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1. Introduction
2. Theory survey
3. Charmed Pentaquark
4. Charmed Pentaquark from B decays
Hadron spectroscopy, Heavy pentaquark, and B decay
Su Houng LeeYonsei Univ., Korea
References: 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
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1. Hadrons that can not be expalined 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
Exotics
duuduudussudus
sudud
, , exoticsnon
1S 0,I
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Mass= 1.54 GeV , width <25 MeV , quark content= uudds
1. LEPS coll., Nakano et.al. PRL 91 012002 (2003)
Introduction
)1520(
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Verification
2. Verification by other group
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4. NA49 hep-ex/0310014
found *(1862) in - - (ddss u) with width< 18 MeV
3. CLAS finds no ++ in K+ P invariant mass
+(udud s) belongs to anti-decuplet
5. Recent CLAS finds no + in gamma d , gamma p in K+ P invariant mass
+(udud s) belongs to anti-decuplet
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Positive results
Negative results
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I3
Y
ud
s3 8
(1232)
(1532)
(1673)
10
N ?
?
10
N(939)
(1190)
(1320)
Baryon Reprsentation
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2. Could not confirm in subsequent experiments
CDF, ZEUS, FOCUS
1. H1 collaboration (Deep Inelastic scattering)
Heavy Pentaquarks (udud c)
c(3099) was found in D* p (uudd bar(c))
with width= 12+-3 MeV
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Experimental summary
1. + controversial questionable
mass 1540 MeV> KN threshold (1435 MeV)
2. c+ controversial questionable
search was done with DN D*N final state (unbound)
> 2800 MeV +
3. Give up, more experiment or theoretical guideline?
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Theory review
Soliton model + Quark model(biased and limited)
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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
Soliton model: original prediction (Diakanov, Petrov, Polyakov 97)
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4. Diakanov Petrov Polyakov applied it to Anti decuplet
which predicted mass= 1540, width=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
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1. Karlinear, Lipkin
diquark: C=3,F=3,S=0
triquark: C=3,F=6,S=1/2
Negative parity if all the quarks are in the lowest s-state
Positive parity if a relative p wave
But with this simple picture, it is not easy to understand small width
Quark models
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2. Jaffe, Wilczek
Positive parity if a relative p wave
(ud) (ud) s
Flavor 3 3 3 10 8
6 3
color 3 3 3 1
3 3
spin 0 0 0
L 0 1 0
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But, a closer look revealed puzzles
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1. Soliton picture is valid at large N_c: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 N_cY
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
Naive Solition model should fail (T. Cohen)
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3. Mass splitting in large N_c:
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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1. SU(2) soliton+ Kaon
2. Successful for hyperon (attractive (s qbar) ) but no pentaquark (repulsive q sbar) from WZ term
2 4( ) ( )Kin Skyrme W ZL U L U L
Bound state approach for SU(3) soliton
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Summary of Solition approach for + (ududs)
1. SU(3) Soliton
Inconsistent application
2. Bound state approach
No bound +
Can not be applied to heavy pentaquark c(ududc)
predict a bound heavy pentaquark c(ududc)
ie. mass is smaller than DN continuum
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2. Could not confirm in subsequent experiments
CDF, ZEUS, FOCUS in 2004, 2005
1. H1 collaboration in 2004 (Deep Inelastic scattering)
Experimental search for Heavy Pentaquarks (udud c)
c(3099) was found in D* p
with width= 12+-3 MeV D p (2810)
D* p (2950)
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Why Heavy Pentaquark
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Solition approach for light pentaquark + (ududs)
1. SU(3) Soliton approach for + : controvery
T. Cohen: Inconsistent application of large Nc vs. Diakanov, …..
2. Bound state approach
No bound + discussions between T. Cohen and Wiegel
Can not be applied to heavy pentaquark c(ududc)
predict a bound heavy pentaquark c(ududc) . ie. mass is smaller than DN continuum
Quark model also predict a bound heavy pentaquark c(ududc) but no light pentaquark +(ududs)
QCD sum rules also predict a bound heavy pentaquark c(ududc) , Y. Sarac, H. Kim, SHLee PRD 06
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Y. Sarac, H. Kim, S. H.Lee (PRD 05)
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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
Possible Quark structure of a pentaquark
u
ds
u
d 2 diquark: C=3,F=3,S=0
relative p wave
Strong diquark correlation
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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 L=0 L=1
2. If recombined into a Kaon and a Nucleon
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
32
cu
M
u
B
mm
C
m
C
3. If recombined into a D-meson and a Nucleon
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Summary of Theory for Pentaquark
1. While there are some controversy over light pentaquark, Soliton approach predict stable heavy pentaquark
2. Constituent quark model also seem to predict only heavy pentaquark
Could not observe heavy pentaqurk from DN final state because it might be bound
Heavy pentaquark can only be observed from Weak decay
May be from B factory? But do we have sufficient data and can one conclude anything if one tries?
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Anti-Charmed pentaquark from B decays
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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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Baryonic decay mode of B+
decay in hadronic language pB c
DB
gDP=3.2, gD*P=1.62/(2+p2)
=700MeV
)( pM)( pM
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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
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SummarySummary
1. While controvery exist over light pentaquark, Many Theories consistently predict bound heavy pentaquark
2. Baryonic decay mode of B+ can be sensibly estimated with previously determined hadronic parameters
3. With present B+ data, can measure c from
If found the first exotic ever, will tell us about QCD and dense matter color superconductivity
pKnB cc and
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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