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Chiral dynamics を尊重した場合の ppK -

Chiral dynamics を尊重した場合の ppK -. ´. A. Dote (KEK), W. Weise (TU Munich). ( How is ppK - if we respect Chiral SU(3) dynamics? ). T. Hyodo (TU Munich / YITP). arXiv:0806.4917v1. Introduction Model - Simple Correlated Model (Revised) - Local K bar N potential based on Chiral SU(3)

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Chiral dynamics を尊重した場合の ppK -

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  1. Chiral dynamicsを尊重した場合の ppK- ´ A. Dote (KEK), W. Weise (TU Munich) ( How is ppK- if we respect Chiral SU(3) dynamics? ) T. Hyodo (TU Munich / YITP) arXiv:0806.4917v1 • Introduction • Model- Simple Correlated Model (Revised) - • Local KbarN potential based on Chiral SU(3) • Result • Summary and future plan “Physics at J-PARC: New aspects of hadron and nuclear studies” 　’08.08.07 @ KEK 3rd building Seminar hall

  2. １．Introduction I=0 KbarN potential … very attractive Highly dense state formed in a nucleus Interesting structures that we have never seen in normal nuclei… K- Akaishi, Yamazaki ATMS B.E. = 47MeV, Γ= 61MeV PRC76, 045201(2007) Ikeda, Sato Faddeev B.E. = 79MeV, Γ= 74MeV PRC76, 035203(2007) Shevchenko, Gal Faddeev B.E. = 50～70MeV, Γ=～100MeV PRC76, 044004(2007) Arai, Yasui, Oka (Λ* nuclei model), Nishikawa, Kondo (Skyrme model), Noda, Yamagata, Sasaki, Hiyama, Hirenzaki (Variational method) … FINUDA experiment B.E. = 116MeV, Γ= 67MeV PRL94, 212303(2005) Kbarnuclei = Exotic system !? To make the situation more clear … ppK- = Prototye of Kbar nuclei Studied with various methods, because it is a three-body system:

  3. １．Introduction We also study ppK- with … • Av18 NN potential … a realistic NN potential with strong repulsive core. • KbarN potential based on Chiral SU(3) theory …Well describe S=-1 meson-baryon scattering and dynamical generation of Λ(1405) • Variational method … Investigate various properties with the obtained wave function.

  4. ２．Model Thanks, Akaishi-san! NN correlation function Single-particle motion Nucleon KN correlation function Kaon Model wave functionー Simple Correlated Model (Revised) ー NN in : 1E, TN=1 ppK- NN in : 1O, TN=0 NN correlation is directly treated.

  5. ２．Model Influence of the improvement TN=1 + TN=0 TN=1 only Additional KbarN attraction NN potential…Tamagaki potential Effective KbarN potential … Akaishi-Yamazaki potential

  6. ２．Model NN potential…Av18 potential • Fitted with a few range Gaussians. • Use one-pion-exchange potential (Central and Spin-Spin) and • L2 potentials in addition to phenomenological central term • (= repulsive core). Centralpotential 1O 1E Strong repulsive core (3 GeV)

  7. ３．Local KbarN potential based on Chiral SU(3) T. Hyodo and W. Weise, PRC77, 035204(2008) 1. Chiral unitary / Relativistic / Coupled Channel 2. Chiral unitary / Relativistic / Single Channel • Energy dependent • Complex 3. Effective local potential / Non-relativistic / Single Channel • Energy dependent • Complex • Local, Gaussian form “Corrected version” ; Energy-dependence improved in low-energy region

  8. ３．Local KbarN potential based on Chiral SU(3) In Chiral unitary model, Resonance position in I=0KbarN channel 1420 MeV not 1405 MeV ! I=0KbarN scatteing amplitude “Uncorrected” “Corrected” Chiral Unitary 1420 Chiral unitary;T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003)

  9. ４．Result • Hamiltonian treated perturbatively. Kbar N N • Try two prescriptions for . Kbar is bound by each nucleon with B(K)/2 binding energy. Notes on actual calculation Kbar N N • Self-consistency on anti-kaon’s energy Controlled by “Anti-kaon’s binding energy” : Hamiltonian of nuclear part Kbar field surrounds two nucleons which are almost static.

  10. ４．Result I=0 channel I=1 channel Notes on actual calculation • Four Chiral unitary models: • “ORB” E. Oset, A. Ramos, and C. Bennhold, Phys. Lett. B527, 99 (2002) • “HNJH” T.Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003) • “BNW” B. Borasoy, R. Nissler, and W. Weise, Eur. Phys. J. A25, 79 (2005) • “BMN” B. Borasoy, U. G. Meissner, and R. Nissler, Phys. Rev. C74, 055201 (2006) 1420

  11. ４．Result Total Binding Energy and Decay Width ORB HNJH BNW BMN × × Corrected Small model and ansatz dependence Total B. E. : 20 ± 3 MeV Γ（KbarN→πY） : 40 ～ 70 MeV

  12. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Kbar N N

  13. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Cf) NN distance in normal nuclei ～ 2 fm Size of deuteron ～ 4 fm Kbar 1.97 fm N N 2.21 fm

  14. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Kbar N N TN=1 … 96.2 % TN=0 … 3.8 % T = 1/2 • NN distance = 2.21 fm KbarN distance = 1.97 fm

  15. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Kbar 1.97 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  16. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, I=0 KbarN 1.82 fm Kbar N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  17. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Kbar I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  18. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, “Λ(1405)” as I=0 KbarN calculated with this potential 1.86 fm I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm Kbar Almost “Λ(1405)” N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  19. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Density distribution NN pair in ppK- vs Deuteron Suppressed by NN repulsive core Quite compacter than deuteron

  20. Structure of ppK- KbarN potential based on “HNJH” “Corrected”, Density distribution KbarN pair in ppK- vs Λ(1405) For comparison, All densities are normalized to 1. Rather similar. Λ(1405) Very different. The I=1 component distributes widely. I=0 in ppK- I=1 in ppK-

  21. Other effects B .E. Width • s-wave KbarN potential 20 ± 3 MeV 40 ～ 70 MeV • Dispersive correction • (Effect of imaginary part) ～ +10 MeV ～ -3 MeV 10 ～ 35 MeV • p-wave KbarN potential 4～ 12 MeV • two nucleon absorption Rough estimation B .E. Width ～ 25 MeV 55 ～ 120 MeV

  22. ５．Summary NN potential = Av18 potential … Strongly repulsive core Spin-spin, L2 terms KbarN potential = Local potential based on Chiral unitary model … Scattering amplitude is reproduced. Single Gaussian form Strong energy dependence Simple correlated model (Revised) … Respect Short-range correlation. Contain TN=0 component as well as TN=1 component. Four Chiral unitary models and Two prescriptions on B(K) Total Binding energy = 20 ± 3 MeV Γ(KbarN → πY) = 40 ～ 70 MeV … Very shallow binding ppK- is studied with +

  23. ５．Summary Contribution of other effects • Dispersive correction: ～ +10MeV to B.E. • p-wave KbarN potential: ～ -3MeV to B.E. , 10 ～ 35MeV to width • Two nucleon absorption: 4 ～ 12MeV to width Structure of ppK- • NN distance in ppK- is smaller than that of deuteron, • rather comparable to that in normal nuclei. NN distance = ～2.2 fm KbarN distance = ～2.0 fm • TN=0 component is slightly (～ 4%) mixed, while TN=1 is dominating in ppK-. • Calculating the size and orbital angular momentum of I=0 KbarN component, • it is found to be very similar to the isolated I=0-KbarN bound system, “Λ(1405)”. I=0 KbarN in ppK- is almost “Λ(1405)” ! … This picture doesn’t contradict with Akaishi-san’s one. PRC76, 045201(2007)

  24. 5．Future plan • Understanding of the difference between our result and • those obtained by other groups. Especially, comparison with Faddeev (Ikeda-san and Sato-san) study Total B. E. = 79 MeV, Decay width = 74 MeV Their KbarN interaction is also constrained by Chiral SU(3) theory. However, it differs from ours very much. Separable potential? Non-relativistic (semi-relativistic) vs relativistic? Energy dependence of two-body system (KbarN) in the three-body system (KbarNN)? …???

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