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Sasa Prelovsek Bled 2008 1
Searching for light scalar tetraquarks Searching for light scalar tetraquarks on the latticeon the lattice
Bled, september 2008Bled, september 2008
Sasa Prelovsek Sasa Prelovsek University of Ljubljana
sasa.prelovsek@ijs.si
Lattice data from collaboration with
Bern-Graz-Regensburg Coll. (BGR)
(Daniel Mohler, Christian Lang, Christof Gattringer)
Sasa Prelovsek Bled 2008 2
OutlineOutline
motivation challenges present simulation and its results previous lattice simulations
Sasa Prelovsek Bled 2008 3
Puzzle of light scalar mesons:Puzzle of light scalar mesons:?or qqqqqq
2/11 II mm2/11 II mm 2/11 II mm
Model independent determination of poles from exp:
sigma: Leutwyler & Caprini 2006
kappa: Descotes-Genon & Moussallam 2006
Sasa Prelovsek Bled 2008 4
Tetraquark with diquark anti-diquark structureTetraquark with diquark anti-diquark structure The most titly bound diquark is SCALAR (“GOOD”) diquark
acTbc
Tbabca suCddCuud as transforms][][ 55
acTbc
Tbabca dsCdsCuus as transforms][][ 55
acTbc
Tbabca udCssCdds as transforms][][ 55
Jaffe 1977
Jaffe & Wilczek PRL 2003
Jaffe, “Exotica”, 2004
SCALAR (“GOOD”) anti-diquark :
aTcb
Tcbabca
aTcb
Tcbabca
aTcb
Tcbabca
udCssCdsd
duCssCusu
suCddCudu
as transforms
as transforms
as transforms
][][
][][
][][
55
55
55
nonet of SCALAR and color singlet states:
)1(]][[
)2/1(]][[
)0(]][[
Iudsdus
Iussdud
Issduud
as transforms
as transforms
as transforms
8133
133
][][ 3,33,3
x
x
qqqqfcfc
:flavor
:color
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Arguments in favor of tetraquark interpretationArguments in favor of tetraquark interpretation L=1 quark-antiquark mesons expected to be above 1GeV:
scalar mesons, axial mesons, tensor mesons
observed m(I=1)>m(I=1/2) for states below and above
1 GeV not possible to explain with pure quark-antiquark states.
This ordering is natural in tetraquark picture.
- states below 1 GeV could be “pure” tetraquarks
- states above 1 GeV could be lin. combinations of (mixing via t’Hooft vertex): t’Hooft, Maiani, Polosa, Isidori, Riquer 2008
a0(980) strongly couples to KK:
qqqqqq and
rearrang.quark
suppressed Zweig
KK]sd[us][
KKud
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Related observations in favor of tetraquarks:Related observations in favor of tetraquarks:
observed observed X,Y,ZX,Y,Z states with charm quarks states with charm quarks
SuccuuccuX
SdccddccdX
PsccsY
SdccudccuJZ
SSSS
SSSS
SS
SSSS
1][][][][:)3875(
1][][][][:)3872(
][][:)4260(
2,][][][][:/)4430(
0110
0110
00
0110
Experiment: Belle, BaBar, BES, Cleo ....
Possible interpreations: tetraquarks [Maiani, Polosa, ...]
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- discard disconnected diagrams
- quenched approximation (we needed two different volumes and different shapes of interpolators)
above two approximations (used in all previous tetraquark simulations)
allow definite quark assignment, no mixing
Present simulation: Present simulation: searching tetraquarks below 1GeV searching tetraquarks below 1GeV a0,f0)a0,f0)
x
xpi uddutxuddue
)0,0](][[),](][[
Calculation of the correlator on the lattice: Calculation of the correlator on the lattice: a=0.15 fm, V=16a=0.15 fm, V=1633 32 , 12 32 , 1233 24 24
.vacqqqqqq
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Present simulation:Present simulation:
- Chirally Improved quarks (BGR Coll.) : ms: physical value
mu,d : mp= 340, 470, 570 MeV
- we study I=0,1/2,1; all previous simulations only I=0
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to distinguish one-particle (tetraquark) state and scattering states in C(t)
I flavor of source/sink scattering states
0 [ud][ud] sigma
1/2 [ud][ds] kappa K
us][ds] a0 K K,
0
0
IC
p
0 t
,..2,1,0
2
nL
nk
Challenge is analysis of correlator:Challenge is analysis of correlator:
tE
n nn
tE nn ewuddunenudduuddutuddutC ]][[]][[)0](][[)](][[)(
222
,2
km
mE
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we distinguish one-particle and scattering states by considering:
En
volume dependence of wn
How to distinguish tetraquark from scattering?How to distinguish tetraquark from scattering?
tEtE ewewtC 1010)(
properties of scattering:
3
32
32
222
221
1
1)(,)(:2/1
4
7)(,)(2:0
Lw
LfLdELdEmmEI
LfLdELdEmEI
kmkmE
treeK
tree
PP
property of (one-particle) tetraquark:
)( 0LOw
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How to extract several states ?How to extract several states ?
Ground state: straight forward!
Excited states: challenge! - fitting two exponentials is VERY unstable; fitting more is impossible
- All previous tetraquark simulations calculated only a single correlator
tmeff ewtCm
tC
tCLogtm 0
00 )()1(
)()(
if
tEtE ewewtC 10
10)(
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Extracting several states:Extracting several states: variational method variational methodIn each flavour channel I=0, 1/2, 1I=0, 1/2, 1
3x3 correlation matrix3x3 correlation matrix evaluated:
3 different smearings at source and the sink:
spatially symmetric Jacobi smearing on quarks: narrow (n) & wide (w)
]][[
]][[
]][[
3
2
1
wnwn
wwww
nnnn
qqqqO
qqqqO
qqqqO
,..1,0)()()()( ntvttvtC nnn
ii
in
tEn
tEtEnn OvneweOew nn )](1[
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Results for I=0Results for I=0
)](1[ tEEnn eOew n
Lnkkkuddu
2)()(:]][[
??)980(,)600( 0f
tmeff ewtm
t
tLogtm 0
00 )()1(
)()(
if
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Results for I=0: ground stateResults for I=0: ground state
if all tree sources behave close to point-like:
then three eigenvalues of 3x3 matrix are:
the whole tower of scattering states comes in a single eigenvalue!
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I=0 ground state as tower of I=0 ground state as tower of
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Results for I=0: Results for I=0: ground stateground state
scattering
particle-one
: weightsspectral
3
0
/1
)(
Lw
LOw
kL
dk
tkfL
tkfkd
tC
i
k
2
),(1
),()2(
)( 33
3
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Results for I=1/2 Results for I=1/2 similar conclusions similar conclusions
as in I=0 channelas in I=0 channel
)800(
2)()(:]][[
L
nkkkKdsdu
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Results for I=1 Results for I=1 analysis of ground state is more complicated:
two towers of scattering states KK, pi etass:
conventional fit of mass at large t
)980(0
)()(
2)()(:]][[
a
kk
LnkkkKdssu
ss
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Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1
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Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1 excited states:
to heavy to correspond to light tetraquark candidates:
I was not looking for interpretation of these states
(they may be also some excited scattering states) ground state:
effective mass and volume dependence of spectral weights
roughly consistent with tower of scattering states
we find no evidence for light tetraquark at mpi=340-570 MeV
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Still hopes for finding tetraquarks!Still hopes for finding tetraquarks! There may still exist possibility for finding tetraquarks on lattice: at mpi<340 MeV Kentucky group found I=0 tetraquark only for mpi<300 MeV
with larger/different operator basis
My current simulations:My current simulations:
- mpi=180-400 MeV, overlap fermions, quenched, I=1/2,1,
variational method, with Kentucky group
- mpi~300 MeV, domain wall fermions, dynamical u,d,s quarks
variational method, using RBC/UKQCD propagators
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Intermezzo: puzzling mIntermezzo: puzzling meffeff
Effect of finite T on PP state:
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Previous tetraquark simulationsPrevious tetraquark simulations all quenched, all discard annihilation contr. study only I=0 channel (Jaffe studies also exotic I=2 channel)
all consider single correlator
Alford & Jaffe, 2000 interpolator one relatively heavy quark mass different L only ground state exploredconclusion: shift does not completely agree with FULL (!) scattering prediction: possible indication of tetraquark
I=0
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Previous tetraquark simulations:Previous tetraquark simulations: Suganuma, Tsumura, Ishii, Okiharu , 2007 0707.3309 [hep-lat]
• diquark antidiquark interpolator
• conventional and hybrid boundary conditions
• only ground state studied
• conclusion: ground state corresponds to scattering
physdu
phys mmm 2,
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N. Mathur, K.F. Liu et al. (Kentucky, XQCD Collaboration) [hep-ph/0607110, PRD, 2006] interpolator range of very small quark masses (overlap fermions) two volumes three lowest states explored: sequential Bayes method conclusion: indication for tetraquark around sigma mass for mpi<300 MeV
Previous tetraquark simulations:Previous tetraquark simulations:
)0()0(
?)600(
)1()1(