Current theoretical topics on Kpp quasi-bound...

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Current theoretical topics on K - pp quasi-bound state in collaboration with Sajjad MARRI and Toshimitsu YAMAZAKI −−− Theoretical interpretation of the results of E15 and E27 −−− KEK Tokai March 5, 2014 Yoshinori AKAISHI

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  • Current theoretical topics onK-pp quasi-bound state

    in collaboration withSajjad MARRI and Toshimitsu YAMAZAKI

    −−− Theoretical interpretation of the results of E15 and E27 −−−

    KEK TokaiMarch 5, 2014

    Yoshinori AKAISHI

  • -500 -500

    K- + p

    MeV -27K =EMeV 04=Γ

    1 2 3 r fm0

    -50

    -200

    -300

    -400

    -500

    nuclKU

    MeV

    Λ(1405)Σ+π

    Λ+π

    K- + pp

    MeV-48K =EMeV61=Γ

    1 2 3 r fm0

    -50

    -200

    -300

    -400

    nuclKU

    MeV

    H2KΣ+π

    Λ+π

    K- + 3He

    MeV-108K =EMeV02=Γ

    1 2 3 r fm0

    -50

    -200

    -300

    -400

    nuclKU

    MeV

    H3KΣ+π

    Λ+π

    Shrinkage!

    N.V. Shevchenko, A. Gal & J. Mares, Phys. Rev. Lett. 98 (2007) 082301E = -55~-70 MeV, Γ = 90~110 MeV

    Y. Ikeda & T. Sato, Phys. Rev. C 76 (2007) 035203E = -80 MeV, Γ = 73 MeV

    Y. Akaishi & T. Yamazaki, Phys. Rev. C 65 (2002) 044005T. Yamazaki & Y. Akaishi, Phys. Lett. B 535 (2002) 70

    DAΦNE Conf. (1999)

    "Λ(1405) Ansatz"

  • Nogami (1963)

    0

    -11.5 MeV

    K-+ p + p threshold

    -29.9 MeVΛ* + p threshold

    )3(41 1

    NK0

    NKaveNK

    == += II VVVis used.

    ( )[ ] 2/11NNK == TI

    ( )[ ] 2/11NNK == TI

    Yamazaki-Akaishi (2002)

    -27.8- i 20.0 MeV

    - 48.0 MeV61conv =Γ MeV

    Possible existence of KbarNN bound state

    ( )escapeΓ ~ 330 MeVA huge escape width !

    - 60.3 MeVNogami missed the ground state.

    S. Maeda

    This state should not be referred to as K-pp.

  • On the missing mass spectrumfrom 3He(K-,n) E15 experiment

    January 24, 2014March 1; revised

  • KH(1): T. Koike & T. Harada, Phys. Lett. B 652 (2007) 262

    KH(2): T. Koike & T. Harada, Phys. Rev. C 80 (2009) 055208

    Other theoretical works

    Phase space suppression factor (Mares-Friedman-Gal)for Im Vopt(E)

    YJNH: J. Yamagata-Sekihara, D. Jido, H. Nagahiro& S. Hirenzaki, Phys. Rev. C 80 (2009) 045204

    NNK EtEV ρ⋅∝ )()(opt

    E=0

    E=-100 MeV

    E=-50 MeV

    BE (Width)

    r [fm]

    [MeV

    ]

    E-indep.

    NNKvV ρ⋅∝eff.

    opt

    ?

    ψϕ vt =

  • K-pp quasi-bound stateT. Koike & T. Harada, Phys. Rev. C 80 (2009) 055208

    3He ( inflight K- , n )

    YADHW

    SGM FINUDA

  • 3He (in-flight K-, n) reaction

    -200 -150 -100 -50 0 50 100

    E(Kpp) MeV

    L=0

    L=0-1

    L=0-2L=0-5

    react-Kpi/h_Kn_Kpp.f

    YA

    np

    K-

    p

    n

    pK-

    p

    1.0 GeV/c

  • 3He (in-flight K-, n) reaction

    -200 -150 -100 -50 0 50 100

    E(Kpp) MeV

    react-Kpi/h_Kn_Kpp.f

    PreliminaryE15

    KH(2)

    YJNH

    KH(1)

    OursΛ

    *+ p

    Σ +π

    + p

  • -200 -150 -100 -50 0 50 100

    E(Kpp) MeV

    pp-Kpp-KRpp-K ---ImRe ViVfV +→

    fR =1.41.2

    1.00.8

    0.6

    3He (in-flight K-, n) reaction

    PreliminaryE15

    No K-pp interaction

    Λ*+

    p

    Σ +π

    + p

  • Momentum transfer to K-−pp relative motion

    react-Kpi/h_Kn_Mod4.f

    0

    100

    200

    300

    400

    500

    600

    2200 2250 2300 2350 2400 2450

    M.M. [MeV/c2]

    [MeV/c]

    n emission

    Δ(1232)

    emission

    N(1440

    ) emi

    ssion

    Q

    °= 0Labθ

    np

    K-

    p

    n, Δ, N*

    pK-

    p

    1.0 GeV/c

    Q

    stimulated byY. Sada's analysis

  • 2200 2250 2300 2350 2400 2450

    3He (in-flight K-, n or Δ or N*)

    (4) (1)

    (2)

    (5)

    (1) YA : n-emission(2) DISTO : n-emission(3) YA : Δ-emission(4) DISTO : Δ-emission

    M.M. [MeV/c2]

    [K-pp]

    °= 0Labθ

    (5) YA : N*-emission(6) DISTO : N*-emission

    (3)(6)

    I.M. = M.M.

    react-Kpi/h_Kn_Mod4.f

  • K-

    NN

    1

    2 3

    43ˆ,

    41ˆ NK1

    12NK0

    12ττττ rrrr +

    =−

    = == II PP

    Variational wave function of K-pp

    ( )[ ] ( ) ( ) ⎥⎦

    ⎤⎢⎣

    ⎡+−+== 3

    1,1213

    0,1213

    0,021 3

    231

    41

    432/1 nNKpNKpNKT

    Λ*p

    ATMS Amalgamation of Two-body correlations into Multiple Scattering process

    { } { }[ ] 2/1ˆ)(ˆ)()()()()(ˆ)(ˆ)( 13131103131023NN123123NN112121012120 =+++=Ψ ======== TPrfPrfrfrfrfrfPrfPrf IIIIIIII

    { } { }{ } { }2fmMeV1NK

    2fmMeV

    0NK

    )66.0/(exp105175)(

    )66.0/(exp83595)(

    rirv

    rirvT

    T

    −−−=

    −−−==

    =

    { } { } { }2fmMeV2fmMeV2fmMeVNN )5.2/(exp5)942.0/(exp270)447.0/(exp2000)( rrrrv −−−−−=

    { } 0=− ΨΨλΨΨδ HfEuler-Lagrange equation

  • K-pp quasi-bound state

    pp K-

    1.90 fmrms distance

    1.36 f

    m

    Which is the main component?

    DISTO

    0

    -40

    -80

    -120

    -160

    -200

    -240

    [MeV]

    K-pp L=0ground state

    (Λ*-p or K--pp)

    K--pp L=1excited state

    Λ*-p L=1excited state

    K- + p + pΛ*+ p

    Stronger KN attraction

    2002

    2007

  • Heitler-London-Heisenberg picture of K-pp

    iPEKE

    iE

    0.201.1433.115

    0.208.27

    −−

    −−

    Λ(1405)

    p K_

    pp K_

    [MeV]K-pp

    [MeV]

    pΛ* Λ*p+21 [ ] iv

    ivv

    iPEKE

    iE

    3.76.522

    3.230.14320.19

    6.305.2140.167

    6.305.47

    excNK

    dirNK

    NN

    −−

    −−

    −−−

    −−

    Real Kbar migratingsuperstrong interaction

    ΔKE = 52

    ΔVNN = -19

    ΔE = -20

    ΔVexc = -53

    -33

    Covalent bonding

    Exchange integralapKbbpKa --

    φφφφ vv +

    Y. Akaishi, T. Yamazaki, M. Obu and M. Wada, Nucl. Phys. A 835 (2010) 67

  • Adiabatic p-p potential in K-pp

    -200

    -150

    -100

    -50

    0

    50

    100

    150

    0.0 0.5 1.0 1.5 2.0 2.5 3.0

    R [fm]

    [MeV fm2]

    1.0 2.0 3.0

    Normal nuclear force : virtual meson exchange

    R2 V(R)

    pp K-

    Super-strong nuclear force : real Kbar migration

    Super strong / Normal ~ 4.1− volume integral ratio −

    pp

  • T. Yamazaki & Y. Akaishi,Proc. Japan Academy, B 83 (2007) 144

    Λ*N system with meson exchangeA. Arai, M. Oka & S. Yasui,

    Prog. Theor. Phys. 119 (2008) 103T. Uchino, T. Hyodo & M. Oka,

    Prog. Theor. Phys. Suppl. 186 (2010) 240

  • AGS calculation of K-pp quasi-bound stateS. Ohnishi, Y. Ikeda, H. Kamano & T. Sato, Phys. Rev. C 88 (2013) 025204

    pi = pj = 100 MeV/c

    150 MeV/c

    Λ*+

    p

    23702270 2343

    NNK

  • 1-particle exchange interaction Isobar propagator

  • 2280 2310 2340 2370

    AGS calculation of Λ*-p quasi-bound stateby Sajjad Marri

    Conversion

  • 2200 2250 2300 2350 2400 2450

    Λ*+

    p

    Σ +π

    + p

    2200 2250 2300 2350 2400 2450

    Λ*+

    p

    Σ +π

    + p

    Λ*p int.

    Missing mass spectrum of Λ*-p system

    Λ* width+ Decay phase volume+ "Auger suppression"

    No Λ* width

    by Green's function method

    QF-Λ*

    Green's function with smearing I. Kumagai-Fuse & Y. Akaishi, Prog. Theor. Phys. 92 (1994) 815

    Faddeev- AGS

    np

    K-

    p

    n

    Λ*p

  • 2150 2200 2250 2300 2350 2400 2450 2500

    Missing mass spectrum of Λ*-p [email protected] o0=θ

    MM MeV/c2

    react-Kpi/h_Kn_Mod5B.f

    DISTO int.

    YA int.

    No Λ*p int.

    Without Λ* width

    With Λ* widthof 50 MeV

    Λ*+

    p

    Σ +π

    + p

    QF-Λ*

    K-+

    p +

    p

    QF- K (0.3,1.0)X 1/5

    nKn""K +→+ −−

    nKp""K 0 +→+−

  • 2150 2200 2250 2300 2350 2400 2450 2500

    °= 0Labθ

    3He (K-, n) reaction [email protected] GeV/c K-

    MM MeV/c2react-Kpi/h_Kn_Mod5B.freact-Kpi/h_Kn_Mod4B.f

    react-piK/Treat1.f

    QF-K

    Λ*+

    p

    Σ +π

    + p

    QF-Λ*

    YA

    K-+

    p +

    pDISTO

  • 2150 2200 2250 2300 2350 2400 2450 2500

    fR = 1.0, 0.9, 0.8

    MM MeV/c2react-Kpi/h_Kn_Mod5B.freact-Kpi/h_Kn_Mod4B.f

    react-piK/Treat1.f

    °= 0Labθ

    3He (K-, n) reaction [email protected] GeV/c K-

    fI = 1.5

  • 2150 2200 2250 2300 2350 2400 2450 2500

    MM MeV/c2

    Deviation spectrum

    react-Kpi/h_Kn_Mod5.freact-piK/Treat2.f

    SpectrumQF spectrum

    (unrestricted)

  • Elementary cross sections

    ΛπnK -- →

    G.P. Gopal et al., Nucl. Phys. B 119 (1977) 362

  • np

    K-

    p

    n

    Yp

    np

    K-

    p

    n

    Yp

    "Hard" process of Y formation

    n-spectator

    1.0 GeV/c1.0 GeV/c

    "Soft" process of Y formationVery small contribution !

    ⎭⎬⎫

    ⎩⎨⎧ −⋅+−

    +∝ )

    23exp()

    23exp(

    11)( 2n2

    2n2n pat

    spas

    phh

    ρ

    npr

    22nK

    42Ypinv

    22n

    42n

    23HeK )()( cppcMcpcMcME −+++=+

    a = 0.386 fm-2, s = 0.00286, t = 12

    )0178.0(0860.025.1)0319.0(1045.047.1)0480.0(1185.054.1

    )(

    p*Λ

    nnYpinv

    −−+−−+−−+

    DDMMDDMMDDMM

    kkM ρh

    GeV/c (Stopped K-)

    n1000 MeV/c

    n 1198 MeV/c-198 MeV/c

    K-

    n-knockout

    -0.57 0.18D-03

    Fermi motion0

  • N.V. Shevchenko,Phys. Rev. C 85(2012) 034001

    1320 1370 1420 1470Minv [MeV/c2]

    Λ(1405)

    Weise/amyTm2.f

    I=0 imaginary part (total cross section)

    KbarN scattering amplitude

  • On the missing mass spectrumfrom D(π+,K+) E27 experiment

    January 24, 2014March 1; revised

  • 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

    MM [MeV/c2]

    Missing mass spectrum of Λ*-p systemfor [email protected]

    n

    π+

    p

    K+

    Y, Y*

    p

    1.7 GeV/c

    Λ*

    Cusp due toΣN-ΛN coupling

  • react-piK/D_piK_Mod1B.f

    2150 2200 2250 2300 2350 2400 2450 2500MM [MeV/c2]

    ΓΛ∗= 50 MeVYA int.

    ΓΛ∗= 0YA int.

    ΓΛ∗= 50 MeVDISTO int.

    ΓΛ∗= 0No Λ*p int.

    ΓΛ∗= 50 MeVNo int.

    Λ*+

    p

    Σ +π

    + p

    Missing mass spectrum of Λ*-p systemfor [email protected]

    o0=θ

    QF-Λ*

  • 2150 2200 2250 2300 2350 2400 2450 2500 2550

    ooo 16,8,0=θ

    Σ(1385)

    o8=θ

    d:QF-Σ*

    h:QF-Σ*

    react-piK/D_piK_Mod1C.freact-piK/D_piK_Mod1Cc.f

    MM [MeV/c2]

  • 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

    o8=θ

    react-piK/D_piK_Mod1B.freact-piK/D_piK_Mod1C.freact-piK/D_piK_Mod1D.f

    react-piK/Treat3.f

    Missing mass spectrum of Λ*-p [email protected]

    MM [MeV/c2]

  • 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

    oooo 16,12,8,0=θ

    Missing mass spectrum of Λ*-p [email protected]

    MM [MeV/c2]

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

    o8=θ

    o12=θ

    Inclusive spectrum

  • 2250 2300 2350 2400 2450 2500

    o8=θ

    MM [MeV/c2]

    Σ*

    Λ*Σ

    Missing mass spectrum of Λ*-p [email protected]

    Λ*-

    p qu

    asi-b

    ound

    sta

    te

  • 2150 2200 2250 2300 2350 2400 2450 2500MM [MeV/c2]

    ΓΛ∗= 50 MeVYA int.

    ΓΛ∗= 50 MeVDISTO int.

    ΓΛ∗= 0No Λ*p int.

    ΓΛ∗= 50 MeVNo int.

    Λ*+

    p

    Σ +π

    + p

    Missing mass spectrum of Λ*-p systemfor [email protected]

    cp /MeV5.100,πpΛ p =+→−

    cp /MeV0.189,πpΣ p0 =+→+

    cp /MeV7.282,pΛpΣ p0 =+→+

    cp /MeV0.476,pΛX pDISTO =+→

    ΣΝ-ΛΝ conversion

    "K-pp"= Λ*-p QBS

    DISTOYA%17

    →S. Maeda, Y. Akaishi & T. Yamazaki,

    Proc. Jpn. Acad. B 89 (2013) 418

  • FINUDAM. Agnello et al.,Phys. Rev. Lett.94 (2005) 212303

    [email protected] Ichikawa et al.,

    Proc. Science (Nara Conf. 2013)

    DISTOT. Yamazaki et al.,Phys. Rev. Lett.

    104 (2010) 132502

    K-pp = Λ*-pwith real Kbar migration

    (17% enhanced int.)

    2200 2300 2400

    Prelim

    inary

    !

  • Λ*

    K-

    p

    Concluding remarks

    The Λ*= Λ(1405) plays an essential role in forming "anti-Kaonic Nuclear Clusters",the simplest one of which is

    K-pp = (K-p)−p = Λ*−p.

    The Λ*−p structure interacting with "super-strong force" due to Kbar migration provides a possible explanation of recent J-PARC data on K-pp.

  • T. Yamazaki, S. Hirenzaki, R.S. Hayano & H. Toki, Phys. Rep. 514 (2012) 1

    K. Suzuki et al., Phys. Rev. Lett. 92 (2004) 072302

    Isovector s-wave πN scattering length, b1 [mπ-1]

    Quark condensate decreases by ~30% at ρ0.

    Deeply bound pion

    Evidence for partial restoration of chiral symmetry in nuclear medium

  • Enhancement of interaction

    Enha

    ncem

    ent o

    f phy

    sica

    l qua

    ntity

    Bin

    ding

    ene

    rgy

    Pote

    ntia

    l ene

    rgy

    Kine

    tic e

    nerg

    y

    Hig

    her-

    orde

    r effe

    ct

    1.0

    1.1

    1.2

    1.3

    1.0 1.1 1.2 1.3

    1.7

    1.6

    1.5

    1.4

    2.1

    2.0

    1.9

    1.8

    2.2

    2.3

    3.1723.3976.56950.16.1532.3759.52845.18.1358.3526.48840.18.1189.3297.44835.16.1026.3062.40930.13.879.2822.37025.10.736.2586.33120.17.599.2336.29315.15.476.2081.25610.14.367.1822.21905.16.262.1569.18200.1

    −−−−−−−−−−−

    BETVf

    (Unit in MeV)

    Enhancement effects by strongly attractive interactionon physical quantities in K-p bound state

    37.1, 00 −=→ ssfsAttractive interaction is enhanced;

    L1405/rangeKE.f

  • -1.2 -1.3 -1.4 -1.5 -1.6 -1.7

    -50

    -100

    -150

    -200

    -250

    0

    [MeV]

    NKs

    NK

    NKK

    NNKNNNK

    NNKK

    0NK=IV

    0NK2

    3 =IV

    0NK2

    3 =IV

    0NK3=IV

    0NK2

    3 =IV

    10% 20%enhancedPDG

    DISTOFINUDA

    FOPI

    Energies of few-body kaonic systemscalculated by Faddeev-Yakubovsky method

    FOPI

    ?

    FINUDADISTO

    PDG

    Λ*(1420)

    S. Maeda, Y. Akaishi & T. Yamazaki, Proc. Jpn. Acad. B 89 (2013) 418

  • V.K. Magas, E. Oset, A. Ramos & H. Toki,Phys. Rev. C 74 (2006) 025206

    FINUDAM. Agnello et al.,

    Phys. Rev. Lett. 94 (2005) 212303

    Λp invariant mass from K-pp

    p

    Λ

    >90%

    "OT

    poin

    t"

    K- +

    p +

    p

  • 1.3

    1.0From K- direct capture on pp

    with FSI

    Angular dependence of K-4He -> Λ+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,

  • Thank you very much!

    AcknowledgmentsY. Ichikawa