Sasa PrelovsekLattice 091 Lattice QCD searches for tetraquarks / mesonic molecules (light scalar...

Sasa Prelovsek Lattice 09 1

Lattice QCD searches for Lattice QCD searches for tetraquarks / mesonic molecules tetraquarks / mesonic molecules

(light scalar mesons & XYZ)(light scalar mesons & XYZ)

Excited QCD 2010, SlovakiaExcited QCD 2010, Slovakia

Sasa PrelovsekSasa Prelovsek University of Ljubljana and Jozef Stefan Institute, Slovenia

[[email protected]]

In collaboration with: In collaboration with:

C.B. Lang, Keh-Fei Liu, N. Mathur, C.B. Lang, Keh-Fei Liu, N. Mathur,

D. Mohler, M. Limmer and T. Draper D. Mohler, M. Limmer and T. Draper

Subject of studySubject of study


Some of observed resonances • hidden charm states X,Y,Z • scalars a0(980), f0(980)are candidates for exotic states like

Presented lattice criteria do no distinguish between tetraquarks / molecules: when saying “tetraquarks” I have in mind both types. Conveying present status of lattice QCD simulations concerning whether tetraquarks exist.

Babarnot Belle,

contentquarkccud

Z ')4430(

)800()980(

]][[]][[:

:

)()1(

0

21

]][[

a

dsdusdsu

suduqq

ImIm

qqqq

:observed

examples

• Compute correlation function in lattice QCD using interpolators with desired JPC and flavor

• Which physical states n contribute?

• Two-particle scattering states have discrete spectrum

Correlator and physical states Correlator and physical states nn


][qq]qq[or))(( qqqqO

tE

n

tEjijiij eweOnnOOtOtC n 1

,..2,1

)0()()(

2222

221

212121

0),()(

kmkmEEE

pjkkPkP

PPPPPP

L

for

TaskTask: is there any state : is there any state

in addition to tower of scattering states? in addition to tower of scattering states?


One-particle (tetraquark) state vs. Two-particle (scattering) state

2222

221

2121

),()(

kmkmE

jkkPkP

PPPP

L

illustration

Resonances have been sucessfully extracted in simulations of toy models: Sasaki&Yamazaki (2006) Lang & Gattringer (1993)

Essential to look for few excited states in addition to the ground state !

• Easy to extract ground state E1 : many lattice simulation determine only ground state from a single correlator

• Essential to extract few excited states in addition to ground state

• Multi-exponential fits to extract several En are unstable

• Generalized eigenvalue problem allows determination of

Finding physical states Finding physical states n:n:


nOE in ,

tE

n

tEjijiij eweOnnOOtOtC n 1

,..2,1

)0()()(

[Luscher, Wolf][Blossier, Sommer, Mendes…]

nOE in ,

2/0)(

0 ,,)()()( 0tt

ttEnnnn

nevtCtvtC


tetraquark scattering st. interpolators

attractive I=0 udud ?

repulsive I=2 no resonance

expected

Recent simulation: is Recent simulation: is tetraquark ? tetraquark ?[S.P., K.F. Liu, Lang, Mohler, Limmer, Draper, Mathur, arXiv: 0910.2749]

first dynamical simulation aimed at tetraquarks

]][[

))((

qqqq

qqqq

of types two

of typesthree

))(( qqqq of typesthree

To extract states with four valence quarks: we omit disconn.contractions in I=0,1/2 (as all previous lattice sim.)

Such would have strong tetraquark component, but it can also have qq component.

Needs confirmation from independent simulation !


tetraquark scattering st. interpolators

attractive I=1/2 udud ? K

repulsive I=3/2 no resonance

expected

Recent simulations: is Recent simulations: is tetraquark ? tetraquark ?[S.P., Liu, Lang, Mohler, Limmer, Draper, Mathur, arXiv: 0910.2749]

]][[

))((

qqqq

qqqq

of types two

of typesthree

))(( qqqq of typesthree

Such would have strong tetraquark component, but it can also have qq component .

Needs confirmation!

Available lattice methods to distinguish:Available lattice methods to distinguish: - one-particle (tetraquark) states - two-particle (scattering) states

A)A) LL-dependence of -dependence of <O<Oii |n> |n>


E) (if st. particle-onefor

st scatteringfor

:follow regimesdistinct two

L if

.

nconstnO

nL

nO

rEEE

nO

i

i

ERRi

.||

1||

1||

2

32

int2

[Niu, Liu, Shen, Gong, PRD80 (2009) Mathur et al., PRD76( 2007) S.P. & Mohler, PRD 79 (2009)]

Trivial to derive for two non-interacting

particles

Available lattice methods to distinguish (cont.):Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states

B) Time B) Time -dependence of correlators at finite T -dependence of correlators at finite T


[S.P. & Mohler, PRD 79 (2009)]

)()( tTEEtii eetC

][

)()()(

)(

1221 tTmtmtTmtm

tTEEtii

PPPP eeeeR

eetC

One-particle

Two-particles

Available lattice methods to distinguish (cont.):Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states

C)C) Energy shiftsEnergy shifts precise simulations can determine


[Sasaki, Yamazaki (2006)Liuming Liu, PoS(lat09) 099]

sign changes

)cot( :state boundfor n indicattio

lenght scattering

shifts phase

a

i

a

mmEE PP

21a

mu/d

Bound state

Scattering state (attractive)


Kentucky coll, [Mathur et al, PRD76 (2007)] o quenched , overlap fermions o Single I=0 interpolator

o three states with sequential Bayes method; needs confirmation using eigenvalue method

Previous simulations: is Previous simulations: is tetraquark? tetraquark?

)()( 55 qqqqO

nE )16(

)12(2

2

LnO

LnO

Sasa Prelovsek Scadron70, February 2008 12

Previous simulations: is Previous simulations: is tetraquark? tetraquark?These simulations extract only the ground stateThese simulations extract only the ground state

Suganuma et al. (2007)

o quenchedo extract ground state from one interpolatoro conventional and non-conventional (hybrid) boundary conditionso ground state is scatteringo no observation for tetraquark for

Alford & Jaffe (2000): slight indication for tetraquark

Loan et al. [Loan, Luo, Lam: 0809.5121, 0907.3609]

,

physdu

phys mmm 2,

]][[ 55 qqCqCqO

Hidden charm: XYZHidden charm: XYZAll these simulations extract only the ground state All these simulations extract only the ground state


X(3872), Y(4260), …. [T.-W. Chiu & T.-H. Hsieh, 2005-2007 ]

o quenched , overlap fermions, relativistic charm o 0.4 ms < mq < mc, meVo a=0.09 fm, L=1.8 fm, 2.2 fmo Ground state from single correlators

]'][[

)'')((

cqqcO

cqqcO

MeVmDmDMeVmcsuc

MeVmcccc

MeVmJmYMeVms

3980)(*)(,*504010:

306080:

4120)()/(,)4140(504100:csc

J/

:sprediction

Is X(3872) tetraquark/molecule ? Is X(3872) tetraquark/molecule ?


BabarD0,CDF,Belle,

)3872(Xcuuc

)24(

)20(2

2

LnO

LnO

MeVDmDmDDXMeVmcuuc 3874*)()(*,)3872(303890: :masses with uarksfor tetraq indication

possible issue: scattering should be found at the same energies, before tetraquarks can be trusted

X(3872): JPC=1++ [Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006) 111503]

]'][[

)'')((

cqqcO

cqqcO

Discovered by CDF in 2009

csuc

csduqcqqc ,,,,

Is Y(4260) tetraquark/molecule ? Is Y(4260) tetraquark/molecule ?


JPC=1-- states [Chiu & Hsieh, PRD73 (2006) 094510]

csduqcqqc

Ycuuc

,,,,

)4260(

BelleCLEO,Babar,

)24(

)20(2

2

LnO

LnO

MeVmcccc

MeVms

YMeVmcuuc

506400:

1004450:csc

)4260(314238:

:sprediction

:masses with uarksfor tetraq indicationpossible issue: near by scattering states should be found, before tetraquarks can be trusted

Available lattice methods to distinguish (again):Available lattice methods to distinguish (again): - one-particle (tetraquark) states - two-particle (scattering) states

C)C) Energy shiftsEnergy shiftsOnly precise simulations can determine them


[Luscher 1986, 1991, Sasaki, Yamazaki :PRD74, 114507]Liuming Liu, PoS(lat09) 099]

sign changes

)cot( :state bound afor indication

lenght scattering

shifts phase

a

i

a

mmELmE

PPO

PP

21

21

),(a

mu/d

Bound state

Scattering state (attractive)

Is X(3872) tetraquark/molecule ? Is X(3872) tetraquark/molecule ?


X(3872) [Liuming Liu, PoS(lat09)099 ]

o dynamical , staggered seao extract ground state from single correlator

1,1

*))(( 5

PC

i

JI

DDcqqcO

a mChange of sign in a: possible indication for bound state related to X(3872)

lenght scattering ammEE DD *

Many scattering lenghts determined by Liu (not with purpose of looking for tetraquarks)[see also Yokokawa et al, PRD74(2006)034504]

Is Z+(4430) tetraquark/molecule ?Is Z+(4430) tetraquark/molecule ?


Z+(4430) [Meng et al., PRD80 (2009) 034503] o JPC unknown

o near to D* D1 threshold: m(D*) + m(D1)= 4430 MeV

o suspected to be D* D1 molecule 1- 1+ o ground state energy determined from correlator

o attractive interaction , but no change in sign of scattering lenghto authors suspect that interaction is no strong enough for bound state

Babarnot Belle,

contentquarkccud

Z ')4430(

0,))(( 1*

5P

ii JDDcqqcO

0 lenght scattering ammEE DD *


Conclusions Conclusions o Do light scalar mesons and have tetraquark component?

We find two light states in I=0 and I=1/2 channels. One is the scattering state, while

the other state may be candidate for or with strong tetraquark component. Confirmation is needed before firm conclusion!

Ultimate study would need to take into account mixing and the interpolators have to cover all these Fock components. Then one could determine the fraction of physical states in terms of various Fock components.

o Are some of hidden charm states XYZ tetraquarks/molecules?

There is some indication for tetraquark/molecular structure of X(3872), Y(4260), Y(4140) from the lattice, but much more work is needed. Few excited states would have to be extracted in addition to the ground state to make

reliable identification for tetraquark/molecular states.

gluevacqqqqqq .

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