searching for light scalar tetraquarks on the lattice
DESCRIPTION
Searching for light scalar tetraquarks on the lattice. Bled, september 2008 Sasa Prelovsek University of Ljubljana [email protected] Lattice data from collaboration with Bern-Graz-Regensburg Coll. (BGR) (Daniel Mohler, Christian Lang, Christof Gattringer). Outline. motivation - PowerPoint PPT PresentationTRANSCRIPT
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
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
Sasa Prelovsek Bled 2008 5
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
Sasa Prelovsek Bled 2008 6
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, ...]
Sasa Prelovsek Bled 2008 7
- 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
Sasa Prelovsek Bled 2008 8
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
Sasa Prelovsek Bled 2008 9
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
Sasa Prelovsek Bled 2008 10
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
Sasa Prelovsek Bled 2008 11
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)(
Sasa Prelovsek Bled 2008 12
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[
Sasa Prelovsek Bled 2008 13
Results for I=0Results for I=0
)](1[ tEEnn eOew n
Lnkkkuddu
2)()(:]][[
??)980(,)600( 0f
tmeff ewtm
t
tLogtm 0
00 )()1(
)()(
if
Sasa Prelovsek Bled 2008 14
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!
Sasa Prelovsek Bled 2008 15
I=0 ground state as tower of I=0 ground state as tower of
Sasa Prelovsek Bled 2008 16
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
Sasa Prelovsek Bled 2008 17
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
Sasa Prelovsek Bled 2008 18
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
Sasa Prelovsek Bled 2008 19
Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1
Sasa Prelovsek Bled 2008 20
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
Sasa Prelovsek Bled 2008 21
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
Sasa Prelovsek Bled 2008 22
Intermezzo: puzzling mIntermezzo: puzzling meffeff
Effect of finite T on PP state:
Sasa Prelovsek Bled 2008 23
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
Sasa Prelovsek Bled 2008 24
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,
Sasa Prelovsek Bled 2008 25
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(