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
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
Sasa Prelovsek Lattice 09 2
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
Sasa Prelovsek Lattice 09 3
][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?
Sasa Prelovsek Lattice 09 4
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:
Sasa Prelovsek Lattice 09 5
nOE in ,
tE
n
tEjijiij eweOnnOOtOtC n 1
,..2,1
)0()()(
[Luscher, Wolf][Blossier, Sommer, Mendes…]
nOE in ,
2/0)(
0 ,,)()()( 0tt
ttEnnnn
nevtCtvtC
Sasa Prelovsek Lattice 09 6
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 !
Sasa Prelovsek Lattice 09 7
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>
Sasa Prelovsek Lattice 09 8
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
Sasa Prelovsek Lattice 09 9
[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
Sasa Prelovsek Lattice 09 10
[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)
Sasa Prelovsek Lattice 09 11
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
Sasa Prelovsek Lattice 09 13
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 ?
Sasa Prelovsek Lattice 09 14
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 ?
Sasa Prelovsek Lattice 09 15
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
Sasa Prelovsek Lattice 09 16
[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 ?
Sasa Prelovsek Lattice 09 17
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 ?
Sasa Prelovsek Lattice 09 18
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 *
Sasa Prelovsek Lattice 09 19
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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