マルチクォーク系としてのマルチクォーク系としてのストレンジ・ダイバリオン及びストレンジ・ダイバリオン及びトライバリオンの研究トライバリオンの研究

前沢 祐 (東京大学 )初田 哲男 (東京大学 )佐々木 勝一 (理研 BNL)

Maezawa, Hatsuda, Sasaki, Prog.Theor.Phys. 114 (2005) 317.Maezawa, Hatsuda, Sasaki, in preparation.

Experimental resultsT. Suzuki et al.

Phys. Lett. B 597, (2004) 263 M. Iwasaki et al. hep-ph/0310018

)3115(0S

)3140(S13

7.3

MeV 7.3117MMeV 6.21

FINUDA CollaborationPRL 94, (2005) 212303

)2255(F

MeV 5.3140MMeV 6.21

MeV 5.2258MMeV 67

Spin and Parity are undetermined.

)channel 0(- IpKStrong attraction

Akaishi and Yamazaki PRC65 (`02) 044005Dote, Horiuchi, Akaishi and Yamazaki, PRC70 (`04) 044313

Hadronic picture

state bound :)1405( NK

High density

03 0center 10

deeply bound kaonic nuclei

NNNK 3310 MeV

ppnK -111 MeV

pnnK -97 MeV

NNK 2370 MeV

ppK -48 MeV

Dibaryon state Tribaryon states

0center 3

Multi-quark pictureuuudddddspnnKS :0

Hexa- and Nona-quark picture

Classification in color, flavor and spin space

Mass formula based on bag model with NG boson cloud

uuuddsppKF :

F flavor octet

Hexa-quark states Nona-quark states

0S flavor 27-pletS several candidates

irreducible representation in flavor spin space

Classification in color, flavor and spin space

Degrees of freedom of multi-quark system

All quarks are in S-orbit. (positive parity)

anti-symmetriccolor-singlet

)2()3()3( JFC SUSUSU

3), (10*, 1), (10*, 2), (8, 1), (8,),( JF)2/1,1(),( ISF

plet-27 -plet*350S SS

I3

1

Possible multiplets for , and )3140(S)3115(0S)2260(F

octetF

)1,1(),(0 ISS3/2) (64, 1/2), (35*, 3/2), (27, 1/2), (27,),( JF

)1or 0,1(),( ISS1/2) (35*, 3/2), (27, 1/2), (27, 3/2), (10*,),( JF

S

Mass formula　 (bag model)

Mass splitting

Mass formula for multi-quark system

breaking effect)3(FSU

Color-magnetic int. effect

NG boson cloud effect

sdu mmm 0

jc

ic

ijs M

R)()(

8

432

3

132

)()(4

)()(4 a

jf

ifK

aj

fi

f

RfRf

jiijs

sq

RVYaJa

JJYIaJFCaYaaM

)(

)()()(NG22

22312

4122

31

2

54

3210

iq jq

g

,, K

Constant independent of quantum numbers

)3115( and )2255(),939( reproduce toAdjusted 0SFN

30

3

4BRa

breaking effect)3(FSU

More strange-quarks Larger mass

sna 1

Color-magnetic int. effect

spin flavor multiplet

Larger Larger mass

nss M

Ra

2

jiijs

sq

RVYaJa

JJYIaJFCaYaaM

)(

)()()(NG22

22312

4122

31

2

54

3210

NG boson cloud effect

small effectbreaking-)3(,, Fs SUaaa 543

8

432

3

132

NG )()(4

)()(4 a

jf

ifK

aj

fi

fij

RfRfV

jiijs

sq

RVYaJa

JJYIaJFCaYaaM

)(

)()()(NG22

22312

4122

31

2

54

3210

spin flavor multiplet

Larger Larger mass

H -particle problemColor magnetic interaction

jij

ci

cij

s MR

)()(

Baryon mass splitting Large coupling constant

02.s

Bound states with S = -2 appear below hadronic thresholds.

Double hypernucleus

He6

Nagara event

MeV 19.025.7 18.011.0

B

)0,0,1(),,( PJIF

BMM H

• B = 2: H dibaryonMeV 50BE Jaffe, PRL 38 (1977) 195

)2/1,2/1,8(),,( PJIFMaezawa et al. PTP 114 (2005) 317MeV 100BE

Permissible parameter region exists?MmM sKsH ),,,(

PRL 87 (2001) 212502

• B = 3: H tribaryon

ParameterParameter space

1st 2nd 3rd 4th

MM KsH ),,(di

NKsH MM ),,(tri

),,( Ks

2.0s36.026.0K

GeV 24.0sm

Bag radius

Scaling lawfm 2.16 R

fm 5.19 R

Masses of hexa-quark

)1,21,8(),,( PJIF

)2260(FH

Masses of nona-quark

)2/3,1,27(),,( PJIF

? )3140(S

)2/1,0*,35(

)2/1,1*,35(

)21,1,27(),,(

PJIF

)3115(0S

bound state?

Comparison to hadron picture

quark picture hadron picture

ppK dibaryon

tribaryon

),2/1( pJIF 1 ),2/1( pJIF 0

candidates several :S

),1(0 pJIS 2/1

),0( pJIS 2/1

Bound state appears

in S = -3

ppnK

),1(0 pJIS 2/3pnnK

Strange dibaryon and tribaryons 　

multi-quark description

Classification in flavor-spin space

Mass formula and permissible parameter region

Summary

Hexa-quark states

• is identified as .• All states appear above hadronic thresholds.

F )1,2/1,8(),,( PJIF

• is identified as .• Other light nona-quark states with ?

0S )2/1,1,27(),,( PJIF

Nona-quark states

3S