Introduction Theory survey Charmed Pentaquark Charmed Pentaquark from B decays

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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