Charm 2006, page 1

Pentaquark Baryons and Tetraquark Mesoniums from

Lattice QCD

• Hadron Calculation with overlap fermion • Pentaquark Baryons and Tetraquark Mesoniums on the Lattice

χQCD Collaboration: A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, B.

Joo, F .X. Lee, K.F. Liu, N. Mathur, S. Tamhankar, H.Thacker, J.B.

Zhang Charm 2006, June 6, 2006

ITP, 2005, page 2

Hadron Mass and Decay ConstantHadron Mass and Decay Constant

)(2

3

)(1

00

00

0 ||2

0||)()(||0

)()((),,(

ttE

p

p

p

ttEtt

x

xpiNN

pp

eEmE

VEepNpN

xxTepttG

The two-point Green’s function decays exponentially at large separation of time

0t t

Mass M= Ep(p=0), decay constant ~ Φ

Charm 2006, page 3

QCD VacuumQCD Vacuum

ππ

ρρ

σσ NN

ΔΔφφ

ΣΣΛΛ

ΞΞ

ωω

KK

SS1111

NN**CreationCreationOperatoOperatorr

QCD QCD VacuumVacuum

CreationCreationOperatoOperatorr

QCD QCD VacuumVacuum

ΘΘ++

????PentaquarkPentaquark

TetraquarkTetraquark????

Charm 2006, page 6

Le Taureau of Pablo Picasso (1945)

Dynamical chiral fermion Quenched approximation with chiral symmetry, and light quark masses

5th stage 11th stage

Charm 2006, page 7

Masses of N, Masses of N, ρρ, and , and ππ

• 16163 3 x 28 quenched x 28 quenched lattice, Iwasaki action lattice, Iwasaki action with a = 0.200(3) fmwith a = 0.200(3) fm

• Overlap fermionOverlap fermion• Critical slowing down is Critical slowing down is

gentlegentle• Smallest Smallest mmππ ~ 180 MeV~ 180 MeV• mmππ L > 3L > 3

Charm 2006, page 8

Evidence of Evidence of ηη’N GHOST State in S’N GHOST State in S11 11 (1535) (1535) ChannelChannel

-- --η η

W > 0

W<0

Charm 2006, page 9

Possible Pentaquark candidatePossible Pentaquark candidate

Possible candidate Signal reported to be “observed” recently θ+(1540)

ud

su d

ud

Su d u

dSu d

NN

KK

NN

KK

uu d

S d

uu d

S d

Not sufficient to study the masses/energies of the Not sufficient to study the masses/energies of the ٭٭ states, particularly in the 1/2states, particularly in the 1/2- - channel.channel. Volume study of spectral weight W is much more Volume study of spectral weight W is much more ٭٭ sensitive.sensitive.

mmKK+ m+ mN N

~ 1432 MeV~ 1432 MeV

m(m(ΘΘ++) ~1540MeV) ~1540MeV

i

tmi

ieWtG )(

1) Need to discern the nature of the states

Lattice Pentaquark Volume Variational Light enough Ghost Lattice Pentaquark Volume Variational Light enough Ghost Group signal claim Test Calculation Quark Mass Group signal claim Test Calculation Quark Mass StateState

Csikor Csikor YesYes No No Yes (2)Yes (2) No No No No et.al et.al NoNo No No Yes (9/6) Yes (9/6) No No No No Sasaki Sasaki Yes Yes No No No NoNo No No No Chiu Chiu et.alet.al Yes Yes NoNo Yes Yes No No No No

Mathur Mathur et.alet.al No No Yes Yes No No Yes Yes YesYes Ishii Ishii et.al et.al NoNo YesYes No No No No No No AlexandrouAlexandrou YesYes Yes Yes No No No No No No TakahashiTakahashi YesYes Yes Yes Yes(2)Yes(2) No No No No

Negele Negele et.al et.al ?? Yes Yes Yes(19)Yes(19)

Lasscock et. alLasscock et. al No No NoNo No No NoNo No No Holland et. alHolland et. al No No NoNo Yes Yes No NoNo No

Lattice Results on Lattice Results on ΘΘ++ PentaquarkPentaquark

Charm 2006, page 12

Status of Lattice Pentaquark Status of Lattice Pentaquark CalculationCalculation

KFL and N. Mathur (hep-lat/0510036)KFL and N. Mathur (hep-lat/0510036)• No convincing evidence for the No convincing evidence for the

claims of observing pentaquarks on claims of observing pentaquarks on the lattice.the lattice.

• Absence of evidence is not evidence Absence of evidence is not evidence of absence.of absence.

• Definite calculation should involve Definite calculation should involve dynamic chiral fermion with light dynamic chiral fermion with light quarks, variational approach, volume quarks, variational approach, volume test, and removal of ghosts.test, and removal of ghosts.

Charm 2006, page 13

Tetraquark MesoniumsTetraquark Mesoniums

QCD allows a state with more than three quarksFour quarks : Two quarks + two anti-quarks Like molecular state? Like di-quark anti-diquark state?

q12q

q21q

0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I))

M (M

eV)

a2(1320)

2+ ¯(1)

f0(1710)

K0*(800)

Charm 2006, page 15

Is aIs a00 (1450) (0 (1450) (0++++) a two quark ) a two quark state?state?

Ground state : Ground state : ππ ηη ghost stateghost state..

First excited state : First excited state : aa00

CorrelationCorrelationfunctionfunctionfor for Scalar Scalar channelchannel

Our results shows scalar mass around 1400-1500 MeV, suggesting Our results shows scalar mass around 1400-1500 MeV, suggesting

aa00(1450)(1450) is a two quark state.is a two quark state.

)(JI PCG ),0(1 )1(1

mmss

Charm 2006, page 17

What is the nature of What is the nature of σσ (600)?(600)?

r

σ (500): Johnson and Teller

Two-pion exchange potential: Chembto, Durso, Riska; Stony Brook, Paris, …

σ enhancement of Δ I = ½ rule

The The σσ in in DD++→→ ππ¯̄ππ++ππ++

σσ

Without a Without a σσ pole pole

With a With a σσ pole pole

MMσσ= 478 = 478 ± ± 24242323 ± ± 17MeV 17MeV ΓΓσσ = 324 ± = 324 ± 4242

40 40 ± 21 MeV± 21 MeV

2423478M

E.M. Aitala et. al. Phys. Rev. Lett. 86, 770, (2001) E.M. Aitala et. al. Phys. Rev. Lett. 86, 770, (2001)

M. Ablikim et al. (BES), Phys. Lett. B598, 149 (2004)

Mσ = 541 ± 39 MeV, Γσ = 504 ± 84 MeV

J/ψ —> ωπ+π-

)(21

, 3

1

55

5

5

dduu

uddu

o

oo

ππππ four quark operator (I=0)four quark operator (I=0)

Charm 2006, page 21

Scattering Length and energy Scattering Length and energy shiftshift

• ππππ energies :energies :

• Threshold energy shift on the finite latticeThreshold energy shift on the finite lattice ::

2 , 2)(

,2)0(

22

LappmppE

mpE

LLL

)(]122)0( 62

20

20

130 LO

LaC

LaC

LampE

Charm 2006, page 22

)]0(0 )(JI ,[ PCG55

Further study is needed to check the Further study is needed to check the volume dependencevolume dependence of the of the observed states.observed states.

Scattering statesScattering states(Negative scattering(Negative scattering length)length)

)0()0( pEpE

)1()1( pEpE

Scattering statesScattering states

Possible BOUND statePossible BOUND state σσ(600)?(600)?

Charm 2006, page 23

Scattering state and its volume dependenceScattering state and its volume dependence ),,|1,,| spn

Vspn

nn

n

tMn

x n

tM

n

x

Mn

W

eW

eVM

n

txTtG

n

n

2|)0(|0

2

|)0(|0

0|))0(),((|0)(

2

2

Normalization condition requires :

Two point function : Lattice Continuum

For one particle bound state spectral weight (W) will NOT be explicitly dependent on lattice volume

Vx

Charm 2006, page 24

Scattering state and its volume dependenceScattering state and its volume dependence ),,|1,,| spn

Vspn

tEE

nn

nn

tEE

nn nnx

x

nn

nn

eVWW

eVMVM

nn

txtxTtG

,

,

222

211

2121

11

21

21

11

21 21

2 2

|)0(|0|)0(|0

0|))0()0(),(),((|0)(

Normalization condition requires :

Two point function : Lattice Continuum

For two particle scattering state spectral weight (W) WILL be explicitly dependent on lattice volume

Vx

Volume dependence of spectral weights

Volume independence suggests the observed state is an Volume independence suggests the observed state is an one particle stateone particle state

WW00

WW11

0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I))

M (M

eV)

a2(1320)

2+ ¯(1)

f0(1710)

K0*(800)

MesoniumsKK Kπ Mesoniumππ Mesonium

qq

Charm 2006, page 27

Mixing of Mixing of ssdduu and ,,

First order approximation: exact SU(3)

MeV 33 ,314703

)1370(

14706

2)1500(

14702

147000014700001470

0

0

0

xxssdduuf

ssdduuf

dduua

xxxxxxxxx

x is annihilation diagram

Charm 2006, page 28

Mixing of with GlueballMixing of with Glueballssdduu ,,

First order approximation: exact SU(3)

MeV 5.414701710

mixed;slight are glueball and )1370(

mix)not (does 14706

2)1500(

14702

1710000014700000147000001470

2

0

0

0

xm

f

ssdduuf

dduua

xxxxxxxxxxxxxxxx

Charm 2006, page 29

Scalar Mesons and Scalar Mesons and GlueballGlueball

)1500(0f)1470(0

0a

)1430(*0K)1430(*

0K

)1430(*0K)1430(*

0K

)1470(0a )1470(0

a

)800(*0K

)980(0f)980(0

a )980(0a)980(0

0a

)800(*0K

)800(*0K )800(*

0K

)( KK

)( K

)1370(0f

)600(

)1710(0fglueball

qq

22qq

Charm 2006, page 30

SummarySummary

• No credible evidence of pentaquarks No credible evidence of pentaquarks in lattice calculationsin lattice calculations

• Plenty of tetraquark mesonium Plenty of tetraquark mesonium candidatescandidates

• σσ(600) is very likely to be a tetraquark (600) is very likely to be a tetraquark mesonium.mesonium.

• Pattern of light scalar mesons may be Pattern of light scalar mesons may be repeated in the heavy-light sectors (?)repeated in the heavy-light sectors (?)

Charm 2006, page 31

Azimuthal anisotropy in Au + Au collisions with = 200 GeV (STAR collaboration)NNS