him 2006-09 shlee 1 1.introduction for exotics 2.hadron production in hic 3.exotics from rhic hadron...
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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
32
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
21
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