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

H3K

Σ+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 MeV

Λ* + 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 MeV

Nogami 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 =1.4 1.21.0

0.8

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) emission

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)( 13131

103131

023NN123123NN

11212

101212

0 =+++=Ψ ======== TPrfPrfrfrfrfrfPrfPrf IIIIIIII

{ } { }{ } { }2

fmMeV1

NK

2fmMeV

0NK

)66.0/(exp105175)(

)66.0/(exp83595)(

rirv

rirvT

T

−−−=

−−−==

=

{ } { } { }2fmMeV

2fmMeV

2fmMeVNN )5.2/(exp5)942.0/(exp270)447.0/(exp2000)( rrrrv −−−−−=

{ } 0=− ΨΨλΨΨδ Hf

Euler-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 systemE15@J-PARC 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 E15@J-PARC1.0 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 E15@J-PARC1.0 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)( 2

n22n2n p

atsp

asp

hhρ

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

pΣ

pΛ

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 E27@J-PARC

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 E27@J-PARC

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 systemE27@J-PARC

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 systemE27@J-PARC

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 systemE27@J-PARC

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 E27@J-PARC

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

E27@J-PARCY. 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

Preliminary

!

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