Current theoretical topics on K - pp quasi-bound state Sajjad MARRI and Toshimitsu YAMAZAKI  Theoretical interpretation of J-PARC E15 and E27 results  MESON2014, Krakow May 31, 2014 Yoshinori AKAISHI RIKEN Nishina Center, Japan

K - + p 123 r fm MeV  (1405) ++ ++ K - + pp 123 r fm MeV ++ ++ K He 123 r fm MeV ++ ++ Shrinkage! -500 N.V. Shevchenko, A. Gal & J. Mares, Phys. Rev. Lett. 98 (2007) E = -55~-70 MeV,  = 90~110 MeV Y. Ikeda & T. Sato, Phys. Rev. C 76 (2007) E = -80 MeV,  = 73 MeV A. Dote, T. Hyodo & W. Weise, Phys. Rev. C 79 (2009) E = MeV,  = 40~70 MeV Y. Akaishi & T. Yamazaki, Phys. Rev. C 65 (2002) T. Yamazaki & Y. Akaishi, Phys. Lett. B 535 (2002) 70 DA  NE Conf. (1999) "  (1405) Ansatz"

On the missing mass spectrum from 3 He(K -,n) E15 experiment n p K-K- p n p K-K- p 1.0 GeV/c etc.

Semi-inclusive neutron spectrum

KH(1): T. Koike & T. Harada, Phys. Lett. B 652 (2007) 262 (2): Phys. Rev. C 80 (2009) Theoretical works Phase space suppression factor (Mares-Friedman-Gal) for Im V opt (E) YJNH: J. Yamagata-Sekihara, D. Jido, H. Nagahiro & S. Hirenzaki, Phys. Rev. C 80 (2009) E=0 E=-100 MeV E=-50 MeV BE (Width) r [fm] [MeV] E-indep. E-dep. real part E-dep. imaginary part

3 He ( in-flight K -, n) reaction E(Kpp) MeV react-Kpi/h_Kn_Kpp.f Preliminary E15 behavior KH (2) YJNH (1) Ours  *+ p  p n p K-K- p n p K-K- p 1.0 GeV/c

K-K- N N Variational wave function of K - pp  *p ATMS Amalgamation of Two-body correlations into Multiple Scattering process Euler-Lagrange equation

N-N distance 2.0 fm Covalent part K - distribution in K - pp  close to free  *(I =0,K - p) Free  * K bar N in  K - pp I = 0 I = 1 "Snapshot" Covalent bonding Direct integralExchange integral “Kaonic hydrogen molecule”

Heitler-London-Heisenberg picture of K - pp  1405) p K _ pp K _ [MeV ] K - pp [MeV] p ** ** p + [ ] Real K bar migrating superstrong interaction  KE = 52  V NN = -19  E = -20  V exc = Covalent bonding Exchange integral a pK bb pK a --  vv  Y. Akaishi, T. Yamazaki, M. Obu and M. Wada, Nucl. Phys. A 835 (2010) 67

Adiabatic p-p potential in K - pp R [fm] [MeV fm 2 ] Normal nuclear force : virtual meson exchange R 2 V(R) pp K-K- Super-strong nuclear force : real K bar migration Super strong / Normal ~ 4.1  volume integral ratio  p p

T. Yamazaki & Y. Akaishi, Proc. Japan Academy, B 83 (2007) 144  *N system with meson exchange A. Arai, M. Oka & S. Yasui, Prog. Theor. Phys. 119 (2008) 103

K - pp quasi-bound state pp K-K fm rms distance 1.36 fm n p K-K- p n p K-K- p 1.0 GeV/c n p K-K- p n ** p

T. Hashimoto p n =0 p n =1000 MeV/c p n =1494 MeV/c p n =1254 MeV/c p n =  = Stopped K : Fermi motion of n "n-knockout window" p n observed ! p Y n 1000 MeV/c - p n n 1000 MeV/c K-K- p p  2812 MeV for p n = MeV for p n =1000 MeV/c -540,1540 MeV/c 0,-494 MeV/c QF-  “n-spectator window”

 *+ p  p  *+ p  p  *p int. Missing mass spectrum of  *-p system   * width + Decay phase volume + "Auger suppression" No  * width by Green's function method QF-  * Green's function with smearing I. Kumagai-Fuse & Y. Akaishi, Prog. Theor. Phys. 92 (1994) 815 n p K-K- p n ** p

AGS calculation of K - pp quasi-bound state S. Ohnishi, Y. Ikeda, H. Kamano & T. Sato, Phys. Rev. C 88 (2013) p i = p j = 100 MeV/c 150 MeV/c  *+ p

1-particle exchange interactionIsobar propagator by S. Marri 50 MeV/c 100 MeV/c 150 MeV/c 200 MeV/c E(Kpp) MeV  *+ p

Missing mass spectrum of  *-p system MM MeV/c 2 react-Kpi/h_Kn_Mod5B.f DISTO int. YA int. No  *p int. Without  * width With  * width of 50 MeV  *+ p  p QF-  * K - + p + p QF- K (0.3,1.0) X 1/5 Faddeev - AGS

Semi-inclusive neutron spectrum T. Hashimoto

Semi-inclusive neutron spectrum Very preliminary ! Higher mom. p ?

On the missing mass spectrum from D(  +,K + ) E27 experiment n ++ p K+K+ Y, Y* p 1.7 GeV/c etc.

Y. Ichikawa et al., Proc. Science (Nara Conf. 2013) Inclusive spectrum

MM [MeV/c 2 ] ** **  Missing mass spectrum of  *-p system  *-p quasi-bound state

QF-   + Simulation by Y. Ichikawa No width Mass distribution Decay width

QF-   Mass distribution Decay width HADES fit Simulation by Y. Ichikawa Decay width

MM [MeV/c 2 ]   = 50 MeV YA int.   = 50 MeV DISTO int.   = 0 No  *p int.   = 50 MeV No int.  *+ p  p Missing mass spectrum of  *-p system for  -  conversion "K - pp"  *-p QBS S. Maeda, Y. Akaishi & T. Yamazaki, Proc. Jpn. Acad. B 89 (2013) 418 Proton (> 280 MeV/c) coincidence by T. Nagae et al.

[MeV] 10% 20% enhanced PDG DISTO FINUDA Energies of few-body kaonic systems calculated by Faddeev-Yakubovsky method (FOPI) FINUDA DISTO PDG  *(1420) S. Maeda, Y. Akaishi & T. Yamazaki, Proc. Jpn. Acad. B 89 (2013) 418

FINUDA M. Agnello et al., Phys. Rev. Lett. 94 (2005) Y. Ichikawa et al., Proc. Science (Nara Conf. 2013) DISTO T. Yamazaki et al., Phys. Rev. Lett. 104 (2010) K - pp =  *-p with real K bar migration (17% enhanced int.) Preliminary !

K-K- K+K+ pp K - pp structure K-K- K+K+ ** p p  *- p structure n p ++ Y. Ichikawa et al., Proc. Science (Nara Conf. 2013) K - pp =  *-p with real K bar migration (17% enhanced int.) Preliminary !

** K-K- p Concluding remarks The  *  (1405) plays an essential role in forming "anti-Kaonic Nuclear Clusters", the simplest one of which is K - pp  (K - p)  p  *  p. The  *  p structure interacting with "super-strong force" due to K bar migration provides a possible explanation of recent J-PARC data on K - pp.

Thank you very much! Acknowledgments Y. Ichikawa

T. Yamazaki, S. Hirenzaki, R.S. Hayano & H. Toki, Phys. Rep. 514 (2012) 1 K. Suzuki et al., Phys. Rev. Lett. 92 (2004) Isovector s-wave  N scattering length, b 1 [m  -1 ] Quark condensate decreases by ~30% at  0. Deeply bound pion Evidence for partial restoration of chiral symmetry in nuclear medium

Enhancement of interaction Enhancement of physical quantity Binding energy Potential energy Kinetic energy Higher-order effect (Unit in MeV) Enhancement effects by strongly attractive interaction on physical quantities in K - p bound state Attractive interaction is enhanced; L1405/rangeKE.f

Nogami (1963) MeV K - + p + p threshold MeV  * + p threshold is used. Yamazaki-Akaishi (2002) i 20.0 MeV MeV MeV Possible existence of K bar NN bound state ~ 330 MeV A huge escape width ! MeV Nogami missed the ground state. S. Maeda This state should not be referred to as K - pp.

 *N bound state A. Arai, M. Oka & S. Yasui, Prog. Theor. Phys. 119 (2008) 103 T. Uchino, T. Hyodo & M. Oka, Prog. Theor. Phys. Suppl. 186 (2010) 240 S=1

N.V. Shevchenko, Phys. Rev. C 85 (2012) M inv [MeV/c 2 ]   1405) Weise/amyTm2.f I  0 imaginary part (total cross section) K bar N scattering amplitude

n p K-K- p n Y p n p K-K- p n Y p "Hard" process of Y formation n-spectator 1.0 GeV/c "Soft" process of Y formation Very small contribution ! a = fm -2, s = , t = 12 GeV/c (Stopped K - ) n 1000 MeV/c n 1198 MeV/c -198 MeV/c K-K- n-knockout D-03 Fermi motion 0

Missing mass spectrum of  *-p system MM [MeV/c 2 ]

 (1405) from HADES G. Agakishiev et al., Phys. Rev. C 87 (2013) M. Hassanvand et al., Phys. Rev. C 87 (2013) PDG 14

V.K. Magas, E. Oset, A. Ramos & H. Toki, Phys. Rev. C 74 (2006) FINUDA M. Agnello et al., Phys. Rev. Lett. 94 (2005)  p invariant mass from K - pp p  >90% "OT point" K - + p + p

From K - direct capture on pp with FSI Angular dependence of K -4 He ->  +p+n+n A huge spike must appear at OT point! MORT's artificial procedure inevitably produces a peak-like fake structure. T. Yamazaki & Y. Akaishi, Nucl. Phys. A 792 (2007) 229. V.K. Magas, E. Oset, A. Ramos & H. Toki,