Kbar N N ????? ???????Faddeev???

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Kbar N N ????????????Faddeev???
???????_at_??????(8/5 09)

• ?? ??
• (?? / ??)

????? ?? ? (??)? ?? ?? (JLab)
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• ??

• ????(????????)
• Kbar N ???????
• ???????Faddeev???
• ??????
• ??????

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????
????K???????????????
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??????
?????????????!! (???????????)
???????????????????
??????????????????? ??????????????? ??????????????
??
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Controversial??????????
??????????
?(1405)
?????????????????????
?(1405)????????????????
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??????????????????
SU(3)???????????????????(Gell-Mann, Zweig
(1964)) ? ?????????????????????????
(valence ????)
valence ??????????????????(??????) ?????????????
??????????????
???????????
Isgur, Karl (1978), (1979) Glozman, Riska
(1996)
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???????????(1405)

• ???????????
• ?????????????????
• ????????????
• ?(1405)??????????????

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???????????(1405)
(?????)???-????????????? ?????????????????
???? ? T????(????)?pole(?)
???-????? ????????

• Chiral Dynamics
• Effective Hamiltonian Approach

Kaiser, Siegel, Weise Oset, Ramos Jido, Hyodo,
Hosaka
Veit et al. Siegel, Weise Hamaie et al.
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Controversial??????????
S-1,I0
?(1405)
??????????

• ??????????????????
• KbarN?????? (??????????)
• T????(1405)????????????
• ????????????????????
• (??????/??? ??)

??????Kbar N ????!!
Taken from Jidos talk
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????
Kbar N ?????3??(Kbar N N ????)????
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Kbar N N ????
Kbar N ????
??????? ( K???????(1405) )
Kbar N pS ???????
?(1405) ????

• KbarN ??????
• 2???????????(Jido et al.)
• Kbar N ?????????????

Kbar N N ????
Kbar N N pSN -p?N ???????
Akaishi, Yamazaki
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KbarN ???????
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• KbarN ???????(Weinberg-Tomozawa?)

Weinberg-Tomozawa term
F ???? , B ?????
Potential model (s-wave meson-baryon scattering)
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• 2???T??(????)

Lippmann-Schwinger equation
regularize loop integral
?????T??????(?)????????
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• KbarN ???????

Our parameters -gt cutoff of dipole form factor
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Resonance poles on KbarN-physical, pS-unphysical
sheet

• E-indep. potential model One resonance pole
• E-dep. potential model Two resonance poles
  (e.g. Jido et al.)

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• ?????(pS??)

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???????Faddeev???
Faddeev??? ? 3????????????
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• Faddeev???

Faddeev Equations

• W 3-body scattering energy
• i(j) 1, 2, 3 (Spectator particles)
• T(W)T1(W)T2(W)T3(W) (T 3-body amplitude)
• ti(W, E(pi)) 2-body t-matrix with spectator
  particle i
• G0(W) 3-body free Greens function

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• ???????????Faddeev???

Alt-Grassberger-Sandhas(AGS) Equations

• Z(pi,pjW) Particle exchange potentials
• t(pnW) Isobar propagators

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• 3??????????(?)?????

Fredholm kernel
Eigenvalue equation for Fredholm kernel
Formal solution for three-body amplitudes
three-body resonance pole at Wpole
Wpole -B iG/2
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??????
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• ?????????????????

L(1405) pole position
??????? 18 MeV, ???/2 19 MeV
KNN pole position
deeply bound state
-45.2-i21.7 MeV
BKppgt 2 BL
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• ?????????????????

L(1405) pole position (KN????)
??????? 13 MeV, ???/2 20 MeV
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• Summary

• The strange dibaryon resonance was studied in
  KbarNN - pYN system.
• We constructed the model of KbarN interaction
  from WT term.
• We solved the Faddeev equations.
• -- We found the resonance pole of strange
  dibaryon
• on KbarNN physical and
  pYN unphysical sheet.
• -- (-B, G) (-45 , 43)MeV
• for energy-independent KbarN
  interaction.
• -- (-B, G) (-14, 42) and (-71, 280)MeV
• for energy-dependent KbarN
  interaction.

• We can expect the energy dependence of the
  potential can be determined by J-PARC/E15
  experiment.

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• Future plan

Photo-production mechanism
reaction
This production mechanism is investigated by
LEPS and CLAS collaborations _at_SPring8, JLab.
Thank you very much for your attention!!
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• Future plan I (pS potential)

E-indep.
E-dep.
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• Model of baryon-baryon interactions

NN potential gt Two-term separable potential
Attraction
Repulsive core
YN potential gt One-term separable potential
Torres, Dalitz, Deloff, PLB174 (86)
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• Numerical results (Pole position of strange
  dibaryon)

KNN physical pSN unphysical energy plane
Martin
Martin -74.4-i33.6
Dalitz -62.9-i20.5
Hemingway -45.2-i21.7
Our results show deeper binding energy of strange
dibaryon than that of the L(1405).

• We find resonance pole of strange dibaryon.
• The energy of strange dibaryon strongly depends
  on KN interaction in I0.

BKppgt2BL
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• Comparison with other studies

• Faddeev equations -gt Full dynamics of KbarNN-pYN
  system
• Variational approach -gt pYN system is
  effectively included

In order to compare our result with DHWs
result, we calculate the energy of strange
dibaryon using cUM for KbarN amplitudes.
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• K-pp system in chiral unitary approach

The binding energy of the strange dibaryon is
shallow in cUM.
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