuov. Cim. 46A 707(1966)Chiral Lagrangian:
e.g., Bernard, Kaiser, Meissner IJMP E4 193 (1995)
meson
baryon
(S-wave) Lippmann-Schwinger equation:
Approximations in WT potential
Energy-dependent potential (E-dep.)
Weinberg-Tomozawa potential (WT)
Energy-independent potential (E-indep.)
Ikeda, Sato PRC76 035203 (2007)Ikeda, Sato PRC76 035203 (2007)e.g., Oset, Ramos NPA635 99 (1998)e.g., Oset, Ramos NPA635 99 (1998)
Cutoff factors
Introduced to regularize loop integral
Introduced to regularize loop integral
Data-fitting
Obtained from a simple model analysis of
Not “observable” !!
Magnitude is arbitrary.
Obtained from a simple model analysis of
Not “observable” !!
Magnitude is arbitrary.
Large error barsLarge error bars
Few data pointsFew data points
WT E-indep. E-dep.
810 1100 1100
550 1100 1100
Pole positionsAnalytic structure on KN-physical (1st-Riemann), -unphysical (2nd-Riemann) sheetAnalytic structure on KN-physical (1st-Riemann), -unphysical (2nd-Riemann) sheet
E-dep.E-dep. E-indep.E-indep.
WTWT
Pole Trajectory
×××
E-indep.E-indep.E-dep.E-dep.
WTWT
Re[E] (MeV)
Varying - coupling constantVarying - coupling constant
1250 1300 1350 1400 14501250 1300 1350 1400 1450
×
0
-50
-100
-150
0
-50
-100
-150
Re[E] (MeV)
× ××
Im[E
] (M
eV
)
Im[E
] (M
eV
)
Summary
Examined the analytic structure of the KN- 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!!