Current theoretical topics on Kpp quasi-bound...

Current theoretical topics onK-pp quasi-bound state

SNP Meeting @ J-PARCAugust 3, 2015

Yoshinori AKAISHI and Toshimitsu YAMAZAKI

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!

-500 -500

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

A. Dote, T. Hyodo & W. Weise, Phys. Rev. C 79 (2009) 014003E = -20+-3 MeV, Γ = 40~70 MeV

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

DAΦNE Conf. (1999) , HYP Conf. (2000) ; rejected from Proc.

"Λ(1405) Ansatz" A. Dote et al.

K-p

J-PARC E31 : D (K-, n)

KbarN scattering amplitude

s

T. Hyodo and W. Weise, Phys. Rev. C 77 (2008) 035204

Akaishi-Yamazaki

Chiral

Chiral SU(3) dynamics

1405"ORB": E. Oset, A. Ramos & C. Bennhold, Phys. Lett. B 527 (2002) 99"HNJH": T. Hyodo, S.I. Nam, D. Jido & A. Hosaka, Phys. Rev. C 68 (2003) 018201"BNW": B. Borasoy, R. Nissler & W. Weise, Eur. Phys. J. A 25 (2005) 79"BMN": B. Borasoy, U.G. Meissner & R. Nissler, Phys. Rev. C 74 (2006) 055201

"JOORM": D. Jido, J.A. Oller, E. Oset, A. Ramos & U.G. Meissner, Nucl. Phys. A 725 (2003) 181

1420

The most relevant issue is:

1405 or 1420 ?

Σπ invariant mass from stopped K- on 4HeJ. Esmaili, Y. Akaishi & T. Yamazaki, Phys. Lett. B686 (2010) 23

χ 2 as a function of 1st pole’s M and Γ.

Data : B. Riley et al., Phys. Rev. D 11 (1975) 3065

Λ(1405) from HADESG. Agakishiev et al., Phys. Rev. C 87 (2013) 025201

M. Hassanvand et al., Phys. Rev. C 87 (2013) 055202

PDG

14

Interpretation of the Λ(1405) shift in HADES dataJ. Siebenson & L. Fabbietti, Phys. Rev. C 88 (2013) 055201

c.m.2

21p.s.2

)1405( )()( 1 qmBWemBWCT i += − φΛ

iiiii immm

AmBWΓ+−

= 221)(

Best fit

Coherent sum

Interference between double poles !

1300 1350 1400 1450 1500 1550MM(ｎ) MeV

QF-K

Λ(1405)PDG

I =1

I =0

np

K- n

pK-

D(K-, n) missing mass spectrum calculation

1.0 GeV/c J-PARCE31

np

K- n1.0 GeV/c

p

QF-K

QF-Λ*

K-pp

E15

Useful informationfor

1300 1350 1400 1450 1500

D(K-, n) missing mass spectrum

react-Kpi/d_Kn_Ls1.f

PK- = 1.0 GeV/c

+ 1.1 – I 12.4- 2.4 – I 14.9- 6.3 – I 17.3-10.8 – I 19.5 -15.8 – I 21.6-21.1 – I 23.5-26.9 – I 25.3

E(Λ*) MeV

MM(ｎ) MeV/c2

I =0 onlyo0n =θ

1300 1350 1400 1450 1500

MM MeV/c2

I =0

I =1

QF-K-

IM(Σπ)

o0n =θMissing-mass spectrum of ( ) mπΣnKD - ±,

1360 1380 1400 1420

I =0

I =1

IM(Σπ) MeV/c2

InclusiveI =0 ΣπI =1 Σπ, Λπ

2611

210

31πΣ

2320

31πΣ

2611

210

31πΣ

00

-

=+=−==

=+=−=

=+=+==

+−

+

III

II

III

Missing and invariant mass spectra

np

K- n

Missing massEigenstate of H(Kp-Σπ)εiHE

G+−

=1

On-shell

Green’s function

Singularities appearabove threshold.

Moon-shaped singularityε =0.1 MeV with Δcosθ =0.002

000

000

11000

0

10

1100

0

011

0

)(

)(

TGGGG

TGGVGG

GGGGGG

VGTG

GTGTV

GGTGV

VTGVT

VHHGG

+=

==

−=−

=

−+=

−+=

+=

=−=−

−−

−

−−

−−

Identity

εε

ε iHEi

+−≡

′→0lim ( ) 0=−= EEE HE, ΨΨΨ

Non-eigenstate of H

+Quasi-free K :

Invariant mass (Σπ, ..)00TGG

εiHEG

+−=

00

1

=

Off-shellΣ

π

Σπ invariant-mass spectrum

1300 1350 1400 1450 1500

+ 1.0 – I 12.5-11.0 – I 19.5 -27.0 – I 25.0

E(Λ*) MeV

Formationweight

“Peak shift”

IM(Σπ) MeV/c2

np

K- n1.0 GeV/c

D Λ*Σ

π

I =0 onlyo0n =θ

( ) 00- πΣnKD ,I =0 main,

no I =1

Σπ invariant-mass spectrumDeuteron-size dependence

1300 1350 1400 1450 1500IM(Σπ) MeV/c2

PK- = 1.0 GeV/c

2241

d fm19940 −=−= .a),arexp()r(ψafa →

f = 100101

0.10.010.001

Free

N

Shevchenko’s interactionPhys. Rev. C. 85 (2012) 034001

1300 1350 1400 1450 1500IM(Σπ) MeV/c2

Shevchenko interactionPhys. Rev. C 85 (2012) 034001

MeV025514062Λ * .i.cM −=


I =0

I =1

Deviation spectrum

Total

1300 1350 1400 1450 1500

IM(Σπ) MeV/c2

I =0

I =1

AMY interaction

MeV025014052Λ * .i.cM −=

Deviation spectrum

Total


1300 1350 1400 1450 1500

react-Kpi/d_Kn_Ls2D.f

IM(Σπ) MeV/c2

I =0

I =1

AMY interaction

MeV025014202Λ * .i.cM −=

Deviation spectrum

Total


IM(Σπ) MeV/c2


K-+p

thre

shol

d

Χ 2 -fitting

must be done !Shev1407AMY1405AMY1420

K-pp

J-PARC E15 : 3He (K-, n)

Semi-inclusive neutron spectrum

np

K-

p

n

pK-

p

1.0 GeV/c

T. Hashimoto et al., Prog. Theor. Exp. Phys. 2015, 061D01

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

Phys. Rev. C 80 (2009) 055208

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

E-dep. real part

E-dep. imaginary part

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

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Density distributions of Kbar-N

r fm

Kbar-N in Λ(1405)

Kbar-N in K-ppx0.625

I = 0

I = 1

KI =0

Λ*

N N

K

Λ*

NNI =0

I =0: 0.5x(1+0.25)=0.625I =1: 0.5x0.75= 0.375

I =0; 0.25I =1; 0.75

Dynamicallyfavored

)(2 rr ρ

T. Yamazaki and Y. Akaishi, Phys. Rev. C 76 (2007) 045201

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) 144Λ*N system with meson exchange

A. Arai, M. Oka & S. Yasui, Prog. Theor. Phys. 119 (2008) 103

K-pp quasi-bound state

pp K-

1.90 fmrms distance

1.36 f

m

2002

2007

np

K-

p

n

pK-

p

1.0 GeV/c

np

K-

p

n

Λ*p

T. Hashimoto

pn=1000 MeV/cpn=1494 MeV/c

QF-Λ

MeV392423HeK =+ cME

2nMeV

2nin

2miss )-1000()( cpEEcM −−=

Quasi-freeY’s in E15 missing mass spectrum

2812 MeV for pn=0

“n-spectator window”

Δπ π

MM GeV/c2

pn=1254 MeV/c

"n-knockout window"

p

Y

1000 MeV/c - pn

K-

p0

QF-Λ1405

QF-Σ

2N absorption

2150 2200 2250 2300 2350 2400 2450 2500

Missing mass spectrum of Λ*-p systemo0n =θ

MM MeV/c2

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- KX 1/5

nKn""K +→+ −−

nKp""K 0 +→+−


"" 31E15EppK −≈−


Preliminary !

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

Without Λ* width

Λ*+

p

Σ +π

+ p

K-+

p +

p

o0n =θ

o20n =θ

o40 o60

DISTO int.

With Λ* widthof 50 MeV

All the integrated spectra

are normalized to unity.

o40o0n =θ

o60

psQF Λ* is obtained by 3N absorption calculation!

observedK-

Y

pp

nn

pseudoQF-Y

3N absorption

pnθ

oo 200n ~=θ

Pseudo-QF Λ*

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

2150 2200 2250 2300 2350 2400 2450 2500

Λ* w

idth

.

Pseudo-QF Λ* and K-pp

psQF Λ*

IM. [MeV/c2]react-Kpi/h_Kn_Mod5B.f

np

K-

p

n

p

DIS

TO in

t.

o0n =θ

Λ* w

idth

DIST

O in

t.

Λ∗

K-pppsQF Λ*

K-pp

J-PARC E27 : D (π+, K+)

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

o8=θ

o12=θ

Inclusive spectrum

K-pp

?

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

104 (2010) 132502

MeV-48K =EMeV61=Γ

MeV-103K =EMeV118=Γ

Theor.Yamazaki-Akaishi

17% enhancedKbarN interaction

E27@J-PARCY. Ichikawa et al.,

Prog. Theor. Exp. Phys. 2015, 021D01

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

DISTOYA%17

→S. Maeda, Y. Akaishi & T. Yamazaki,

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

cp /MeV5.100,πpΛ p =+→ −

cp /MeV0.189,πpΣ p0 =+→+

cp /MeV7.282,pΛpΣ p0 =+→+

cp /MeV0.476,pΛKpp pDISTO =+→

ΣΝ-ΛΝ conversion

"K-pp"= Λ*-p QBS

Coincidenceby T. Nagae et al.

K-

K+

pp

K-pp structure

Which isof ground?

K-

K+

Λ*

p

p

Λ*- p structure

n p

π+

K-pp = Λ*-pwith real Kbar migration

(17% enhanced int.)

2200 2300 2400

Preliminary

!

E27@J-PARCY. Ichikawa et al.,

Prog. Theor. Exp. Phys. 2015, 021D01

3.87.7 ≤≤ θ

QF-Σ∗+

Simulation by Y. Ichikawa

No width

A stable particle withLorentzian mass distribution

An unstable particlewith decay width

p*Σ*Σ HHH +=

p*Σ*Σ*ΣΣQF T)iWE(H * ++⎯⎯ →⎯

⎥⎦

⎤⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

+−−=−∝

επδ

iHEIm)HE(S

XX

11

3.87.7 ≤≤ θ

QF-Λ∗

Mass distribution

Decay widthHADES fit

Simulation by Y. Ichikawa

Decay width

~15 MeV

K-pp quasi-bound state

pp K-

1.90 fmrms distance

1.36 f

mDISTO

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

2150 2200 2250 2300 2350 2400 2450 2500

L= 0

4≤L

12≤L

2≤L

Angular-mom. decomposition of the Λ*-p pair

QF Λ*

react-piK/D_piK_Mod1B.f

n

π+

p

K+

Λ*

1.7 GeV/c

L8≤L

1≤L

L= 0

MM [MeV/c2]

Λ*+

p

Σ +π

+ p No Λ*p int.

DISTO Λ*p int.

~40 MeV

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.

Strangelet

[ ]11 −⊗Σ −+ ZA

[ ]ZA 1−⊗Σ0

[ ]11 +⊗Σ − ZA-

[ ]ZA 1−⊗Λ

[ ]ZA 2−⊗ΛΛ

[ ]ZA 1−⊗Ξ0

[ ]11 +⊗Ξ − ZA-

[ ]1+⊗π ZA-

[ ]ZA [ ]1+ZA [ ]2+ZA

S=0 nucleiS=-1S=-2

500

400

300

200

100

0

Excitation energy(MeV)

)K,K( - +

)K,(),,K( -- ++ ππ)K,(),,K( - ++− ππ

)N,K( -

[ ]ZA⊗0K[ ]1+⊗ ZA-K

Nuclei of 2nd generationThe s quark combined with ubar

plays a leading role in forming a dense and cold nucleus.

(p,K+),

Yamazaki diagram

A new paradigm of nuclear physics“Swan Nuclear Physics”

Nuclei of

1st generation

Thank you very much!

Current theoretical topics on Kpp quasi-bound...

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