K-中間子原子核研究の現状 Prototype of kaonic nuclei “K-pp” Akinobu Doté (IPNS/KEK) 1. Introduction • • Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological KbarN potential Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN) 2. Variational calculation of K-pp with a chiral SU(3)T. Hyodo (TITech), based KbarN potential W. Weise (TU Munich) 3. Recent status of the study of K-pp • • Theoretical side Experimental side 4. Summary and future plan JAEA seminar ’10.05.13 @ JAEA, Tokai, Japan 1. Introduction Expanding the nuclear world 原子核 = 陽子・中性子からなる有限量子多体系、 安定核 … 約300種 Large isospin 不安定核…約3000種、RIBF@理研で展開 http://www.rarf.riken.go.jp/newcontents/contents/facility/RIBF.html Expanding the nuclear world 原子核 = 陽子・中性子からなる有限量子多体系、 安定核 … 約300種 Large isospin 不安定核…約3000種、RIBF@理研で展開 Strangeness ハイパー核 … J-PARC (JAEA+KEK) で展開 Kaonic nuclei Another form of nuclear system with strangeness K- Nucleus containing K- meson Actors in Kbar nuclei Leading actors 1435Mc2 [MeV ] 1405 p N n 1325 938 940 Energy [MeV] 0 K Key person 498 K 494 K 1250 p + KΛ(1405) uud 1 1 Baryon J , I udd 2 2 Σ + π- bound state I=0 Proton-K with 30MeV binding energy? 1 ds Meson J 0 , Not I 3 quark 2 Λ + πstate? us ← can’t be explained with a simple quark model… Σ 1190 1115 1406 1 J , I 0 Λ 2 uds Baryon Excited state of Λ Supporting players ,0 ,0 1116 :1189, 0 :1193, 940 :1197 :140, 0 :135 1 J , I 0 2 Baryon 1 J , I 1 2 p,n Baryon J 0 , I 1 Meson uds : uus, 0 : uds, : dds : ud , 0 : 1 uu d d , : du 2 Actors in Kbar nuclei Leading actors 1435Mc2 [MeV ] 1405 p N n 1325 938 940 Energy [MeV] 0 K Key person 1 1 J , I 2 2 p + KΛ(1405) uud udd Baryon Σ+π 1 ds J 0 , I Λ + π Meson 2 Σπ channel is open us at about 100 MeV below Σ the Proton-K- threshold. 498 K 494 K 1250 1190 1115 1406 1 J , I 0 Λ 2 uds Baryon Excited state of Λ Supporting players ,0 ,0 1116 :1189, 0 :1193, 940 :1197 :140, 0 :135 1 J , I 0 2 Baryon 1 J , I 1 2 p,n Baryon J 0 , I 1 Meson uds : uus, 0 : uds, : dds : ud , 0 : 1 uu d d , : du 2 What is Kaonic nucleus? Kaonic nucleus • Bound by strong interaction • Inside of nucleus K• The nuclear structure may be changed, if the interaction is so attractive. Deeply bound below πΣ threshold (main decay channel) KNNN… Possible to exist as a quasi-bound state with narrow width ΣπNN… K nuclear state Studies with a phenomenological KbarN potential • Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002) Phenomenological KbarN potential (AY KbarN potential) 1. free KbarN scattering data 2. 1s level shift of kaonic hydrogen atom 3. binding energy and width of Λ(1405) Strongly attractive KN I 0 V Λ(1405) = I=0 K- p quasi-bound state with 27 MeV binding energy By a calculation of a few kaonic nuclei with a simple model, 3HeK- turns out to be deeply bound by 100MeV with a narrow width of 20MeV. Deeply bound kaonic nuclei ! • A. Doté, H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004) Systematic study of various light kaonic nuclei (3HeK- to 11CK-) with AMD + G-matrix (effective NN potential ) + AY KbarN potential shows their interesting properties… ① Deeply bound and Dense ppnK pppK pppnK 6 Be K 9 BK 11 CK - ② Drastic change of structure Kaon's B.E. [MeV] Width (πY ) [MeV] Averaged density [fm-3] 110.3 96.7 105.0 104.2 118.5 117.4 21.2 12.5 25.9 33.3 33.0 46.0 0.53 0.66 0.43 0.37 0.33 0.36 ③ Isovector deformation 8Be 8BeK- ④ proton satellite pppK- Theoretical studies of nuclear system with anti-kaons • Light nuclei with a single antikaon 3HeK- ~ 11CK- studied with AMD + G-matrix + AY potential E(K)≒100MeV • Light nuclei with double antikaons 3HeK-K- etc studied with AMD + G-matrix + AY potential E(2K)≒200MeV • Medium to heavy nuclei with multi-antikaons Studied with Relativistic Mean Field - D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007); PRC77, 045206 (2008) - T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009) … Antikaon part is based on non-linear chiral Lagrangian Strongly repulsive KbarKbar interaction Saturation for the number of antikaons In case of 15O+xK-, central nuclear density and –B/x are saturated for x>8. • Nuclear matter with antikoans Neutron star, kaon condensation… 2. Variational calculation of K-pp with a chiral SU(3)-based KbarN potential Are kaonic nuclei really exotic? •The phenomenological KbarN potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. AY potential Chiral SU(3) KbarN πΣ ηΛ KΞ Are kaonic nuclei really exotic? •The phenomenological KbarN potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. •The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed?? More theoretical study of the most essential kaonic nucleus K-pp system “Prototype of kaonic nuclei” studied with a chiral SU(3)-based KbarN potential K-pp Variational calculation of with a chiral SU(3)-based KbarN potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). 1E Strong repulsive core (3 GeV) K-pp Variational calculation of with a chiral SU(3)-based KbarN potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential Local KbarN potential based on Chiral SU(3) I=0 KbarN scattering amplitude T. Hyodo and W. Weise, PRC77, 035204(2008) Chiral Unitary Effective potential In Chiral unitary model, Resonance position in I=0 KbarN channel 1420 MeV not 1405 MeV ! 1420 Chiral unitary; T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003) K-pp Variational calculation of with a chiral SU(3)-based KbarN potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude I=0 Kbarobtained N resonance “Λ(1405)”appears with coupled channel chiral dynamics. at 1420 MeV, not 1405 MeV Single channel, Energy dependent, Complex, Gaussian-shape potential Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. J 0 , T 1/ 2, TZ 1/ 2 Kbar FKN1 N FKN2 FN N N L 0, S NN 0 Fij C ( ij ) a a 2 ( ij ) exp ba r i r j K-pp Variational calculation of with a chiral SU(3)-based KbarN potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude I=0 Kbarobtained N resonance “Λ(1405)”appears with coupled channel chiral dynamics. at 1420 MeV, not 1405 MeV Single channel, Energy dependent, Complex, Gaussian-shape potential Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. Four variants of chiral unitary modes Total B. E. G(KbarN→Y) × M N mK B K s M N mK B K 2 : 20 ± 3 MeV : 40 ~ 70 MeV Shallow binding and large decay width KbarN potential based on “HNJH” Structure of K-pp “Corrected”, Kbar N N s M N mK B K KbarN potential based on “HNJH” Structure of K-pp “Corrected”, Kbar 1.97 fm N N 2.21 fm Cf) NN distance in normal nuclei ~ 2 Size of deuteron fm ~ 4 fm s M N mK B K KbarN potential based on “HNJH” Structure of K-pp “Corrected”, Kbar 1.97 fm N NN distance = 2.21 fm KbarN distance = 1.97 fm Mixture of TN=0 component = 3.8 % N s M N mK B K KbarN potential based on “HNJH” Structure of K-pp “Corrected”, I=0 KbarN 1.82 fm Kbar l 2 0.4 N NN distance = 2.21 fm KbarN distance = 1.97 fm Mixture of TN=0 component = 3.8 % N s M N mK B K KbarN potential based on “HNJH” Structure of K-pp I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm l 2 0.4 l 2 1.9 N NN distance = 2.21 fm KbarN distance = 1.97 fm Mixture of TN=0 component = 3.8 % “Corrected”, Kbar N s M N mK B K KbarN potential based on “HNJH” Structure of K-pp I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm l 2 0.4 l 2 1.9 “Corrected”, s M N mK B K “Λ(1405)” as I=0 KbarN calculated with this potential 1.86 fm Kbar l 2 0.0 Almost “Λ(1405)” N NN distance = 2.21 fm KbarN distance = 1.97 fm Mixture of TN=0 component = 3.8 % N KbarN potential based on “HNJH” “Corrected”, s M N mK B K Structure of K-pp Density distribution: KbarN pair in K-pp vs “(1405)” “Λ(1405)” Kbar Isospin 0 KbarN pair N Isospin 0 “K-pp ” N Isospin 1 KbarN pair Kbar N Isospin 0 and 1 mixed “(1405)” almost survives in K-pp! K-pp Variational calculation of with a chiral SU(3)-based KbarN potential s-wave KbarN potential (Variational calculation) B .E. 20 ± 3 MeV • Dispersive correction (Effect of imaginary part) +6~ +18 MeV • p-wave KbarN potential ~ -3 MeV • Two nucleon absorption A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Width 40 ~ 70 MeV 10 ~ 35 MeV 4~ 12 MeV K-pp … Rough estimation Total B .E. Total Width 20 ~ 40 MeV 55 ~ 120 MeV Very large… 3. Recent status of the study of kaonic nuclei Prototype of kaonic nuclei “K-pp” Kbar nuclei = Exotic system !? To make the situation more clear … K-pp= Prototye of Kbar nuclei Studied with various methods, because it is a three-body system: •Doté, Hyodo, Weise •Akaishi, Yamazaki •Ikeda, Sato •Shevchenko, Gal , Mares •Wycech, Green Variational with ATMS with Faddeev with Faddeev with a chiral SU(3)-based a phenomenological a chiral SU(3)-derived a phenomenological All calculations predict that Variational with a phenomenological K •Arai, Yasui, Oka Λ* nuclei model continued by Uchino, Hyodo, Oka •Nishikawa, Kondo Skyrme model KbarN potential KbarN potential KbarN potential KbarN potential K-pp barN PRC79, 014003(2009) PRC76, 045201(2007) PRC76, 035203(2007) PRC76, 044004(2007) can be bound. potential (with p-wave) PRC79, 014001(2009) PTP119, 103(2008) PRC77, 055202(2008) There are several experiments: Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN) Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti) Recent results of calculation of K-pp and related experiments Width (KbarNN→πYN) [MeV] 0 20 40 60 80 100 120 140 0 Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) -20 -40 Akaishi, Yamazaki [2] (Variational, Phenomenological) -60 -80 Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Exp. : DISTO [6] (Finalized) -100 -120 Exp. : FNUDA [5] -140 [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010) Using S-wave KbarN potential constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Recent results of calculation of K-pp and related experiments Width (KbarNN→πYN) [MeV] 0 20 40 60 80 100 120 140 0 Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) -20 -40 Akaishi, Yamazaki [2] (Variational, Phenomenological) Wycech, Green [7] -60 (Variational, phenomenological, P-wave) Ikeda, Sato [4] -80 (Faddeev, Chiral SU(3)) Exp. : DISTO [6] (Finalized) -100 -120 Exp. : FNUDA [5] -140 [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010) Using S-wave KbarN potential constrained by experimental data. [7] PRC79, 014001 (2009) … KbarN scattering data, Including P-wave KbarN potential, Kaonic hydrogen atom data, and other effects. “Λ(1405)” etc. Recent results with various calculations of K-pp B. E. Γ (mesonic) Method KbarN Int. Channels at final step 20 ± 3 40 ~ 70 Variational Chiral SU(3) KbarN AY 47 61 Variational Phenom. KbarN IS 60 ~ 95 45 ~ 80 Faddeev (AGS) DHW SGM Exp. FINUDA DISTO 50~70 90 ~ 110 115±7 67±14 103±3±5 118±8±10 Faddeev (AGS) K- absorption, p+p→K++Λ+p, Chiral SU(3) (Separable) KbarN, πY Phenom. (Separable) KbarN, πY Λp inv. mass Λp inv. mass (Finalized) All four calculations shown above are constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave KbarN potential is used. Recent results with various calculations of K-pp B. E. Γ (mesonic) Method KbarN Int. Channels at final step 20 ± 3 40 ~ 70 Variational Chiral SU(3) KbarN AY 47 61 Variational Phenom. KbarN IS 60 ~ 95 45 ~ 80 Faddeev (AGS) DHW SGM 50~70 90 ~ 110 Faddeev (AGS) Chiral SU(3) (Separable) KbarN, πY Phenom. (Separable) KbarN, πY DHW vs AY Difference of the used KbarN interactions. Comparison of AY potential and Chiral-based potential Coupled channel Chiral dynamics AY potential Weinberg-Tomozawa term derived from Chiral SU(3) effective Lagrangian Two poles (double pole); one couples strongly to KbarN, KbarN strongly πΣ ηΛto πΣ. KΞ the other couples Λ(1405) = a quasi-bound state of I=0 KbarN at 1405MeV. Appears in I=0 KbarN channel. Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣ channel. I=0 KbarN resonance @ 1420MeV. I=0 KbarN resonance @ 1405MeV. • Energy independent potential • No πΣ-πΣ interaction • Energy dependent potential • Somewhat strongly attractive πΣ-πΣ interaction Comparison of AY potential and Chiral-based potential I=0 KbarN full scattering amplitude Quite different in the sub-threhold region Almost same in the on-shell region Recent results with various calculations of K-pp B. E. Γ (mesonic) Method KbarN Int. Channels at final step 20 ± 3 40 ~ 70 Variational Chiral SU(3) KbarN AY 47 61 Variational Phenom. KbarN IS 60 ~ 95 45 ~ 80 Faddeev (AGS) DHW SGM 50~70 90 ~ 110 Faddeev (AGS) Chiral SU(3) (Separable) KbarN, πY Phenom. (Separable) KbarN, πY DHW vs AY In Chiral SU(3) theory, the πΣ-πΣ interaction is so attractive to make a resonance, while AY potential doesn’t have it. “Λ(1405)” is I=0 KbarN bound state at 1420 MeV or 1405 MeV? AY potential is twice more attractive than Chiral-based one. Recent results with various calculations of K-pp B. E. Γ (mesonic) Method KbarN Int. Channels at final step 20 ± 3 40 ~ 70 Variational Chiral SU(3) KbarN AY 47 61 Variational Phenom. KbarN IS 60 ~ 95 45 ~ 80 Faddeev (AGS) DHW SGM 50~70 90 ~ 110 Faddeev (AGS) Chiral SU(3) (Separable) KbarN, πY Phenom. (Separable) KbarN, πY DHW vs IS Although both are based on Chiral SU(3) theory, results are very different from each other. • Separable approximation? • Different energy dependence of interaction kernel Vij? • πΣN three-body dynamics … may not be included in DHW. (Y. Ikeda and T. Sato, PRC79, 035201(2009)) Variational cal. vs Faddeev ??? Discrepancy between Variational calc. and Faddeev calc. The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory, but … Variational calculation (DHW) Faddeev calculation (IS) Total B. E. = 20±3 MeV, Decay width = 40~70 MeV Total B. E. = 60~95 MeV, Decay width = 45~80 MeV A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, 014003 (2009) Y. Ikeda, and T. Sato, Phys. Rev. C76, 035203 (2007) Why ? Separable potential used in Faddeev calculation? Non-relativistic (semi-relativistic) vs relativistic? Energy dependence of two-body system (KbarN) in the three-body system (KbarNN)? …??? Variational cal. vs Faddeev ??? Discrepancy between Variational calc. and Faddeev calc. The KbarNsystem potentials used in both areKbar constrained with Chiral SU(3) theory, Three-body calculated withcalculations the effective N potential but … K N Variational calculation K (DHW) N = EK bar NN Total B. E. = 20±3 MeV, Decay width = 40~conserved 70 MeV N N A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, 014003 (2009) K Faddeev calculation π π K (IS) … N N N N +… Σ E. = 60Σ~95 MeV, Total B. Decay width = 45~80 MeV Y. Ikeda, and T. Sato, Phys. Rev. C76, 035203 (2007) A possible reason is πΣN thee-body dynamics Y. Ikeda and T. Sato, PRC79, 035201(2009) In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective KbarN potential. Experiments related to K pp Experiments related to K-pp • FINUDA collaboration (DAΦNE, Frascatti) • K- absorption at rest on various nuclei (6Li, 7Li, 12C, 27Al, 51V) • Invariant-mass method p p K-p If it is K-pp, … Total binding energy = Λ Decay width = Strong correlation between emitted p and Λ (back-to-back) 6 3 115 5 4 MeV 2 67 14 MeV 11 3 Invariant mass of p and Λ PRL 94, 212303 (2005) Experiments related to K-pp • Re-analysis of KEK-PS E549 - K- stopped on 4He target - Λp invariant mass Strong Λp back-to-back correlation is confirmed. Unknown strength is there in the same energy region as FINUDA. T. Suzuki et al (KEK-PS E549 collaboration), arXiv:0711.4943v1[nucl-ex] • DISTO collaboration - p + p -> K+ + Λ + p @ 2.85GeV - Λp invariant mass - Comparison with simulation data K- pp??? B. E.= 103 ±3 ±5 MeV Γ = 118 ±8 ±10 MeV T. Yamazaki et al. (DISTIO collaboration), PRL104, 132502 (2010) Dr. Fujioka’s talk (KEK workshop, 7-9. Aug. 08) J-PARC will give us lots of interesting data! E15: A search for deeply bound kaonic nuclear states by 3He(inflight K-, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) 3Hemeasured. All emitted particles will be E17: Precision spectroscopy of kaonic atom 3d→2p X-rays --- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken) 4. Summary and future plan 4. Summary Kaonic nuclei are exotic system !? • Kaonic nuclei are another form of nuclear system involving strangeness. They might be exotic system because of the strong attraction of I=0 KbarN potential. • AMD calculation with G-matrix method using a phenomenological KbarN potential (AY potential) shows that kaonic nuclei may have lots of interesting properties: Deeply bound and narrow width dense system with interesting structure… • However, these properties have not been established and there are some questions. Variational calc. of K-pp with a chiral SU(3)-based KbarN pot. • B. E. =20±3 MeV, Γ(KbarNN → πYN) = 40 – 70MeV • With p-wave KbarN pot., dispersion correction, and two-nucleon absorption, B. E. =20 – 40 MeV, Γ = 55 – 120MeV • Two protons distance = 2.2fm ≒NN mean distance of normal nucleus • Λ(1405) structure (correlation) remains in K-pp. K-pp is a shallowly bound and not so dense system. 4. Summary Current status of studies of K-pp The most essential Kbar nuclei “K-pp” (KbarNN, Jp=1/2-, T=0) has been investigated in various ways. But the situation is still controversial… Theory Variational Variational Faddeev Faddeev + + + + Phenom. KbarN Chiral-based KbarN Phenom. KbarN Chiral-based KbarN B.E. = 47MeV, B.E. = 20±3MeV, B.E. = 50~70MeV, B.E. = 60~95MeV, Γ= 61MeV Γ= 40~70MeV Γ=~100MeV Γ= 45~80MeV PRC76, 045201(2007) PRC79, 014003(2009) PRC76, 044004(2007) PRC76, 035203(2007) Experiment (Unknown object which seems related to K-pp) FINUDA DISTO B.E. = 115MeV, B.E. = 103MeV, Γ= 67MeV Γ= 118MeV PRL94, 212303(2005) PRL104, 132502 (2010) … if it is K-pp Discrepancy between theoretical studies of K-pp • DHW (Variational with Chiral-based) vs AY (Variational with phenomenological) … Difference of KbarN attraction Λ(1420) scheme and Λ(1405) scheme • DHW (Variational with Chiral-based) vs IS (Faddeev with Chiral-based) … πΣN three-body dynamics (might be also different energy dependence of interaction kernel? ) 4. Future plan • What is the object measured experimentally? A bound state of K-pp, or another object such as πΣN ??? Only what we can say from only this spectrum is “There is some object with B=2, S=-1, charge=+1”… • Since the signal position is very close to π+Σ+N threshold, the πΣN degree seems important in the observed state. • As pointed out by Dr. Ikeda and Prof.Sato, the πΣN dynamics may be important. (especially, in case that K-pp is deeply bound???) Coupled channel Complex Scaling Direct treatment of πΣN degree, dealing with a resonant state, based on variational scheme. Thank you for your attention!
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