him 2006-09 shlee 1 1.introduction for exotics 2.hadron production in hic 3.exotics from rhic hadron...

HIM 2006-09 SHLeeHIM 2006-09 SHLee

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1. Introduction for Exotics

2. Hadron production in HIC

3. Exotics from RHIC

Hadron Physics at RHIC

Su Houng LeeYonsei Univ., Korea

Thanks to: Former collegues and students Present students: Y. Park, Y. Sarac, Y. Heo, K. Kim Post doc: K. Ohnishi


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Introduction for Exotics


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1. Hadrons that can not be explained by quark-antiquark, or 3 quarks

2. That are bound by strong interaction

3. Reasons for its search are similar to that for superheavy Element in low energy nuclear Physics

Understand QCD sQGP

Definition of Exotics

cuucuudussudus

ccudscudsudud

, , ExoticsNon

, , Exotics


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Mass= 1.54 GeV , width <25 MeV , quark content= uudds

1. LEPS coll., Nakano et.al. PRL 91 012002 (2003)

Experiment - First claim

)1520(


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In Carbon target , but

Experiment - Recent claim

)1520(

))1540(( ))1520((


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Positive results Negative results

Recent CLAS experiments find no + in +d or +p

Give up, more experiment or theoretical guideline?


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1. SU(3) soliton

2 4( ) ( )Kin Skyrme W ZL U L U L

†exp( ) 0( , ) ( ) ( )

0 1

where ( ) has 8 angles

i rU x t R t R t

R t

2. Quantizing the 8 angles, the Hamiltonian becomes

3 72 2

1 41 2

1 1ˆ ˆ' '2 2

RotA A

A A

H J JI I

10 8 8101 2

3 3,

2 2E E E E

I I

I=J Hedghog

Theory : prediction (Diakanov, Petrov, Polyakov 97)


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4. Diakanov Petrov Polyakov applied it to Anti-decuplet

which predicted M= 1540, =30 MeV

8'2 3

cN BJ

1. only SU(3) representations containing Y=1 are allowed

2. moreover, the number of states 2I+1 at S=0 or Y= Nc/3 must determine the spin of the representation through 2J+1 because I=J in the SU(2) soliton

one spin state for given representation

3. With constraint coming from WZ term Y

3T

max

1 2

3 3Y p q

3cN

Y

10


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1. Soliton picture is valid at large Nc:Semi-classical quantization is valid for slow rotation: ie. Valid for describing excitations of order 1/

N_c, so that it does not mix and breakdown with vibrational modes of order 1

2. Lowest representation SU(3)f (p,q) at large Nc

Y

3T

max

1 2

3 3Y p q

3cN

Y

Quantization constraint requires max

2

3 3 3cNp q

Y

1. Octet

2. Decuplet

3. Anti decuplet

(lowest representation containing s=1)

1(1, )

2cN

3(3, )

2cN

3(0, )

2cN

3cN B

Y S

Theory: why it can be wrong (T. Cohen)


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3. Mass splitting in large Nc:

3 72 2

1 41 2

1 1ˆ ˆ' '2 2

RotA A

A A

H J JI I

1

10

82

8

0

1

3 1( ),

3(1)

4

2

c

c

NE E O

EN

I

E OI

Anit decuplet octet mass splitting is mixes with vibrational mode and inconsistent with original assumption and has undetermined correction of same order

Rotation is too fast and may couple to vibrational modes, which might be important to excite q qbar mode, hence describing anti decuplet state with naive soliton quantization might be wrong


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diquark: C=3,F=3,S=0

triquark: C=3,F=6,S=1/2

Jaffe, Wilczek model

Karlinear, Lipkin model

Theory: Quark model of a pentaquark

u

ds

u

d 2 diquark: C=3,F=3,S=0

relative p wave

Strong diquark correlation

u

d

su

d


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1. In QCD q-q are also attractive if in color anti-triplet channel.

aq

aq

aq

bq

abc

Color Spin Interaction in QCD

kiki

M SSmm

C

kiki

B SSmm

C

In perturbative QCD, 2CB=CM This term is called color spin interaction


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Color spin interaction explains hadron spectrum

Works very well with 3CB=CM = constant

Nucleon

u u d

2222

2 2

1duuduu

q

B

duduuuki

B

ssssssm

C

ssssssmm

C

Baryon Mass difference Meson Mass difference

MeV 1500 MeV, 500 MeV, 300 csdu mmmm


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Why there should be a heavy pentaquark

1. For a Pentaquark

su

d du

2. If recombined into a Kaon and a Nucleon

su

dd u

MeV 290 4

3

4

322

u

B

u

B

m

C

m

C

MeV 430 4

3

4

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su

M

u

B

mm

C

m

CMeV 240

4

3

4

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cu

M

u

B

mm

C

m

C

3. If recombined into a D-meson and a Nucleon

c

c

1. For a charmed Pentaquark


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Other possible states - Tetraquark

1. For a Tetraquark

Au

d B

2. For the meson and meson

Bu d

tetraquark2E

4

3

4

3

BA

B

u

B

mm

C

m

Cmeson-2E

4

3

4

3

Bu

M

Au

M

mm

C

mm

C

A

A B Etetraquark-E2meson

u u 663 MeV

u s 530

s s 374

u c 397

s c 218

c c 39

b b -88

DD-

BB-


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Where to search: Baryonic decay mode of B+

decay in hadronic language pB c

*,DD

Bc

p

c

p

b

u

W c

ud

c

p

b

u

W

c

Larger By Nc


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Pentaquark decay mode of B+

c

Dp

K

Weak decay Branching ratio is 0.092

Using pevious fit, we find the branching ratio to be 14.4x10-7

gDpx gKp/gKp

lower limit in B-factory events 32)7.0)(092.0)(104.14)(10( 479

Can search for it in Belle S.H.Lee. Y. Kown. Y. Kwon , PRL (06)


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Hadron Production in HIC


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Success of statistical model

P. Braun-Munzinger, J. Stachel (95 …)


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Recent Star data - I

1)/)1520((

)/)1520((*

*

pp

AuAu


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Theoretical Explanation – Muller, Kanada-En’yo

Quark Coalescence model = Statitical model + overlap integral

su

d du

QGP

s

ud s

i

iii kxFdkdxW 2|||),(

]22

exp[),(2

2

2,

mT

k

a

xkxF ixi

i

...]exp[ iii xik

)/exp(

)/exp(22222*

2222

bkbxk

bkbx

1)/)1520(( assuming

1)/)1520((

)/)1520((

*

*

*

pp

pp

AuAu


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Statistical model = quark coalescence + overlap

Explicit example i

in

iin kxFdkdxW 2||H|),(

]22

exp[),(22

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mT

k

mT

kkxF

..])()(

exp[)(||| 221

22

221

212 kkb

b

xxkk n

in

])1

(exp[ ]2

exp[ 222

22

kmT

bb

rkdrdk

MT

PW nn

2/2 )

11(

1/

n

n

mTb

WW

Exotic production in HIC will follow statistical model

modified only by the wave function overlap integral and hadronic phase


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Exotic particle production: elementary vs HIC

Exotic particle production from elementary processes

su

d du

QGP

su

d du

+

Exotic particle production from Heavy Ion collision


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Example

+(1540) production in Au+Au at RHIC in central rapidity region

Statistical model

J. Randrup, PRC 68 (2003) 031903, N =1

Coalescence model

Chen, Greco, Ko, Lee, Liu, PLB 601 (2004) 34, N =0.2

Hadronic regeneration or dissociation is not so large


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Exotics from RHIC

1. RHIC (STAR)FAIR (GSI)


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Possible Decay mode of charmed Pentaquark

cu

d du

+

L=1

exotic Decay mode Final states Branching ratio

udusc uds() +uc(D0) + k0 0 (k+ -)

+ k0 - +

2.3 % (3.8 % )

5.97 %

uud(p) +sc (Ds-) P + k0 -

P + k+ - -

2.82 %

9.2 %

ududc udu (p)+dc (D-) P + k0 -

P + k+ - -

2.82 %

9.2 %

udd (n)+uc (D0) n + k0 0 (k+ -)

n + k0 - +

2.3 % (3.8 % )

5.97 %


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Rough estimate of events at RHIC

cu

d du

+

Central collision (0-10%)

dNcc/dy = 2.2 (phenix)

Final state Decay mode Final states Branching ratio

ududc udu (p)+dc (D-) p + k0 -

P + k+ - - 2.82 %

9.2 %

udd (n)+uc (D0) n + k0 0 (k+ -)

n + k0 - +

2.3 % (3.8 % )

5.97 %

00045.003.0148

12.2

ratio Branching]/exp[//

TmdydNdydN pDc


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Possible Decay mode of Tetra-quark

cu dc

exotic Decay mode Final states Branching ratio

uscc uc (D0)+sc (Ds-) D0 (k0 0 , k+ -k0 - + )

Ds-(k0k- , k-k+ -) 3.6 % ( 4.4 %)

udcc dc (D-)+uc (D0) D- (k0 -l k+ - - ) +

D0 (k0 0 , k+ -k0 - + )


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Who can do it : STAR collaboration?

kD0

0

kD


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Who can do it : FAIR ?


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SummarySummary

1. While controvery exist over light pentaquark, Many Theories consistently predict bound heavy pentaquark

2. Quark model also predict metastable tetraquark

3. RHIC can be a very useful exotic factory

If found the first exotic ever, will tell us about QCD and dense matter color superconductivity


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ReferencesReferences

• Experiments• T. Nakano , Phys. Rev. Lett. 91 (03) 012002.• K.~H.~Hicks, Prog. Part. Nucl. Phys. 55 (05) 647.

• Skyrme model controversy• T.D.Cohen, Phys. Lett. B 581 (04) 175• H. Walliser and H. Weigel, Eur. Phys. J. A 26 (05) 361. • D.Diakonov, V.Petrov and M.V.Polyakov, Z. Phys.A 359 (97) 305

• Theory• H. J. Lipkin, Phys. Lett. B 195 (87) 484.• Fl. Stancu, Phys. Rev. D 58 (98) 111501. • D. O. Riska, N. N. Scoccola, Phys. Lett. B 299 (93) 338.• Y.Oh, B.Y. Park, D.P. Min, Phys. Lett. B 331 (94) 362. Phys. Rev. D 50 (94) 3350.• R.L.Jaffe, F.Wilczek, Phys. Rev.Lett. 91(2003) 232003.

• present work• H. Kim, Y. Oh, S.H.Lee, PLB 595 (04) 293: • Y. Sarac, H.Kim, S.H.Lee, PRD 73 (06) 014009 • S.H.Lee, Y. Kown, Y. Kown, PRL 96 (06) 102001

him 2006-09 shlee 1 1.introduction for exotics 2.hadron production in hic 3.exotics from rhic hadron...

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